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GES · 59 topics

Mathematics

G3N tutors you through the full GES Mathematics syllabus offline — from Strand 1: NUMBER — Number: Counting, Representation, Cardinality & Ordinality, Strand 1: NUMBER — Number Operations (Addition, Subtraction, Multiplication and Division), Strand 1: NUMBER — Fractions and more — with adaptive lessons, instant quizzes, flashcards and exam-ready summaries.

Study Mathematics now All GES subjects
Syllabus

What you’ll cover in Mathematics.

The complete topic outline G3N teaches, mapped to the GES curriculum.

Basic 1

8 topics
Strand 1: NUMBER — Number: Counting, Representation, Cardinality & Ordinality
  • Describe numbers and the relationship between numbers 0 to 100
    • Use number names, counting sequences and how to count to find out "how many?"
    • Count by 1s (forwards and backwards) between two given numbers between 0 and 100; or by 2s and 10s; Identify and correct errors or omissions in counting or skip counting sequences
    • Count to answer "how many?" questions about as many as 100 objects arranged in a line, a grid or a circle; Show that the count of a group of up to 100 objects does not change regardless of the order in which the objects are counted or the arrangement of the objects
    • Estimate the number of objects in a small group (up to 100) and describe the estimation strategy used; Select an appropriate estimate among all those given for a group of up to 100 objects and justify the choice
    • Represent the number of objects in a group with a written numeral 0 to 100. Use ordinal numbers to describe the position of objects up to 10th place Learning
  • Describe numbers and the relationship between numbers 0 to 100. CONT'D
    • Identify numbers in different positions around a given number (0 100)
    • Display a number chart with numbers multiples of say 4 between 0 and 100 and have learners identify numbers in different positions around a given number. Put learners in convenient groups and give each group a number grid and have them identify numbers in different positions around a chosen number. 4 8 1 16 18 11 28 44 69 67 76 96
    • Use number names and non-standard units for measuring (lengths and volumes) to count to find out "how long or how much?"...up to 100
    • Have learners use their feet, hand-span and referent materials to find how long a table, window and door frames are etc., by counting the number of times their feet, hand-span and referent materials are able to do this
    • Have learners use empty containers such as bottles, cups etc. to determine the capacity of other bigger containers by counting to find how much (the number of times) the bottles, cups etc. are able to do this Learning
  • Describe numbers and the relationship between numbers 0 to 100. CONT'D
    • Use comparative language to describe the relationship between quantities/numbers up to 100 using place value and the number line
    • Use 1-to-1 correspondence or matching to solve problems that involve comparing 2 sets having between 1 to 100 objects and explain how he/she solved the problem (finding which set has more or less, which groups have the same as)
    • Use the terms "more than", "less than" or "the same as" when comparing two groups having between1 to 100 objects
    • Put groups between 1 to 50 objects in increasing or decreasing order and justify his/her answer or explain what he/she did to find the answer
    • Identify numbers and groups of objects that are that are 1 more or less than a number (for numbers 1 to 100
    • Use the number line to compare and order whole numbers from 0 to 100 Learning
    • Represent the comparison of two number up to 100 using the symbols ">, < or ="
    • Use the terms "more than", "less than" or "the same as" when comparing two numbers between1 to 50
  • Describe numbers and the relationship between numbers 0 to 100 CONT'D
    • Describe the relationship between quantities/numbers up to
    • Use one-to-one correspondence, matching or counting to identify whether the number of objects in one group of up to 20 objects is greater than, less than or equal to the number of objects in another; describe the relationship between the two groups or numerals using the terms greater than, less than, or equal to
    • Build a group that has more than, less than, or the same number as a given set
    • Demonstrate an understanding of the relative size of numbers up to 100 by:
    • Order groups of 1 to 20 objects and then a small set of numerals between 1 and 20, and justifying the arrangement
    • Describe the relative size of numbers up to 100 (i.e., say whether one number is a lot or a little bigger or smaller than another, or 5 more than another number)
    • Place given numerals between 0 and 50 on a number line that has 0, 5 10 and 20 indicated as benchmarks
    • Act out and solving problems (pictures and words) that involve comparing quantities (i.e., Johnson has 3 mangoes, Adwoa has 7. what can you say?) Learning
Strand 1: NUMBER — Number Operations (Addition, Subtraction, Multiplication and Division)
  • Develop a conceptual understanding of addition and subtraction
    • Demonstrate understanding of addition as joining and finding how many altogether and subtraction as separating and finding how many left; numbers 0 to 20
    • Acting out a given story problem presented orally. For instance
    • Sena has 8 bottle caps. She takes 5 more bottle caps from Kofi. How many bottle caps does Sena now have?
    • Kojo has 15 pencils. He gave 7 to Ato. How many pencils are left? Indicating if the scenario in a story problem represents an addition or a subtraction and justifying the answer
    • Creating a story problem for subtraction or addition or for a given number sentence (+ and within 20)
    • Daniel's family have 6 electric bulbs in the house. Two of the bulbs are not working. How many bulbs can Daniel's family use? Thinking; Justification of Ideas; Development and Leadership Attention to Precision
  • Demonstrate an understanding of the concept of equality
    • Use objects and pictorial models to solve word problems involving joining, separating and comparing sets within 20 and unknowns as any one of terms in problems such as 9 +7 = [], 13 +[] =19 and 14-[]=3
    • Explaining that = means "the same as'
    • Identifying if two quantities or groups of objects are equal or not and justifying answers
    • Using the symbol = to record equal relationships (e.g., 3 = or + = )
    • Representing a pictorial or concrete equality in symbolic form (e.g., represent + = as 3 + 2 = 5)
    • Use a symbol ( ____ ) to represent the unknown in an addition or subtraction statement. Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of the concept of equality. CONT'D
    • Use relationship between addition and subtraction to demonstrate understanding of equality for numbers within 20
    • Demonstrate an understanding of the relationship between addition and subtraction by: transforming a subtraction as an equivalent addition and vice versa (For example, subtracting eight from 10 (10 8) is the same as identifying the number that must be added to 8 to make 10) 10 - 8 = What? Means 8 + What? = 10
    • Generate and solve word problem situations when given a number sentence involving addition and subtraction of numbers within 20
    • Write addition and subtraction problems, learners in their groups discuss and generate word problems to match the number sentences Learning
  • Demonstrate fluency with addition and subtraction relationships
    • Use strategies for solving basic addition facts (and related subtraction fact) to10. (Note: The focus is on developing strategies to find answers, not memorising number facts. That comes in P2 and P3)
    • Naming the number that is 1 more, 2 more, 1 less, or 2 less than a number given by the teacher or another pupil (for numbers up to 20 only)
    • Naming the double of a number to 10
    • Identifying 10 more or less than a number between 0 and 20, and eventually between 0 and 100
    • Identifying combinations to 5 or 10 (i.e., given a number, quickly identify how many more must be added to get 5 or 10) Thinking; Justification of Ideas; Development and Leadership Attention to Precision
  • Apply strategies for adding and subtracting to
    • Use counting on, counting down and missing addend strategies for adding and subtracting within 20
    • Relating counting to addition (i.e., recognizing that adding 2 is the same as counting on 2)
    • Counting on (i.e., for 5 + 3, start at 5 and count on 3 places... 6, 7, 8 The answer is 8.)
    • "Making 10s" (i.e., if 7 + 2 + 3, do 7 + 3 = 10 first then add 2. The answer is 12. Or if given 7 + 2 + 3, change the order of the addends to 7 + 3 + 2 to produce combinations that add to 10; Or if given 2 + 6 + 4, add the two last addends first to produce 2 + 6 + 4 = 2 + 10 = 12 Or if given 8 + 3, change question to 8 + 2 + 1 = 10 + 1 = 11)
    • "Making doubles" (i.e., if 5 + 4, do 4 + 4 = 8 then add 1. The answer is 9. Or if given 6 + 7, change question to 6 + 6, which give 12 then add 1. The answer is 13). Relating subtraction to counting down (i.e., Recognizing that subtracting 3 is the same as counting down 3) (i.e., for 15 - 3, start at 15 and count on 3 places... 14, 13, 12. The answer is 12.)
    • Relating subtraction to comparison or finding the difference (Recognizing that subtracting 5 from 8 is the same as ` 5 is how many less than 8; or `8 is how many more than 5
    • "Using addition to subtract" or re-writing as addition sentence and finding the missing addend (i.e., if given 7 - __ = 5, change the question to the addition 5 + ___ = 7. The answer is 2, so 7 - 2 = 5. 7 - What? = 5 means 5 + What? = 7 Thinking; Justification of Ideas; Development and Leadership Attention to Precision
  • Apply strategies for adding and subtracting to 20 CONT'D
    • Solve one-step word problems involving addition and subtraction within 20 using a variety of strategies
    • Use a variety of strategies (objects, drawings, mental strategies, counting on, doubles etc.) to solve addition word problems to 20 involving adding to, putting together and with unknowns in all positions
    • Ama has 10 mangoes and receives 3 more mangoes How many mangoes does she have altogether?
    • Use a variety of strategies (objects, drawings, mental strategies, counting down, etc.) to solve subtraction word problems to 20 involving taking from, taking apart and comparing and with unknowns in all positions
    • Kojo has 15 pencils. He gave 7 to Ato. How many pencils are left?
    • Kafui had 5 pencils. Kwame had 3 pencils. How many more pencils did Kafui have than Kwame? Thinking; Justification of Ideas; Development and Leadership
Strand 1: NUMBER — Fractions
  • Develop an understanding of halves using concrete and pictorial representations [Exclude notation here]
    • Understand the fraction one-half as the quantity obtained by taking 1 part when a whole is partitioned into two equal parts
    • Use concrete objects to explain the fraction half as the quantity obtained by taking 1 part when a whole object is partitioned into two equal parts
    • Use pictorial representations to explain the fraction half as the quantity obtained by taking 1 part when a whole object is partitioned into two equal parts
    • Use pictorial representations to help learners sort fractions into those that are halves and those that are not halves Thinking; Justification of Ideas; Development and Leadership One whole one half STANDARDS PRACTICES AND
  • Develop an understanding of halves using concrete and pictorial representations [Exclude notation here] CONT'D
    • Count in halves using concrete and pictorial representations of halves
    • Show several halves of concrete objects (like half oranges, half piece of stick, half piece of card, etc and have them count them in halves (using the language one-half, two-halves, three-halves, etc.)
    • Show learners several pictorial representations of halves and have them count (using the language one-half, two-halves, three-halves, etc.) Thinking; Justification of Ideas; Development and Leadership
Strand 1: NUMBER — Money
  • Identify coins, their values and the relationships among them in order to recognize the need for monetary transactions
    • Recognise Ghanaian coins by name, including one pesewa five pesewas, ten pesewas, twenty pesewas, fifty pesewas and one cedi by value and describe the relationship among them
    • Display the various coins currently being used for transaction in Ghana and initiate discussion on the need for monetary transaction. Learners touch feel and say the features of each coin
    • Introduce the one pesewa, five pesewas, ten pesewas, twenty pesewas fifty pesewa and guide learners learn to identify and recognize the money by name and value
    • State the relationship between 2p and 10p; 5p and 10p; 2p and 20p; 1p Thinking; Justification of Ideas; Development and Leadership Attention to Precision
Strand 2: Algebra
  • Recognize, create, extend and describe non numerical and simple numerical patterns
    • Demonstrate an understanding of repeating patterns with 2 to 4 repeating elements
    • Identifying, duplicating, extending or creating a simple
    • Number patterns (1, 2, 3, 4, 1, 2, 3, 4... ___) with 2 to 4 repeating elements
    • Shape patterns (e.g....) with 2 to 4 repeating elements
    • Sound (clap, clap, snap, snap, clap, clap, snap, snap...) with 2 to 4 repeating elements, or
    • Action patterns (stand up, sit down, clap, stand up, sit down, clap...) with 2 to 4 repeating elements
    • Identifying and describing errors or missing elements in number, shape, sound or action patterns with 2 to 4 repeating elements (e.g
    • 2 4 6 2 ___ 6)
Strand 3: GEOMETRY AND MEASUREMENT — 2D and 3D Shapes
  • Analyse attributes of two dimensional shapes and three-dimensional objects to develop general concept about their properties
    • Distinguish between attributes that define a two dimensional figure or three-dimensional figure and attributes that do not define the shape Display 2D cut out shapes and 3D objects and have learners:
    • Identify 2D shapes (triangles, squares, rectangles, circles) on the surfaces of 3D objects (cubes, cylinders, spheres, rectangular prisms) in the classroom or beyond; Identify what features define a shape or an object (e.g. triangles are closed and have three sides) and other features (colour, orientation or size)
    • Sort a given set of 2D shapes and 3D objects using a given single feature or criteria (size, shape, etc.) and explain the sorting rule, feature or criteria used to sort them; Describe the difference between two given pre-sorted sets of familiar 3D objects or 2D shapes and the feature or criteria used to sort them
    • Identify 3D objects in the environment that have parts similar to a given 2D shape (e.g., find the parts of a can or bucket that are similar to a circle)
    • Create a composite 2D shape from 2D shapes (i.e., build a new shape using triangle, circles, rectangles, or squares, or build a rectangle using squares or a square using triangles etc.) and describe it. (Make several of the logic block set below with card or plywood and paint them) Citizenship
  • Analyse attributes of two dimensional shapes and three-dimensional objects to develop general concept about their properties CONT'D
    • Identify three-dimensional shapes, including spheres ones, cylinders, rectangular prisms (including cubes), and triangular prisms and describe their attributes using formal geometric language
    • Sort a given set of 3D shapes using a given single feature or criteria (size, shape, etc.) and explain the sorting rule, feature or criteria used to sort them
    • Describe the difference between two given pre-sorted sets of familiar 3D shapes and the feature
    • Identify two-dimensional shapes, including circles triangles, rectangles and squares as special rectangles, rhombuses and hexagons and describe their attributes using formal geometric language
    • Sort a given set of 2D shapes using a given single feature or criteria (size, shape, etc.) and explain the sorting rule, feature or criteria used to sort them
    • Describe the difference between two given pre-sorted sets of familiar 2D shapes and the feature Thinking; Justification of Ideas; Development and Leadership Attention to Precision
Strand 3: GEOMETRY AND MEASUREMENT — Measurement Length, Mass and Capacity
  • 1 Tell the position of objects relative other objects in
    • Learners tell their sitting position relative to other children in the classroom. For example, Yaw is on the third line (row), three places from Ama and to the left of Kwesi Thinking; Justification of Ideas; Development and Leadership Attention to Precision
  • Demonstrate an understanding of Measurement
    • Develop an understanding of measuring as a process of comparing pairs of items using words such as smaller, longer, thinner, heavier, bigger etc
    • Learners bring together pairs of objects on the same flat surface to compare to find out which is taller Learning
Strand 4: Data — Data Collection, Organisation, Interpretation, Presentation and Analysis
  • Organise, represent and interpret data
    • Organise and represent (using pictures/objects) data with up to three categories
    • Have a picture of learners in front of the class and ask the learners to use two different pictures/objects to represent the number of males and females. Repeat with pictures of animals
    • Using a one-to-one correspondence to solve simple problems (i.e. how many altogether, how many more or less) problems requiring interpretation of the concrete representation of pictures as in E.g. 1 above
    • Organise a given set of data into three categories find the total number of data points and determine how many are in each category and compare the number in any two category
    • Learners use tally charts with data relevant to their daily lives (e.g. favourite drinks, eye colour, pets etc) to analyze and compare data in a picture graph
    • Learners construct pictures graphs in groups as well as individually based on data given them Learning

Basic 2

8 topics
Strand 1: NUMBER — Counting, Representation, Cardinality & Ordinality
  • Count and estimate quantities from 0 to 1000
    • Use number names, counting sequences and how to count to find out "how many?"
    • Skip count forwards and backwards and from 1000 respectively by 2s, 5s and 10s, starting at 0 or at multiples of 2, 5, 10, 50 and 100; Identify and correct errors or omissions in counting or skip counting sequences
    • Count by 2s, 5s or 10s, to answer "how many?" questions about as many as 100 or 1000 objects
    • Estimate the number of objects in a group of up to 1000 describe the estimation strategy used; Select an appropriate estimate among all those given and justify the choice Thinking; Justification of Ideas; Development and Leadership
  • Count and estimate quantities from 0 to 1000 CONT'D
    • Identify numbers in different positions around a given number in a number chart. (1-1000)
    • Display a number chart with numbers between 0 and 100 and have learners identify numbers in different positions around a given number. Put learners in convenient groups and give each group a number grid and have them identify numbers in different positions around a chosen number. For example, choose 18 and identify numbers above, below, to the right or to the left etc. 24 48 75 12 16 18 86 40 115 259 134 529 203 325 719 686 685 915 982 827
    • Use number names and non-standard units (marked 10s and 1s) for measuring (lengths and volumes) to count to find out "how long or how much?" up to 999
    • Have learners use their feet, strides, arms, hand-span and referent materials such as sticks or threads to find how long a table, window and door frames etc., by counting the number of times their feet, hand-span and referent materials is able to do this
    • Have learners use empty container such as bottles, cups etc. to determine the capacity of other bigger containers by counting to find how much (the number of times) the bottles, cups etc. is able to do this Thinking; Justification of Ideas; Development and Leadership
  • Count and estimate quantities from 0 to 1000 CONT'D
    • Demonstrate a conceptual understanding of place value of whole numbers between 0 and 100
    • Develop a conceptual understanding of place value of whole numbers between 0 and 1000 by:
    • Explain and show- with bundles of 10s and 1s and a tens frame the meaning of each digit in a 2-digit number (when the two digits are different, as well as when the two digits are the same) and representing the number in a tens frame (Use other possible representations of place value which include manipulatives such as threaded 100s, 10s, and loose bottle caps; and multi-base ten material (units, flats and squares) with numeral cards
    • Decompose or partition numbers to 1000 into hundreds, tens and ones (e.g.: 153 = 100 + 50 + 3, or 153 = 100 + 53)
    • Explain why the value of a digit depends upon its placement within a numeral
    • Read a number by indicating the value of each digit (i.e., reading 43 as forty-three and not four three
    • Partition or decompose numbers to 100 and then to 1000 into equivalent expressions (e.g.: 47 = 20 + 20 + 7, or 30 + 10 + 7, etc.) Thinking; Justification of Ideas; Development and Leadership Tens Frame Hundred Tens Ones
  • Count and estimate quantities from 0 to 1000 CONT'D
    • Represent number quantities up to 1000 in equivalent ways focusing on place value and equality
    • Demonstrate an understanding of how place value determines the relative size of numbers up to 1000 by: describing the relative size of two or more numbers (i.e., saying whether one number is a little or a lot bigger or smaller than another and justifying the answer)
    • Represent and describe numbers to 1000 in equivalent ways (e.g 147 is 3 less than 150, is 7 more than 140, is almost half of 300, is a little larger than 145 but a lot larger than 15, etc.)
    • Arrange groups of up to 100 objects in equal groups in more than 1 way and describe the arrangement; or describe the arrangement and how many are left over (e.g. arrange 66 as two groups of 33 or six groups of 11, or 3 groups of 22 or 5 groups of 12 and 6 left over)
    • Use place value to compare and order whole numbers up to 100 using comparative language, numbers, and symbols (>, <, or =)
    • Identify which of two given numbers is bigger (or smaller), explain why, and represent the relationship using the symbols< and >
    • Put a small group of numbers in increasing or decreasing order and justify the order using place value
    • Identify the missing numbers in a section of number line from 1 to 100 or in a hundreds chart and justifying the answer using place value
  • Demonstrate conceptual understanding of operations of addition and subtraction with sums up to 100
    • Use conceptual understanding of addition and subtraction to add, and subtract numbers to 100
    • Add a given set of numbers in two different ways (e.g. 35 + 54 and 54 + 35 or 18 + 12 + 3 and 3 + 18 + 12) and explaining why the order in which numbers are added does not change the sum
    • Explain why the difference or sum is the same as the initial number when 0 is added or subtracted from a number (e.g., why 27 + 0 = 27 or 55 0 = 55)
    • Match a word problem to a missing addend (e.g.,3 4 + ___ = 57) missing subtrahend1 (e.g. 27 - __ = 24) or missing minuend (__ - 54 = 63) statement
    • Create an addition or subtraction number sentence and word problem for a number up to 100 (i.e., given the solution 53, create an addition or subtraction sentence with an answer of 53 and a corresponding word problem). Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of the concept of "not equal to" to solve addition and subtraction problems with sums up to 100
    • Use the concept of "equal to" and "not equal to" to solve addition and subtraction problems with sums up 100
    • Explaining that that' "" means "not the same as" or "not equal to"
    • Constructing and drawing two sets that are not equal, explaining why they are not equal and recording the relationship using the symbol (e.g., ); Changing two given sets, equal in size, to create sets that are not equal (e.g., change = to ), explain the changes made and why Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of the concept of "not equal to" to solve addition and subtraction problems with sums up to 100 CONT'D
    • Determining whether two sides of a given number sentence are equal or not and using the appropriate symbol to represent the relationship (e.g., 16 8 + 5)
    • Using a symbol () to represent an unknown in addition/subtraction statements to 100
    • Demonstrate an understanding of the relationship between addition and subtraction by describing a subtraction as an equivalent addition and vice versa; i.e. finding the missing addend. (For example, that subtract 40 28 is the same as finding the number that must be added to 28 to make 40). 40 - 28 = What? Means 28 + What? = 40 Or if given 40 - 28 = ___ change question to 28 +__ = 40. The answer is 12, so 40 - 28 = 12). Thinking; Justification of Ideas; Development and Leadership
  • Develop and use strategies for mentally computing basic additions and subtraction facts to
    • Use mental strategies for basic addition facts to 19 and related subtraction facts to 19
    • Demonstrate fluency with addition and subtraction-related relationships by: Quickly naming numbers that are 1, 2, or 10 more or less than a number between 1 and 100, or 5 more than a number that is a multiple of 5 Quickly Identifying the double of a number between 1 and 12 Add and subtract combinations to 10 quickly and accurately
  • Develop and use strategies for mentally computing basic additions and subtraction facts to 19 CONT'D
    • Other sstrategies to use when adding
    • `counting up" when adding
    • 'making doubles because doubles are easier to add (e.g., instead of 4 + 6 use 5 + 5)
    • 'making doubles + or 1 ' (e.g., instead of 4 + 5 use 4 + 4 + 1; instead of 4 + 5 use 5 + 5 -1) 'making 10s' (e.g., instead of 7 + 5 use 7 + 3 + 2; instead of 7 + 5 use 5 + 5 + )
    • Some strategies to use when subtracting
    • Counting down (i.e., for 15 - 3, start at the big number, 15, and count on 3 places... 14, 13, 12. The answer is 12.) turning a subtraction into an addition, because additions are often easier (e.g., 7 - 3 = __ can be rephrased as 3 + __ = 7) Learning
  • Develop and use conventional and personal strategies for computing additions up to 100
    • Use conventional strategy to add and subtract within 100
    • Use objects (groups of tens and ones) or drawings to model addition and subtraction of 1 and 2 digit numbers (with answers within 100), with and without regrouping) and record the process symbolically, using an addition or subtraction frame. Addition Frame Subtraction Frame Tens Ones Tens Ones +
    • Use personal strategies to add and subtract within 100
    • Decompose a number into easier numbers to add and doing partial sums- Decomposing one number into easier numbers to add E.g., when adding 28 + 47, record think 20 + 40 + 8 + 7, which is the same as 60 + 15 which is the same as 75 Thinking; Justification of Ideas; Development and Leadership
  • Develop and use conventional and personal strategies for computing additions up to 100 CONT'D
    • `Friendly jumps" strategy, where one of the numbers is decomposed into a friendlier number and added in "chunks" or by "friendly jumps" e.g. when adding 26 + 32, start with 26, add 10 three times to get 56 (26 + 10 + 10 + 10), then add on 2 to get 58. The answer is 58. (NOTE: This strategy is similar to the first strategy of decomposing)
    • Moving part of one number to the other number to create numbers that are easier to add E.g. when adding 29 + 56, move 1 from 56 to 29 to create the expression 30 + 55 = 85)
    • Compensation Adding more to a number to make it friendlier then subtracting the amount added from the answer e.g. when adding 26 + 39, add 1 to 39 to create the expression 26 + 40, which gives 76, then subtract from the answer the 1 that was added; 76 -1 = 75, so the answer is 75
    • Solve one-step and multi-step word problems involving addition and subtraction within 100 using a variety of strategies based on place value, including algorithms
    • Yaw has 32 books. Aisha added 13 more books to Yaw's books. How many books do they have altogether?
    • Mr. Haruna gave 45 books to Yaa' She gave 11 of the books to her sister. How many books are left?
    • Araba needs 8 Ghana cedis to buy exercise books. She has only 5 Ghana cedis. How much money does she need in order to buy the books? Learning
Strand 1: NUMBER — Fractions
  • Develop an understanding of halves and fourths using concrete and pictorial representations [Exclude notation here]
    • Understand the fraction one-half and one-quarter as the quantity obtained by taking 1 part when a whole is partitioned into two or four equal parts
    • Use concrete objects to explain the fraction one-fourth as the quantity obtained by taking 1 part when a whole object is partitioned into four equal parts
    • Use pictorial representations to explain the fraction one fourth as the quantity obtained by taking 1 part when a whole object is partitioned into four equal parts
    • Use pictorial representations to help learners sort fractions into those that are halves and those that are one-fourths. Thinking; Justification of Ideas; Development and Leadership Identity
  • Develop an understanding of halves and fourths using concrete and pictorial representations [Exclude notation here] CONT'D
    • Count in halves and quarters (fourths) using concrete and pictorial representations) of halves and fourths
    • Show several fourths of concrete objects (or card cut outs) and have them count them in fourths (using the language one-fourth, two- fourths, three-fourths, etc.)
    • Show learners several pictorial representations of fourths and have them count (using the language one-fourth, two-fourths, three-fourths, etc.)
    • Determine the number of halves and quarters in a whole
    • Show learners several pictorial representations (or card cut outs) of halves, fourths and wholes and ask them to state the relationship between (i) a whole and one-half; (ii) a whole and one-fourth, and (iii) one- half and one-fourth. Thinking; Justification of Ideas; Development and Leadership
Strand 1: NUMBER — Money
  • Determine the value of coins and notes in order to solve monetary transactions
    • Recognise Ghanaian coins, and currency notes to include at least 1 cedi, 2 cedis, 5 cedis, 10 cedis, 20 cedis and 50 cedis and determine the value of a collection of coins and notes up at least 50 Ghana cedis
    • Display the Ghanaian cedi (coins and notes) currently being used for transaction in Ghana and initiate discussion on the need for monetary transaction. Learners touch feel and say the features of each coin
    • Introduce the notes (i.e. 1 cedi, 2 cedis, 5 cedis 10 cedis etc.) in turns and have learners examine and talk about its features Thinking; Justification of Ideas; Development and Leadership
Strand 2: ALGEBRA — Patterns and Relationships
  • Recognize, create, extend describe, and use patterns and rules to solve mathematical tasks
    • Demonstrate an understanding of increasing and decreasing number patterns
    • Identify the pattern rule used to create a pattern that increases or decreases by 2, 5 or 10. (i.e. in the pattern 2, 4, 6, 8,... - the rule is "add 2 or jump by 2) and extend the pattern for the next 2 or 3 terms
    • Identify errors or omissions in increasing or decreasing patterns (e.g. 5, 10, 20, 25, 30...) and explain the reasoning and strategy used to identify the pattern
    • Identify, create and describe the rule for simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects
    • Find the missing terms in the following:
    • 9, 1, 3, 5, 9, 1, 3, 5, ___; ___
    • 2, 4, 6, 8, 10, ___; ___
    • 5, 10, 15, 20___, ___; or
Strand 3: GEOMETRY AND MEASUREMENT — 2D and 3D Shapes
  • Describe and analyse 2D shapes and 3D objects
    • Identify the common features or attributes of a collection of 3D objects (spheres, cylinders, cones, pyramids, cubes) of different dimensions or orientations
    • Recognise and name 3D objects having specific features or attributes (number of equal faces, types of faces, number of corners, etc.)
    • Sort a collection of 3D objects by 1 or 2 features and explain the sorting rule use
    • Identify examples of these 3D objects in the classroom and community
    • Identify the common features or attributes of a collection of 2D shapes (squares, triangles, rectangles, circles, pentagons, hexagons) of different dimensions or orientations
    • Recognize, draw and name 2D shapes having specific features or attributes (for example a given number of angles or edges/sides
    • Sort a collection of 2D shapes by 1 or 2 features or attributes and explain the sorting rule used
    • Identify examples of these 2D shapes in the classroom and community. For example, look at pictures or a short video (or look outside from a window with a grown-up) around the classroom and the school compound. Point out items to them and encourage them to name the 2D shape in the items Thinking; Justification of Ideas; Development and Leadership
  • Describe and analyse 2D shapes and 3D objects CONT'D
    • Create two-dimensional shapes based on given attributes, including number of sides and vertices
    • Identify the 2D faces of a given 3D object
    • Identify 3D objects in the environment that have parts similar to a given 2D shape (find the parts of a can or bucket that are similar to a circle)
    • Learners identify the number of sides, faces and vertices of 2D plane figures
    • Learners draw 2D shapes with given sides or vertices Thinking; Justification of Ideas; Development and Leadership
Strand 3: GEOMETRY AND MEASUREMENT — Position/Transformation
  • Demonstrate that the length of an object does not change with its placement or direction
    • Prove that the placement or direction of a shape or object does not change its length
    • Put sticks of equal length in different places and directions and ask learners to identify the longest; viz. which stick in the figure is longest? Then ask them to pick the sticks and put them side by side to see if they have equal length. Thinking; Justification of Ideas; Development and Leadership
  • Use non-standard units for measuring lengths heights, mass and distance around objects
    • Demonstrate an understanding of how to measure lengths capacities or mass - directly or indirectly - using non-standard units
    • Identifying which of two non-standard units would be a better choice for of lengths to be measured and object to be used to measure (thumb width, paper clips, pencil lengths, etc.), estimates, and actual measures. Have learners copy table in their exercise book, record their personal estimates and then work with a partner to measure and record the actual measurements. As learners work, go around the classroom to ensure they are using appropriate procedures for Item Non-standard unit Estimated length Actual length Math textbook thumb widths or bottle caps Math textbook pencil lengths or match sticks Desk hand widths Desk pencil lengths or match sticks
    • Explain why the number of non-standard units an object measures varies depending upon the size of the non-standard unit used (example: why the lengths with pencils). Thinking; Justification of Ideas; Development and Leadership
Strand 3: GEOMETRY AND MEASUREMENT — Measurement- Length, Capacity, Mass and Time
  • Use non-standard
    • Selecting an appropriate non-standard unit for measuring the length height, distance around, capacity or mass (weight) of a given object, estimating the length, capacity or mass (weight) in non-standard units, and then comparing the estimate with the actual measure
    • Comparing and ordering objects by length, height, distance around capacity or mass (weight), using non-standard units, and describing the relative size of the objects (Give learners a series of 3 objects. Have them measure the objects using a non-standard unit and then arrange them from shortest to longest, based on the results)
    • Develop an understanding of measuring as a process of comparing three or more items
    • Learners bring together several collection of objects in their environment and compare (directly and indirectly) using words such as smaller, smallest, longer, longest, bigger, biggest, heavier, heaviest etc. Thinking; Justification of Ideas; Precision
  • Use standard
    • Recognize the need for standard unit of measurement of length
    • Mark a learner's height on the wall and ask 4 learners to use their hands pan to measure the height. On the basis of the different measures that would be obtained, get learners to establish the need for use of standard units
    • Estimate the measure in non-standard units, and then comparing the estimate with the actual measure. E.g. Bring two learners of different heights to the front of the class, take the height of one pupil. On the basis of that height ask a pupil to estimate the height of the other pupil and then measure the actual height to compare with their estimation Learning
  • Develop an
    • Read the calendar and solve problems involving the number of days in a week and number of months in a year
    • Using the calendar to do the following:
    • Identify or read the day of the week and the month of the year for a given calendar date
    • Identify the day (or month) that comes before or after a given day (or month)
    • Name, order and count the days in a week and the months in a year
    • Ask learners to say the rhyme "Thirty-days has September"
    • Use arbitrary units and hour on the clock to measure time to complete simple events
    • Ask learners to tell how much time (in terms of arbitrary unit timers like claps, water timers, etc.) it would take to
Strand 4: DATA — Data Collection, Organisation, Presentation, Interpretation and Analysis
  • Collect and record data about self and others and use it to answer and pose questions
    • Use tallies, checkmarks, charts, lists or objects to collect and organize data to answer and pose questions about themselves, others, or surroundings
    • "What is our favourite food or colour or sport?"
    • Answer and/or pose questions, and justify the answers, based on the organized data learning
  • Construct and interpret concrete graphs and pictographs
    • Draw and interpret concrete graphs and pictographs
    • Use one-to-many correspondence to create concrete graphs or pictographs to represent data collected (up to 3 categories of data)
    • Using a one-to-one correspondence solve simple problems (how many altogether, comparing, or take apart problems) on concrete graphs or pictographs. learning

Basic 3

9 topics
Strand 1: NUMBER — Counting, Representation, Cardinality & Ordinality
  • `
    • Use number names and the counting sequence to count and estimate quantities up to 10,000
    • Skip count forwards and backwards from 0 to 10,000 by 10s, 50s 100s, 500s and 1000s starting at any point. Identify and correct errors or omissions in a skip counting sequence
    • Count to tell the number of objects in given collection of objects by selecting the most appropriate of three estimates for a given collection of objects and justify the choice
    • Represent numbers or quantities to 1000 with written numerals
    • Write number words for given multiples of ten to 9999 and for multiples of 100 to 99990 Thinking; Justification of Ideas; Development and Leadership
  • `
    • Identify numbers in different positions around a given number in a number chart
    • Display a number chart with numbers between 0 and 10,000 and have learners identify numbers in different positions around a given number. Put learners in convenient groups and give each group a number grid and have them identify numbers in different positions around a chosen number. For example, choose 34 and identify numbers above, below, to the right or to the left etc. 1204 848 1175 112 253 2418 3806 1640 4615 4909 634 2990 6320 3832 7479 4768 910 8091 9802 9007 Thinking; Justification of Ideas; Development and Leadership
    • Describe numbers and the relationship between numbers from 0 to 10,000 in equivalent ways using the place value concept
    • Demonstrate a conceptual understanding of place value of whole numbers between 100 and 10,000 by:
    • Explaining and showing - with bundles of hundreds, tens and ones - the meaning of each digit in a given 3-digit number (when the three digits are different, as well as when two or more of the digits are the same) and representing the number in a hundreds frame
    • Explaining why the value of a digit depends upon its placement within a numeral
  • Count and estimate quantities from 0 to 10,000.CONT'D
    • Using other possible representations of place value which include manipulatives such as threaded 100s, 10s, and loose bottle caps; and multi-base ten material (units, flats and squares)
    • Ask pupils to model number quantities up to 10,000 using square grid paper or multi-base materials. For instance, with multi- base block, a cube = 1 unit; a rod = 10; a flat = 100 and a block = 1000; learners model 327 with the appropriate materials
    • Decompose numbers up to 1000 into 100s, 10s, and 1s expressions (e.g.: 5000 = 1000 + 1000 + 1000 + 1000 + 1000 or 4036 = 4000 + 30 + 6; etc.)
    • Explain why the value of a digit depends upon its placement within a numeral
    • Read a given number up to 1000 by indicating the value of each digit (i.e., reading 435 as four hundred and thirty-five and not four three five. Thinking; Justification of Ideas; Development and Leadership Hundreds frame Ten Thousands Thousands Hundreds Tens Ones
  • Count and estimate quantities from 0 to 10,000.CONT'D
    • Compare and order whole numbers up to 10,000 and represent comparisons using the symbols >, <, or =
    • Demonstrate an understanding of how place value determines the relative size of whole numbers (between 100 and 10,000) by:
    • Describing the relative size of two numbers (i.e., saying whether one number is a little or a lot bigger or smaller than another and justifying the answer)
    • Identifying which of two given numbers is bigger (or smaller) explaining why using place value and representing the relationship using the symbols< and >
    • Putting a small group of numbers in increasing or decreasing order and justifying the order using a hundreds frame, a number line or place value
    • Identifying the missing numbers or errors in a section of number line from 100 to 10,000 or in a hundreds chart and justifying the answer using place value
    • Solving word problems that involve comparing quantities to 1000 (i.e., Agbo has 230 chickens. Dzifa has 460. What can you say?) Thinking; Justification of Ideas; Precision
  • Develop an understanding of positive and negative numbers
    • Describe situations having opposite directions or values
    • Invite pairs of learners to play the "opposite game" (i.e. a learner performs an action and the partner does the opposite whilst the rest of the class serve as referees)
    • Make a space down the centre of the classroom and mark with chalk cross and ask a pair to stand on the cross with their back facing. the learners then move in the opposite direction a straight line
    • Use real life contexts to deduce positive and negative number representations
    • Draw a large picture showing the sea, mountains above the sea and space below sea level. Provide pictures of items such as a fish, a whale, a boat, car, house, an octopus etc. Ask the learners where they would place each of the items on your picture. Encourage them to say "above the sea level" or "below the sea level". When all the items are stuck, discuss how high the plane might be and how low the octopus might be and so on. Introduce the "minus" sign to indicate under the sea level Thinking; Justification of Ideas; Precision
  • Identify negative numbers up to -10
    • Describe situations using positive and negative values
    • Draw a number line on the floor or any convenient place. Ask a pair to stand on the cross (centre) with their back facing. The learners then move in the opposite direction a straight line on the number line. Have learners move on the opposite direction on the number line and name the numbers as shown: Learners also build their own number line to include -10 A blank number line
    • Count forwards and backwards with positive and negative whole numbers through zero
    • Display the number line, mention a number and ask learners to move/hop from the number to another number through zero. Thinking; Justification of Ideas; Precision
  • Develop and use standard strategies for adding and subtracting within 1000
    • Use standard strategy or procedure to do addition or subtraction within 1000
    • Explain the purpose of a symbol like a square or an underline in a given addition or subtraction mathematics sentences with one unknown (e.g.: 227 + = 609)
    • Create an addition or subtraction question with an unknown for a classmate to solve, and using either or ___ to represent the unknown
    • Solve an addition or subtraction question with one unknown, using a variety of strategies and explaining the strategy used
    • Use the methods of decomposition to find the sums and difference of numbers within 1000 Thinking; Justification of Ideas; Development and Leadership
  • Demonstrate an understanding of the concept of "equality" and "not equal to" in addition and subtraction problems with sums up to 1000
    • Use the concept of "equal to" and "not equal to"
    • Explain that "" means "not the same as" or "not equal to" learners construct two sets that are not equal, explaining why they are not equal and
    • Change two given sets, equal in size, to create sets that are not equal (e.g change = to ), explain the changes made and why
    • Learners determine whether two sides of a given number sentence are equal or not and using the appropriate symbol to represent the relationship (e.g., 160 80 + 50) Thinking; Justification of Ideas; Development and Leadership
Strand 1: NUMBER — Number Operations (Addition, Subtraction, Multiplication and Division)
  • Demonstrate an understanding of the concept of "equality" and "not equal to" in addition and subtraction problems with sums up to 100 CONT'D
    • Learners demonstrate an understanding of the relationship between addition and subtraction by describing a subtraction as an equivalent addition and vice versa; i.e. finding the missing addend. (For example, that subtract 40 28 is the same as finding the number that must be added to 28 to make 40). 40 - 28 = What? Means 28 + What? = 40 Or if given 40 - 28 = ___ change question to 28 +__ = 40. The answer is 12, so 40 - 28 = 12). Thinking; Justification of Ideas; Development and Leadership Attention to Precision
  • Develop and use strategies for mentally computing basic addition and subtraction facts within 100
    • Use strategies to mentally add and subtract whole numbers within 100
    • Use strategies studied in B1 and B2 (counting up, counting down, making doubles, making doubles plus or minus 1 or 2, making 10s, rearranging order of additions to make friendlier combinations, converting a subtraction into an addition and solving the addition) to demonstrate mastery of basic addition facts to 18 (and related subtraction facts)
    • Make doubles when both numbers are close to doubles or when one number is close to the double of the other by:
    • Decomposing one of the numbers to create doubles (e.g. when adding 25 + 26, think 25 + 25 + 1) or
    • Shifting a quantity from one number to the other to create doubles (e.g., when adding 24 + 26, think 25 + 25, or when adding 69 + 23, think 70 + 22)
    • Make 10s when one number is close to 10 or to multiples of 10 by shifting a quantity from one number to the other to create a multiple of 10 (e.g. for example, instead of 28 + 47, think 30 + 45, which is the equivalent of moving 2 from 47 to 28 or think 25 + 50, which is the equivalent of moving 3 from 28 to 45) Thinking; Justification of Ideas; Precision
  • Develop and use strategies for mentally computing basic addition and subtraction facts within 100 CONT'D
    • Making 10s when the 2nd number is to 10 or to a multiple of 10 by compensation (i.e., adding something to the number, then adjusting the answer by adding the same amount to the answer e.g. for 48 19, subtract: 48 - 20 which is 18, then add 1 to that answer to get 19)
    • Subtracting by counting up in friendly jumps. Start at 2nd number and jump up by friendly jumps to get to the first number and add up all the friendly jumps made (e.g.,71-36, start with 36 and make friendly jumps until you get to 71, for example 36 + 10 + 10 + 10 + 5 gives 71. The jumps made were 10 + 10 + 10 + 5, or 35 places in total. So the difference between 71 and 36 is 35) Learning
  • Develop and apply personal and standard strategies for adding and subtracting within 1000
    • Use a variety of personal strategies for adding within 1000 Addition frame Hundreds Tens Ones +
    • Use objects (groups of 100s, 10s and ones) or drawings to model addition and subtraction of 1 to 3 digit numbers (with answers to 1000) and record the process symbolically, with and without a 100s frame
    • Use a variety of personal and standard strategies to solve different types of subtraction and addition equations and problems with missing numbers in all positions
    • Splitting or partial sums, or adding 100s together first, then 10s together, then 1s, and then adding those partial sums together (see example of 168 + 384 to right) Learning
  • Develop and use strategies for mentally computing basic addition and subtraction facts within 100 CONT'D
    • Decomposing or partitioning the second number to create numbers that are easier to add and adding on in "friendly jumps" (e.g., when adding 36 + 35, start with 36, add 10 three times to get 66 (36 + 10 + 10 + 10), then add on 5 to get 71. The answer is 71.)
    • Adding from left to right (adding 10s first and then ones) or using the splitting/partial sums strategy (e.g., to add 52 + 34, think 50 + 30 and 2 + 4
  • Use strategies to mentally add and subtract whole numbers within
    • Look for doubles, and then changing the subtraction question into an addition and solving it (e.g. for 24 - 12, think 12 + 12 = 24 so 24 - 12 is 12 )
    • Make doubles when the two numbers that are close together or close to doubles by:
    • Decomposing the second number to make doubles (e.g. when subtracting 48 25, think 48 24 1) or
    • Compensating to make doubles: adding something to the second number to make a double, then adjusting the answer by adding the same amount to the answer (e.g. for 48 - 23 think 48 - 24 = 24. Then add 1 to 24 to get 25, which i E.g. 3 is the answer) Thinking; Justification of Ideas; Development and Leadership Attention to Precision
  • Develop and apply personal and standard strategies for adding and subtracting within 1000 CONT'D Eg. 2. Adding on by friendly jumps strategy, where one of the numbers is decomposed into a friendlier n
    • Making 10s or 100s when adding a number that is close to a multiple of 10 or 100 by moving a quantity from one number to another, for example when adding 296 + 568, move 4 from 568 to 296 to make 300 (see example to right)
    • Compensation strategy adding more than is required to create an easier number to add usually a multiple of 10 or 100 - and then subtracting that same amount from the answer (for example, when adding 126 + 39, add 1 to 39 to create the expression 126 + 40, which gives 166, then subtract from the answer the 1 that was added; 166 -1 = 165, so the answer is 165)
    • Decomposing or splitting the second number into partial subtractions that are easier to subtract (e.g. when subtracting 127 - 38, decompose 38 and subtract in friendlier jumps - 127 - 20- 10- 8 or see examples in text boxes)
    • Starting at the second number and counting up in friendly jumps (e.g., when subtracting 127 18, start at 18 and count up by 100 to get 118, then count up 9 to get 127...so the answer is 109)
    • Compensation strategy - Subtracting more than is required (to turn the 2nd number into a friendlier number), then adding the extra amount to the answer (for example, when subtracting 547 -296, subtract 547 300 = 247, then add 4 to the answer to get 251) Learning
  • Develop and apply personal and standard strategies for adding and subtracting within 1000 CONT'D
    • Constant difference Adding (or subtracting the same amount from each number to make one number "friendlier", knowing that it does not change the answer (e.g., instead of 158 47, do 161 - 50 which is 111)
    • Develop and explain estimation strategies to estimate the solution for a given word problem involving addition or subtraction sums up to 1000
    • To estimate the sum of 430 + 561, use 400 + 500. The sum must be close to 900; to estimate the different of 660 and 430, use 600 and 400 or 700 and 400. The difference must be close to 200 or 300.)
    • Show an understanding of the property of commutativity
    • Give addition problems and have learners interchange the position of the addends and solve. for example 236 + 453 = and 453 + 236 = Learning
  • Demonstrate an understanding of multiplication up to 5 x 5
    • Represent and explain multiplication using equal groupings Learners make formation of sets of equal object from a given quantity. For example with 12 straws Learners make groupings such as: Learning
  • Demonstrate an understanding of multiplication up to 5 x 5 CONT'D
    • Represent and explain multiplication using rectangular arrays
    • To find 2 3 = ? Learners arrange 2 straws vertically (legs) and put across it with 3 horizontal ones (arms). Learners count the number of intersections
    • Learners model different multiplication sentences Learners mention the number of dots (intersections) for other learners to model fence. Note: Alternatively, learners may draw vertical lines to represent the legs and horizontal lines across them to represent the arms and then count the number of intersections as the product
    • Develop and build the multiplication chart (up to 9 x 9) and have learners practice reading the chart learning
  • Demonstrate an understanding of multiplication up to 5 x 5 CONT'D
    • Learners should also be encouraged to model multiplication on the number line
    • Draw a 6 by 6-multiplication chart and use it as a game board to play the 3-in-a-line game with a pair of dice or playing cards. Players take turns in throwing a pair of dice and mark (or cover) the product made in a throw with his/her marker (or counter)
    • Learners find doubles of given numbers and skip count in 3, 4, and 5 Thinking; Justification of Ideas; Development and Leadership Attention to Precision PRACTICES AND
  • Demonstrate an understanding of division
    • Use concrete and pictorial representations to explain division as equal sharing or partitioning equally into given groups and finding how many are in each group
    • Give a quantity of straws (e.g. 12) and invite 4 learners to share equally among themselves by picking one at a time in turns until all straws are finished and then asking each learner to count and tell the number of straws they received
    • Use concrete and pictorial representations to explain division as repeated subtraction or determining the number of times given equal groups can be obtained in (i.e. goes into or can be subtracted from) a given number
    • Give a quantity of straws (e.g. 12) and have learners make equal groups formation of 3 straws in each group and then have learners count the number of equal groups formed
    • Use concrete and pictorial representation to explain division as inverse of multiplication
    • Explain that division can be carried out as an inverse of multiplication by the following process: For example, to solve 12 3. Write: 12 3 = What? Which means 3 What? = 12 Learners use the multiplication chart to identify the number which multiplies 3 to obtain 12 Learners choose the number as the answer to the problem That is 12 3 = 4 Thinking; Justification of Ideas; Development and Leadership
Strand 1: NUMBER — Fractions
  • Develop an understanding of fractions using concrete and pictorial representations and write fractions in words and symbols
    • Understand a unit fraction by explaining the fraction as the quantity obtained by taking 1 part when a whole is partitioned into f equal parts and that a fraction is the quantity obtained by taking parts of the size
    • Use several pictorial representations (or card cut outs) to introduce unit fractions like half, thirds, fifths, tenths, etc. and ask learners to identify the fractions A, B, C, D, and E
    • Introduce the fraction notation by explaining the fraction one-half as the quantity obtained by taking 1 part when a whole is partitioned into 2 equal parts and is represented by 1; ask learners to write symbols for the fractions A, B, C, D, and E
    • Ask learners to match pictorial representations of fractions to their symbols learning
  • Develop an understanding of fractions using concrete and pictorial representations and write fractions in words and symbols CONT'D
    • Use several pictorial representations (or card cut outs) to introduce multiples of unit fractions like thirds, fifths, tenths, etc., show the notations, 3, 4, etc. and ask learners to draw and label fractions with their symbols
    • Ask learners to colour given fractions in given shapes with equal portions or match fractions to shaded regions
    • Understand, explain and demonstrate that fractions can be used to represent parts of a group of objects, point on a line, or distances on a number line [Read and write fractions using words and symbols. (E.g. one-half, two halves, thirds, fifths etc.)]
    • Use concrete objects and pictorial representations to explain the fraction half as the quantity obtained by taking 1 part when a group of object is partitioned into two equal parts
    • Ask learners to colour given fractions of given groups of object or match fractions to given groups of objects Learning
  • Develop an understanding of fractions using concrete and pictorial representations and write fractions in words and symbols CONT'D
    • Ask learners to cut given fractions from a given (e.g. 12cm long) card, bar or stick
    • Ask learners to locate the missing fractions on the number line Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
  • Develop an understanding of fractions using concrete and pictorial representations and write fractions in words and symbols CONT'D
    • Compare and order unit fractions and fractions with like denominators by using concrete models, pictorial representations and number line
    • Use pictorial representations to compare pairs of fractions. Which is larger, 3 and 1 ? Arrange from smallest to largest 3, 2 and 5
    • Use fraction charts to compare pairs of fractions. Which is larger, 3 and 1 ? Arrange from smallest to largest 3, 2 and 5 Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
  • Determine the value of coins and notes in order to solve monetary transactions
    • Use different denominations of money (1,2, 5, 10, 20, 50 cedis notes an pesewas coins) to buy and give change
    • Solve word problems involving money including 1,2, 5, 10 and 20 cedi denominations and giving change Display a chart with items and their prices as in the example below Ask learners to copy and complete the table (based on items and their prices in the picture and find the change to receive in each case Shopping money Items to buy Change to receive Thinking Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
Strand 1: NUMBER — Money
  • Determine the value of coins and note in order to solve monetary transactions CONT'D
    • Solve word problems involving money including 1,2, 5, 10, 20, 50 cedi denominations Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
Strand 2: ALGEBRA — Patterns and Relationship
  • Recognise, create, extend describe, and use patterns and rules to solve mathematical tasks
    • Demonstrate an understanding of increasing and decreasing patterns by extending the next two or three terms and identifying errors or missing elements
    • Identify the pattern rule used to create more complex increasing or decreasing pattern and extend the pattern for the next 2 or 3 terms
    • 3, 6, 9, 12, 15... - the rule is "add 3 or take 3 steps forward or
    • 30, 27, 24, 21, 18... - the rule is take 3 steps backwards or subtract 3)
    • Create a pattern for a given pattern rule (e.g., create a pattern for the rule "add 10")
    • Identify errors or missing elements in an increasing or decreasing pattern and justify the answer e.g
    • 5, 10, 20, 25, 30... or
    • 45, 40, 35, 30, __, 20
Strand 3: Geometry and Measurement — 2D & 3D Shapes
  • Analyse the relationships among and between 2-D shapes and 3-D objects according to a variety of attributes, including measurement
    • Describe 3D objects according to the shape of the faces, the number of edges and vertices. Sort regular and irregular polygons including triangles, quadrilaterals, pentagons, heptagons according to the number of sides
    • Identify a variety of 3D shapes (cubes, spheres, cones, cylinders, pyramids and prisms) by:
    • Identifying and counting the faces, edges and vertices:
    • Describing the shape of the faces
    • Constructing a skeleton of an object and describing the relationship between the skeleton and the object
    • Sort a collection of 3D objects according to the number/nature of faces, number of edges or number of vertices and describe sorting rule used
    • Identify regular and irregular 2D shapes (triangles, rhombus, rectangles, squares pentagons, hexagons, octagons) having different dimensions and orientations by the number and nature of sides
    • Draw and identify angles
  • Analyse the relationships among and between 2-D shapes and 3-D objects according to a variety of attributes, including measurement cont'd
    • Use cut-out paper as a square corner to determine angles which are right angles and angles which are not right angles
    • Identify polygons with square corners and those without square corners in and around their environment using cut-out papers
    • Use attributes to recognize rhombuses, parallelograms trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
    • Give cut-out shapes of different types of quadrilaterals and have learners examine their features. Learners discuss the characteristics and regroup them as rhombuses, parallelograms, trapezoids, rectangles, and squares and draw these quadrilaterals learning
Strand 3: Geometry and Measurement — Position/ Transformation
  • Demonstrate that the length of an object does not change with its placement or direction
    • Represent whole numbers as distances from any given location on a number line
    • Learners draw the number line, place rod A on different number points and count the number of unit intervals it covers in order to determine its length. Do same to rods B, C and D. learning; Attention to Precision
Strand 3: Geometry and Measurement — Measurement Length, Mass, Time
  • Demonstrate an understanding of a metre and centimetre (cm, m) units for measuring length
    • Model and describe the relationship between the units metre and centimetre
    • Guide learners to study the calibration on the tape measure, metre rule and ruler
    • Identify objects that measure approximately 1 cm or 1m; Estimating the length of given objects using these base objects as a reference point or point of comparison
    • Identify the appropriate standard unit (cm or m) for measuring the length of a given object
    • Estimate, then measure, using a ruler and recording the length and width of 2 D shapes or the length, width and height of given 3D objects
    • Draw a line segment of a given length with a ruler, grid paper etc
    • Demonstrate the relationship between 100 cm and 1 m using concrete materials
    • Select and justify referents for metre and centimetre
  • Demonstrate an understanding of a metre and centimetre (cm, m) units for measuring length
    • Estimate lengths, heights and perimeter of regular and irregular shapes using referents and verify by measuring, using a ruler or tape
    • Measure and record the perimeter of a given regular or irregular shape and explain the strategy used
    • Construct shapes for a given perimeter (cm or m); Construct more than one shape for the same given perimeter to demonstrate that many shapes are possible for a given perimeter
    • Estimate the perimeter of a given shape (cm, m) using personal reference points for length, then measure to assess the accuracy of the estimation Abilities; Justification of Ideas; Precision
  • Demonstrate an understanding of kilogram and gram (Kg, g) unit for and litre (ml, l) for measuring capacity
    • Model and describe the relationship between the units Kilogram and gram as well as litres and millilitres
    • Identify objects that weigh approximately 1 g or 1 kilogram (or that hold 1 ml or 1 l). Estimating the mass, or capacity of given objects using these objects as a reference point or point of comparison
    • Identify the appropriate standard unit (g or Kg; ml or l;) for measuring the mass or capacity of a given object
    • Estimate, then measure, using a scale (or graduated cylinder) and recording the mass (capacity) of common, everyday objects to the nearest g or kg (or ml or l)
    • Explain the relationship between 1000 g and 1 kg using a model or balance or between 1000 ml and 1 l using a graduated cylinder Abilities; Justification of Ideas; Precision
  • Demonstrate an understanding of time taken by events in days, weeks and months
    • Estimate masses and volumes using referents and verify by
    • Bring to class a collection of different types of objects and have learners estimate their weights or volumes using direct or indirect comparisons and then later verify the estimate by using standard measuring tools Abilities; Justification of Ideas; Precision
  • Demonstrate an understanding of time taken by events in days, weeks and months
    • Use arbitrary units to measure time taken to complete simple events
    • Identify personal referents for minutes or hours (i.e., 10 minutes is about the time it takes to...or 3 hours is about the time it takes to...)
    • Identify activities that can or cannot be accomplished in minutes, hours, days months and years
    • Ask learners to time, using watches or clock and tell how much time (in minute and seconds) it would take to i. Walk round the school building; ii. measure and compare distances between objects inside the room; iii. measure and compare distances between objects inside the room; etc
    • Give learners the start and end times of events and ask to determine the duration of the event. E.g. 5. Complete the table Sporting event Start Finish How long? Ampe 10.30 a.m. 10.45 a.m. Netball 9.00 a.m. 10.00 a.m. Basket ball 2.00 p.m. 3.50 p.m. Football 3.30 p.m. 5.00 p.m. Abilities; Justification of Ideas; Precision
  • Demonstrate an understanding of time taken by events in days, weeks and months
    • Use arbitrary units to measure time taken to complete simple events
    • Identifying personal referents for minutes or hours (i.e., 10 minutes is about the time it takes to...or 3 hours is about the time it takes to...)
    • Identifying activities that can or cannot be accomplished in minutes, hours, days months and years
    • Ask learners to time, using watches or clock and tell how much time (in minute and seconds) it would take to iv. walk round the school building; v. measure and compare distances between objects inside the room; vi. measure and compare distances between objects inside the room; etc
    • Give learners the start and end times of events and ask to determine the duration of the event E.g. 5. Complete the table Sporting event Start Finish How long? Ampe 10.30 a.m. 10.45 a.m. Netball 9.00 a.m. 10.00 a.m. Basket ball 2.00 p.m. 3.50 p.m. Football 3.30 p.m. 5.00 p.m. Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
  • Demonstrate an understanding of time taken by events in days, weeks and months cont'd
    • Read dates on the calendar, order dates of events and count days weeks, months and years taken by given events 30 days has September, April, June, and November. All the rest have 31, Except for February alone, which has 28 days clear, and 29 in each leap year
    • Ask learners to say the rhyme "Thirty-days has September"
    • Use the calendar to do the following:
    • Identify or read the day of the week and the month of the year for a given calendar date
    • Identify the day (or month) that comes before or after a given day (or month)
    • Name, order and count the days in a week and the months in a year
    • Identify certain events and when they occur within the year (Christmas, Easter local festivals, leap years, FIFA world cup etc.) Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
  • Demonstrate an understanding of time taken by events in days, weeks and months cont'd
    • Relate the number of seconds to a minute, minutes to an hour and days to a month in a problem-solving context 60 seconds one minute; 60 minutes one hour; 24 hours one day; 7 days one week 52 weeks one year; 12 months one year
    • Develop understanding of the relationship between seconds, minutes, hours, days and months. Ask learners to say the rhyme on units of time (in the box)
    • Solving problems requiring an understanding of number of seconds in a minute, the number of minutes in an hour and the number of days in a month Abilities; Justification of Ideas; Precision; Look for Patterns and Relationships
Strand 4: Data — Data Collection, Organisation, Presentation, Interpretation and Analysis
  • Collect first-hand data and organise it using tallies checkmarks, charts, lists or line plots to answer and pose questions
    • Gather and record Data
    • Use tallies, checkmarks, charts, lists or tables to collect and organize data to answer a question
    • Use tallies, checkmarks, charts, lists or tables to answer questions, and justify the answers, based on the organised data Abilities; Justification of Ideas; Precision
  • Construct and interpret concrete graphs and pictographs to solve problems
    • Draw and interpret concrete graphs and pictographs to solve problems
    • Identify common features of bar graphs that use one-to-many correspondence and use that understanding to create concrete graphs or pictographs, complete with title, labeled axes, key or legend, to represent data collected (up to 3 categories of data)
    • Using a one-to-many correspondence solve simple problems (how many altogether, comparing, or take apart problems) requiring interpretation of one-to- many bar graphs (up to 3 categories of data) Abilities; Justification of Ideas; Precision MATHEMATICS SUBJECT PANEL MEMBERS AND REVIEWERS NAME INSTITUTION Writing panels Prof. Eric Magnus Wilmot University of Cape Coast Dr. Prince H. Armah University of Education, Winneba Dr. Forster Ntow University of Cape Coast Prof. Douglas D. Agyei University of Cape Coast Mr. Emmanuel Acquaye Consultant, NEWAGE Strategies, Koforidua Mr. Miracule Gavor USAID Learning Numeracy Project Mr. Stephen Nukpofe Abetifi College of Education Mr. Charles B. Ampofo Kibi Presbyterian College of Education Mr. Edward Dadson Mills Methodist B Junior High School, Winneba Expert Reviewers Prof. Damian Kofi Mereku University of Education, Winneba Prof. Olivier M. Pamen African Institute of Mathematical Sciences (AIMS) Prof. S.K. Amponsah Kwame Nkrumah University of Science and Technology Curriculum Adviser Dr. Sam K. Awuku OPM (Oxford Policy Management) Supervisor

Basic 4

11 topics
Strand 1: NUMBER — Counting, Representation & Cardinality
  • Demonstrate an understanding of quantities and place value for multi-digit whole numerals up to 100,000
    • Model number quantities, place value for multi-digit using graph sheets or multi-base materials up to 100,000
    • Ask learners to model number quantities up to 100,000 using graph sheets or multi-base materials. For instance, with multi-base block, a cube = 100 unit; a rod = 1000; a flat = 10,000 and a block = 100,000; learners model 32,300 with the appropriate materials
    • Ask learners to model the number 12,500 shading graph sheet square
  • Demonstrate an understanding of quantities and place value for multi digit whole numerals up to 100,000. CONT'D different coloured-paper and ask them to model or pick given amounts up to
    • Read and write numbers in figures and in words up 100,000
    • Play the place value number wheel game: Use the hundred thousand number wheel to generate 6-digit numbers and represent the number generated on a place value frame. Throw a number of pebbles (or stones) onto the number wheel, identify the number of pebbles landing in each place value ring, and state the number generated in the wheel (i.e. 2 landed in the ten-thousand' ring making the number twenty-thousand or 20,000). NB: The representations to use also include verbal, and numerals. Learners must match number word cards to the figures
  • Demonstrate an understanding of quantities and place value for multi digit whole numerals up to 100,000 CONT'D
    • Ask learners to write given numbers on the expanded form of the number: 14031=10,000 + 4,000 +30 + 1
    • Display a number chart or number line with multiples of 500 between 10000 and 50000 and lead learners to identify numbers in different positions around a given number. Look for Patterns
  • Demonstrate an understanding of quantities and place value for multi digit whole numerals up to 100,000 CONT'D
    • Identify numbers in different positions around a given number in a number chart
    • Display a number chart in multiples of 500 between 10,000 and 100,000 and lead learners identify numbers in different positions around a given number. Put learners in pairs and give each group a number grid and have them identify numbers in different positions around a chosen number. 10,000 10,500 11,000 11,500 12,000 12,500 20,000 20,500 21,000 21,500 22,000 22,500 30,000 30,500 31,000 31,500 32,000 32,500 40,000 40,500 41,000 41,500 42,000 42,500 50,000 50,500 51,000 51,500 52,000 52,500 60,000 60,500 61,000 61,500 62,000 62,500
    • Compare and order whole numbers up to 10,000 and represent comparisons using the symbols "<", "=", ">"
    • Learners identify numbers which are 1,000 and 10,000 more or less than a given five-digit or six-digit number. E.g. 2400 is 1,000 less than 3400. Learners use words such as: "equal to" "greater than" "less than" and later use symbols such as "<", "=", ">" to compare numbers up to 100,000 taking into consideration the place value of each digit in the given number. E.g. 1200 = 1200; 27345 > 26355
    • Learners work together in their groups to order a given set of numbers in ascending or descending order verbally and in writing. E.g. 1020, 1025, 2673, 2873
    • Give two numbers between 10,000 and 100,000 to each group and encourage learners to say as many things as possible about the two numbers. For instance, 21345 and 21534; 21345 is less than (smaller than) than 21534 or 21534 is bigger than (greater than) 21345, or 21345 is almost 200 less than 21534 etc. Look for Patterns
  • Demonstrate an understanding of quantities and place value for multi digit whole numerals up to 100,000 CONT'D
    • Round (off, up, down) whole numbers up to 10000 to the nearest thousands, hundreds and tens
    • Learners round off numbers to the nearest 1000, 100 and 10. For instance; 9500 is approximately 10,000 and 9100 as approximately 9,000
    • Learners round up and round down to estimate sums and differences NB: To round down learners consider the smaller of the two approximated numbers, while round up considers the bigger of the two numbers. The table below may bring the meaning of these two concepts clearer
    • Learners work together round up and round down to estimate sums and differences. For instance. as approximately 400 because is approximately while is approximately, therefore 14765 Round up Round down Round off to the nearest ten 14970 14760 14970 to the nearest hundred 14800 14700 14800 to the nearest thousand 15000 14000 15000 Look for Patterns 230 230 200 160 200
  • Demonstrate an understanding of quantities and place value for multi-digit whole numerals up to 100,000. CONT'D
    • Skip count forwards and backwards in 50s and 100s up and from 10000
    • Put learners into convenient groups. A learner mentions a number and another makes skip count in 50s or 100s to include the fifth count. For instance. Learner 1: Shout out "240".... Learner 2: 290, 340, 390, 440, 490, etc. Learner 3; Shout out "1285" skip counting down in 100s Learner 4; 1185, 1085, 985, 885, 785....etc
    • Skip count forwards and backwards by 50s and between 1000 and 10000 that are multiples of 50s and 100s but make an error or leave out a number. Challenge learners to identify or correct error Look for Patterns
  • Demonstrate understanding of Roman numerals up XXX (30)
    • Develop an understanding of Roman Numeral system up XXX (i.e. 30)
    • Display Roman numeral charts (1-30) arranged in sequential order and lead learners to identify the numerals. Learners identify the main characters of the roman numerals used to build the table up to 30 i.e. I, II, III, IV, V, X, Call out a numeral and have learners point at it from the chart
    • Have learners match the Roman numerals to the Hindu-Arabic numerals for instance I = 1; V= 5: X= 10, XV= 15. Mention some numerals randomly and have learners point at it on the chart Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate understanding of Roman numerals up XXX (30) CONT'D
    • Count and convert Hindu Arabic numerals to Roman numerals up to 30 and vice versa
    • Learners read the chart sequentially forwards and backwards, vertically (up and down), zig-zag diagonally and randomly without pointing to the numbers. Invite 2-3 learners to read to the class. Call a Roman numeral and ask learners to write
    • Give learners a numeral in the Hindu Arabic system and have learners convert to roman numeration and vice versa for instance XXIV = 24 Thinking; Justification of Ideas; Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate an understanding of factors, multiples and squared numbers
    • Determine set of factors of a given numbers up to 50
    • Learners make formation of sets of equal object from a given quantity. For example with 12 straws Learners make groupings such as:
    • Learners pair grouping and the number of equal objects for each formation as factors 4 groups of 3 straws (4, 3) 3 groups of 4 straws (3, 4) 6 groups of 2 straws (6, 2) 1 group of 12 straws (1, 12) 2 groups of 6 straws (2, 6) 12 groups of 1 straw (12, 1)
    • Learners collect from the pairs and form a set as the factors of the given number. For example the set of factors of 12 = {1, 2, 3, 4, 6, 12} Thinking; Justification of Ideas; Patterns and Relationships, 3 4 3, 4 4 3 4, 3 2 6 2, 6 STANDARDS INDICATORS AND
  • Demonstrate an understanding of factors, multiples and squared numbers CONT'D
    • Determine the highest common factor (HCF) of any two whole numbers between 1 and 50
    • Learners list the factors of two or more given whole numbers; 12 and 24 to list the factors. That is: 12 = {1, 2, 3, 4, 6, 12} 24 = {1, 2, 3, 4, 6, 8, 12, 24} Learners determine the set of the common factors E.g. The common set factors of 12 and 24 =. Learners select the highest common factor of 12 and 24 as 12
    • Learners may use Venn diagrams to find the common factors and then the highest common factor by placing the factors in the regions of the shapes. The highest common factor of 12 and 20, in the diagram is 4 Note: Do not introduce formal set theory and notation. Numbers in the common regions of the two shapes
    • Determine the lowest common multiple (LCM) of at least any two given numbers up to 100
    • Learners identify and the list the set multiples of given numbers using skip counting E.g. The set of multiples 5 = { 5, 10 15........100} and the etc. of multiples of 10 = {10, 20, 30,........100}
    • Learners list the set of common multiples of any two or more given numbers between 0 and 100
    • The set of common multiples of 5 and 10 ={10, 20, 30,... 100}. Learners select the least of the common multiple of the given numbers, and identify the least common multiple (LCM). The LCM of 5 and 10 is 10.,,,,, STANDARDS INDICATORS AND
  • Demonstrate an understanding of factors, multiples and squared numbers CONT'D
    • Recognise the relationship between factors and multiples
    • Factors represent the numbers that we can multiply to get a bigger number called the product or multiple. Since12 = 4 3, we can say 4 and 3 are factors of 12; and 12 is a multiple of 3 or a multiple of 4. Break given multiples into factors and pairs of factors of given numbers
    • Investigate even and odd numbers
    • Investigate numbers that are multiples of 2, 3, 4 and 5. How do you know a number is a multiple of 2? a multiple of 3? a multiple of 4? and a multiple of 5? (This is also known as the divisibility test)
    • Generate and analyse patterns in square numbers
    • Put learners into convenient groups and provide each group adequate number of bottle tops, an A4 sheet and a 30cm ruler and ask them to generate square numbers by continuing the arrangement shown below up to the 10th number; [i.e. 1, 4, 9, 16, 25, 36... ) 1 4 9 16........................... for Patterns and Relationships
  • Demonstrate an understanding of factors, multiples and squared numbers CONT'D
    • Investigate the relationship between square numbers and the sum of consecutive odd numbers
    • Represent square numbers using factors
    • Learners draw a square whose side is 1 unit by 1 unit and determine the area; repeat the activity for a 2 unit, 3 unit and 4 unit squares
    • Learners work in groups to continue the pattern to include the factors of 144. (Key Concept: when a number has been multiplied by itself we say the answer is a square number hence 1 =; =; = and we can write three squared as = ) for Patterns and Relationships:
  • Interpret negative and positive numbers in context
    • Describe real life situations using positive and negative values
    • Brainstorm learners on happenings which may be represented with positive and negative numbers (e.g. having savings with a bank and owing a bank; profit and loss etc.) Movement on the number line to the right and left of zero
    • Count forwards and backwards with positive and negative whole numbers through zero
    • Learners count from a given interval of positive and negative numbers on the number line. For example, count from 10 backward through zero to negative -8
Strand 1: NUMBER — Number Operations
  • Recall basic multiplication fact up to B B4.1.2.1.1 Determine basic multiplication facts up to
    • To find 2 3 = ? Learners arrange 2 straws vertically (legs) and put across it with 3 horizontal ones (arms). Learners count the number of intersections
    • Learners model different multiplication sentences, for example 3 4 Learners mention the number of dots (intersections) for other learners to model fence Note: Alternatively, learners may draw vertical lines to represent the legs and horizontal lines across them to represent the arms and then count the number of intersections as the product
    • Draw a 6 by 6 multiplication chart for the numbers 5 to 10 and use it as a game board to play the 3-in-a-line game with a pair of dice or playing cards. Players take turns in throwing a pair of dice and mark (or cover) the product made in a throw with his/her marker (or counter). The winner is the one who obtains three products in a line
    • Learners find doubles of given numbers; find squares of given numbers and skip count in 4, 5, and 8 of Ideas; Collaborative learning; Attention to Precision; Look for Patterns and Relationships: Global Citizenship STANDARDS INDICATORS AND
  • Describe and apply mental mathematics strategies and number properties to determine answers for basic multiplication facts to 81 and related division facts
    • Apply mental mathematics strategies and number properties, such as skip counting from a known fact using doubling or halving using patterns in the 9s facts using repeated doubling or halving to determine answers for basic multiplication facts to 81 and related division facts
    • Describe the mental mathematics strategies used to determine a given basic fact, such as skip count up by one or two groups from a known fact (e.g., if 5 7 = 35, then 6 7 is equal to 35 + 7 and 7 7 is equal to 35 + 7 + 7) skip count down by one or two groups from a known fact (e.g., if 8 8 = 64, then 7 8 is equal to 64 8 and 6 8 is equal to 64 8 8) doubling (e.g., for 8 3 think 4 3 = 12, and 8 3 = 12 + 12) patterns when multiplying by 9 (e.g., for 9 6, think 10 6 = 60, and 60 6 = 54; for 7 9, think 7 10 = 70, and 70 7 = 63) repeated doubling (e.g., if 2 6 is equal to 12, then 4 6 is equal to 24 and 8 6 is equal to 48) repeated halving (e.g., for 60 4, think 60 2 = 30 and 30 2 = 15) relating division to multiplication (e.g., for 64 8, think 8... = 64)
    • Recall multiplication facts to 81 and related division facts of Ideas; Attention to Precision; Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate
    • Apply mental mathematics strategies for multiplication, such as annexing then adding zero halving and doubling using the distributive property
    • Determine the products when one factor is a multiple of 10, 100, or 1000 by annexing zero or
    • Apply the distributive property to determine a given product involving multiplying factors that are
    • Multiply multi-digit numbers efficiently
    • Multiplication of whole numbers using the "expand and box" method (partial decomposition method). Lead learners to multiply a 3-digit number by a 1-digit number as shown below, for example 448 2 =? 400 40 8 2 800 80 16 448 2 = (400 2) + (40 2) + (8 2) = 800 + 80 + 16 = 800 + 80 + (10 + 6) = 800 + 90 + 6 = 896
    • Multiplication of whole numbers using the lattice method Have learners draw a 2 by 1 rectangular box for solving 54 3
    • Have learners draw a 2 by 2 rectangular box for solving 34 17 Thinking; Justification of Ideas; Patterns and Relationships Thinking; Justification of Ideas; Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate an understanding of division (2- or 3-digit by one digit number)
    • Determine basic division fact up to 81
    • Investigate numbers that are multiples of 2, 3, 4 and 5. How do you know a number is divisible by 2 3, 4 and 5 (This is also known as the divisibility test)
    • Draw a 6 by 6 multiplication chart and use it as a game board to play the 3-in-a-line game with a pair of dice or playing cards. Players take turns in throwing a one dice and mark (or cover) a number that can be divided by the results (i.e. a quotient). The winner is the one who obtains three numbers in a line
    • Divide 2-digit numbers by 1-digit number efficiently
    • Division as repeated subtraction (using the long division method). Explain division as a way of repeatedly subtracting a divisor number from a given dividend until there is none left and then determining the number of times the divisor is taken from the dividend. For example, 25 5 = ? Learners count the number of times 5 was subtracted from 25, which is 5 times. Hence, = Thinking; Justification of Ideas; Citizenship Thinking; Justification of Ideas; STANDARDS INDICATORS AND
  • Translate and solve word problems involving the four basic operations on whole numbers
    • Division using the estimation of multiples of 10, 100 and others of the divisor. For Example to solve 276 3 = ? Learners use estimations: (they may have to use multiples of divisor to select a convenient estimate) "About how many groups of 3 can fit into 276?" The estimation used here is 40. So 3 40 = 120. Subtracting 120 from 276 to get 156. The next estimation used is 50. So 3 50 = 150. Subtracting 150 from 156 to get 6. The next estimation used is 2. And 2 3 = 6. Subtracting 6 from 6 to get 0. There is nothing more to share. To find the final answer add the estimations: 40 + 50 + 2 = 92. Therefore 276 3 = 92 Note: This strategy is nicknamed the "Big 7" because the division box looks like a 7
    • Solve multi-step word problems involving the four basic operations
    • Learners model mathematical statements from a given word problem involving addition and multiplication and solve using the strategies learnt
    • Learners model mathematical statements from a given word problem involving division and subtraction and solve using the strategies learnt
    • Learners role play a given word problem involving addition and multiplication and solve
    • Learners role play a given word problem involving subtraction and division and solve
    • Learners model mathematical statements from a given word problem involving division and multiplication and solve using the strategies learnt The relationship between operations and the use of calculator and spreadsheet to assess the reasonableness of answers should be stressed Thinking; Justification of Ideas
Strand 1: NUMBER — Fractions
  • Develop an understanding of equivalent and improper fractions
    • Generate unit fractions and locate a unit fraction, e.g. one-eighth, on a number line by defining the interval from 0 to 1 as the whole and partitioning it into 8 equal parts and that each part has size
    • Use number line to locate one eight by defining the interval from 0 to 1 as the whole and partitioning it into 8 equal parts
    • Ask pupils to draw several lines, 30 units each, and mark the ends 0 and 1. For each line ask them to partition the interval from 0 to 1 into each of the following unit fractions, 1, 1, 1, and
    • Ask pupils to use the number chart they have drawn to read fractions that are equivalent e.g. = 2 = 6.... Thinking; Justification of Ideas; STANDARDS INDICATORS AND
  • Demonstrate an understanding of strategies for comparing, adding and subtracting fractions (same denominator, or one being a multiple of the others)
    • Recognise and name equivalent fractions using pictorial representations and number line to determine the Lowest Common Denominator (LCD)
    • Use fraction chart to illustrate the concept of equivalent fractions (i.e. equal fractions that have different fractional units or denominators) i.e. one-half is 2-fourths, 3-sixth or 4-eighths
    • Illustrate the relationship between fractions and their equivalences by observing the different fractional units or denominators (i.e. the numerator is multiplied by the number of units the denominator is further broken into)
    • Ask pupils to colour fractions that are equivalent to given fractions or write more equivalent fractions for give n fractions
    • To determine the equivalent fractions of given fractions, find the Lowest Common Denominator (LCD) and use this to express the equivalent fractions that are comparable Thinking; Justification of Ideas; for Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate an understanding of strategies for comparing, adding and subtracting fractions (same denominator, or one being a multiple of the others) CONT'D
    • Find the simplest form of given fractions by dividing through by the highest common factor (i.e. by cancelling through by factors)
    • Use pictorial representations to illustrate the simplest form of a fraction; e.g. = 3 =
    • Find the simplest form of a given fraction divide through by the highest common factor
    • Find the simplest form of a given fraction, express the numerator and denominators as factors and cancel through common factors
    • Find the simplest form of a given fraction, divide through by the highest common factor. Thinking; Justification of Ideas; for Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate an understanding of strategies for comparing, adding and subtracting fractions (same denominator, or one being a multiple of the others) CONT'D
    • To find the simplest form of a given fraction, express the numerator and denominators as factors and divide through by common factors
    • Recognise fractions that are greater than one (i.e. improper fractions), draw and label such fractions with their symbols
    • Use several pictorial representations (or card cut outs) to introduce improper fractions (i.e. where the fraction is bigger than 1 or the numerator in larger than the denominator). Examples are and (i.e. nine-fourths and seven-sixths) and show how they are expressed as mixed fractions (i.e. 2 and 1 ). Ask pupils to change given improper fractions to mixed fractions
    • Ask pupils to express given coloured mixed fractions as improper fractions or draw and colour given improper fraction (e.g. seven- fourths, eleven-eights, etc.)
    • Use number line to present more mixed fractions for pupils to identify and state their improper fractions of Ideas; Collaborative Learning; Attention to Precision; Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate an understanding of strategies for comparing, adding and subtracting fractions (same denominator or one being a multiple of the others)
    • Compare and order fractions with like denominators by using pictorial representations and finding equivalent fractions using the Lowest Common Denominator (LCD)
    • Use number line or fraction chart to illustrate the concept of comparable fractional units or denominators; i.e. halves, fourths and eighths are comparable; i.e. half can be changed to equivalent fractions in fourths and eighths, and fourths can changed to eighths. Also thirds can changed to sixths
    • Use number line or fraction charts to compare and order unit fractions. Which is larger and or and ? Arrange from smallest to largest,, and
    • To arrange the fractions, and, from largest to smallest, find the Lowest Common Denominator (LCD) and use this to express the equivalent fractions of Ideas; Collaborative Learning; Attention to Precision
  • Demonstrate an understanding of strategies for comparing adding and subtracting fractions (same denominator, or one being a multiple of the others). CONT'D
    • Provide examples of where fractions are used
    • Discuss the contexts below in which fractions are used in real life and provide materials for pupils to act them out Selling liquids oil, kerosene, drinks, etc. Sharing pizza or birthday cake - half, quarter, eighths, etc. Buying objects in packets egg, drinks, (half crate), Buying cloth for sewing dresses half, one-fourths or quarter, etc
    • Tell the time by half/quarter past, and half/quarter to. Draw clock-faces with times (i.e. half/quarter past or to) for pupils to read the time
    • Drawing circle graphs that represent halves, fourths and eighths. The graph shows the ages of pupils in Primary 4. If there are 40 pupils in the class, ask questions for pupils to interpret the graph STANDARDS INDICATORS AND
  • Develop an understanding of decimals (tenths and hundredths) using concrete and pictorial representations and write decimal fractions as base ten numbers with place value
    • Describe and represent decimals (tenths and hundredths) concretely, pictorially and symbolically
    • Use pictorial representations or number line to revise tenths and hundredths and ask pupils to identify the fractions (i.e. A, B, C, D, & E)
    • Use the tenth and hundredth place value chart to illustrate how to write the fraction as a base ten number with the introduction of the decimal point "" after ones place in the place value chart
    • Give pupils several common fractions (including improper fractions) to convert into tenths and hundredths and write their decimal names
  • Develop an understanding of decimals (tenths and hundredths) using concrete and pictorial representations and write decimal fractions as base ten numbers with place value
    • Round decimals to the nearest tenth
    • Explain the rule for of rounding decimals, which is similar to that of rounding whole numbers. That is, rounding to the nearest tenth means that the rounded figure has one digit after the decimal mark. Rounding to the nearest hundredth means that the rounded figure has two digits after the decimal mark
    • Use a table with several decimals fractions and explain the rule for of rounding decimals. Give pupils a table of decimal fractions round to the nearest tenths or hundredths
    • Ask students to change fractions to decimal writing their results to the nearest tenths or hundredths Thinking; Justification of Ideas; Patterns and Relationships Fraction Round to Nearest Result A 0.38 0.4 B 4.085 C 56.584 D 18.096 E 30.084 STANDARDS INDICATORS AND
  • Develop an understanding of decimals (tenths and hundredths) using concrete and pictorial representations and write decimal fractions as base ten numbers with place value
    • Use models to explain the result of addition and subtraction of decimals (up to hundredths)
    • To add 0.64 and 0.39, means sum + which is 64+39 = = 1.03. That is, since both are hundredths fractions (i.e. have 2 decimal places) we can line up the decimal points to align the place values and add as whole numbers
    • To add 0.6 and 0.39, one number is in tenths and other is in hundredths (i.e. one has 1 decimal place and the other 2 decimal places) it is important to line up the decimal points to align the place values and add as whole numbers
    • To subtract 0.6 from 1.39, means
  • Demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially and symbolically)
    • Model or recognise percent (as a fraction related to hundredths) using concrete models, pictorial representations and number line
    • Use several pictorial representations or number line to introduce tenths and hundredths and ask pupils to identify the fractions (i.e. A, B, C, D, & E)
    • Use long division method to convert and write fractions as decimals in the number chart
    • Give pupils several common fractions (including improper fractions) to convert into hundredths and write their decimal names or use long division; e.g. = = 75%. Thinking; Justification of Ideas; to Precision; Look for Patterns and Relationships Fractio n Decimal Places Percent A 0.10 10% B 0.43 43% C 0.50 D 0.35 E F STANDARDS INDICATORS AND
  • Demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially and symbolically) COND
    • Compare and order a mixture of common, decimal and percent fractions (up to hundredths)
    • To compare and order a mixture of common, decimal and percent fractions, express them in one form (i.e. either common, decimal or percent); e.g. to order ' 0.78 and 85% (i) we can express all as decimals = 80; 0.78 and 85%, hence the order from least to the largest is 0.78, and 85%; (ii) we can also express all as percentages = 80 = 80%, 0.78 = 79%, and = 85%, hence the order from least to the largest is 0.78, and 85%
    • To compare and order a mixture of common, decimal and percent fractions you can locate the fractions on the number and order them. Thinking; Justification of Ideas; Patterns and Relationships
Strand 2: Algebra — Patterns and Relationships
  • Demonstrate an understanding of how to identify and describe patterns found in tables and charts, including a multiplication chart
    • Describe the pattern found in a given table or chart
    • Using a hundred chart, ask students to colour each number as they skip count by 2s and describe the pattern created. Repeat for 3, 4, 5, 6, 7, 8, and 9. Ask students to describe what changes they notice as the numbers increase. Note to what extent students: (i) identify all, some or none of the multiples of a given number. (ii) are able to predict and extend the pattern. (iii) are able to describe the pattern by relating it to similar designs in the real world (e.g., students may say it looks like a checker board)
    • Determine the missing element(s) in a given table or chart
    • Provide students with a chart with missing numbers and ask them to identify the missing numbers and explain their reasoning
    • Identify the error(s) in a given table or chart
    • Provide a mapping table containing errors. Ask students to identify and explain where the pattern has errors Number of Tables Number of Chairs 1 4 2 8 3 12 4 18 5 20 6 24 Thinking; Justification of Ideas; Development and Leadership and Relationship STANDARDS INDICATORS AND
  • Translate among different representations of a pattern, such as a table, a chart or concrete material
    • Create a concrete representation of a given pattern displayed in a table or chart
    • Provide a table showing a pattern (involving one operation) such as the one below. Students can complete the table and create a concrete representation using linking cubes or other manipulatives Figure 1 2 3 4 5 6 7 8 Number of Cubes 3 6 9 ? ? ? ? ?
    • Create a table or chart from a given concrete representation of a pattern
    • Present learners with a geometric design series, such as the one shown below. Ask them to extend the pattern and record it in a T-chart. Ask learners what the 10th step would be. What would the 12th step be? What would the 20th step be? #1 #2 #3 #4 Design # # of Square 1 1 2 2 3 3 4 4 Thinking; Justification of Ideas; Development and Leadership and Relationship STANDARDS INDICATORS AND
  • Represent, describe and extend patterns and relationships using charts and tables, to solve problems
    • Translate the information in a given problem into a table or char
    • Given the numerical pattern, ask students to extend the pattern and explain how they determined the pattern and its missing elements
    • Ask students to use manipulatives to represent this pattern and describe the relationship between the chart and the concrete representations
    • Identify and extend the patterns in a table or chart to solve a given problem
    • Give students two tables with patterns that are related in some way. Students should first extend each one by three more numbers. Then they should explain how the two patterns are alike and how they are different
    • Students could make up their own pairs of patterns and challenge other students to discover how they are alike and how they are different A B 1 2 2 4 4 8 Pattern A Pattern B 1 5 1 2 2 10 2 7 3 15 3 12 4 20 4 17 5 25 5 22 Thinking; Justification of Ideas; Development and Leadership and Relationship
Strand 2: Algebra — Unknowns, Expressions and Equations
  • Express a given problem as an equation in which a symbol is used to represent an unknown number
    • Write a given problem as an equation in which a symbol is used to represent an unknown number
    • Ask students to explain the purpose of the box symbol in the following equation: 15 = 8
    • Express a given pictorial or concrete representation of an equation in symbolic form
    • Provide a pictorial representation of the following and ask students to write equations with unknowns for each situation. Students need not solve their equations. (i) The perimeter of a triangle is 12 cm. One side is 3 cm and another side is 4 cm. What is the length of the third side? (ii) Mansa has three types of stickers. She has 25 stickers, 3 are Cocoa stickers and 18 are Cashew stickers. How many of the third type does she have? (iii) Kojo's age and his sister's age add up to 18. If Kojo is 12, how old is his sister? Thinking; Justification of Ideas; Development and Leadership and Relationship STANDARDS INDICATORS AND
  • Solve one-step equations involving a symbol to represent an unknown number
    • Solve a given one-step equation using manipulatives
    • Ask students to solve the following using a pan balance: (i) 7 + = 12 (ii) 19 = 11
    • Describe orally, the meaning of a given one-step equation with one unknown
    • Ask students to solve the following equations and explain their thinking (i) 13 = 20 (ii) 25 + = 100
    • Solve a given equation when the unknown is on the left or right side of the equation
    • Ask students to solve the following using base ten materials: (i) 109 + = 164 (ii) 50 = 150
    • Solve a given one-step equation using "guess and check"
    • Ask students to explain what the represents in the number sentences shown. Ask them to place numbers in the symbols to make the number sentence true
  • Solve one-step equations involving a symbol to represent an unknown number CONT'D
    • Represent and solve a given addition or subtraction problem involving a "part part-whole" or comparison context, using a symbol to represent the unknown
    • Ask students to represent and solve these problems: (i) Eunice is Anita's older sister. The difference between their ages is 21 years. Anita is 37 How old is Eunice? (ii) Ms. Akoto allowed 7 students to go to the washroom. There were 15 students left in the room. How many students are in the class?
    • Create a problem for a given equation with one unknown
    • Provide an equation such as 14 + = 21 or 25 - = 18. Ask students to create a matching story problem and solve it. Observe to what extent students are able to:
    • Create a story to match the equation
    • Explain the meaning of the unknown variable; and
    • Solve the problem in one or more way Thinking; Justification of Ideas; Development and Leadership and Relationships
Strand 3: GEOMETRY AND MEASUREMENT — 2D and 3D Shapes
  • Identify the lines of symmetry of regular and irregular 2D shapes
    • Complete drawings of shapes to make them symmetrical
    • Give learners graph sheets to copy the incomplete 2D shape and it complete to make a symmetrical picture
    • Give learners photocopied worksheets with several incomplete 2D shapes to complete with marked line of symmetry to complete the drawing
    • Identify the lines of symmetry of regular and irregular 2D shapes (triangles and quadrilateral)
    • Give learners photocopied worksheets with symmetrical and non-symmetrical objects to sort and explain why they are symmetrical or not showing the lines of symmetry Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Identify the lines of symmetry of regular and irregular 2D shapes
    • Give learners photocopied worksheets with symmetrical and non-symmetrical 2D shapes to cut out and sort, and explain why they are symmetrical or not showing the lines of symmetry
    • Give learners cut-out 2D fold shapes to investigate the number of lines of symmetry
    • Give learners 2-D shapes to copy and draw their lines of symmetry Thinking; Justification of Ideas; Development and Leadership
Strand 3: GEOMETRY AND MEASUREMENT — Position / Transformation
  • Describe the position of objects in space using the cardinal points
    • Tell the position and motion of objects in space using the cardinal points north south, east and west
    • Put pupils in convenient groups a give each group with a worksheet on graph with different labelled coordinates; some with axes labelled and other not etc. Pupils discuss their worksheets in their groups, then with whole class, describing coordinates, axes and pointing out errors on graphs if any
    • Pupils describe the position and motion of objects: e.g. The point P is to the west of point T but to the north of the A
    • Ask learners to locate the coordinates (i.e. ordered pairs of the location) of the Points; e.g. B is (2 3) and T is (2,2) Thinking; Justification of Ideas; Development and Leadership
Strand 3: GEOMETRY AND MEASUREMENT — Measurement- (Perimeter and Area)
  • Demonstrate understanding of perimeter of regular and irregular shapes
    • Estimate perimeter using referents for centimetre or metre
    • Using pupils' referents for centimetre or metre estimate and calculate perimeter of any object in the classroom (e.g. exercise book, floor tiles, math set, etc.) then measure with a ruler of tape and calculate the actual perimeter and compare the answers
    • Measure and record perimeter for regular and irregular shapes in cm and m
    • Ask pupils to use a ruler to measure all the sides of a regular shape and sum up the result to obtain the perimeter P = 16cm
    • Pupils to explore the area of irregular cut-out shapes using graph sheets. Pupils to trace the shape on the graph sheet and count out the unit squares Thinking; Justification of Ideas; Development and Leadership Identity STANDARDS INDICATORS AND
  • Demonstrate understanding of perimeter of regular and irregular shapes CONT'D
    • Given an irregular shape with its sizes, ask pupils to sum up the sizes to obtain the perimeter
    • Develop and apply a formula for determining perimeter of square and rectangle
    • Use cut out shapes to demonstrate how to determine the perimeter of 2-D shapes. Ask pupils to measure the sides of the cut out shape and add the results to obtain the perimeter
    • Given a rectangular cut out shape, ask pupils to measure the sides of the shape and determine the perimeter of the shape Therefore the perimeter of the triangle given is AB + AD + BC + CD. Thus 4cm + 2cm + 4cm + 2cm = 12cm Thinking; Justification of Ideas; Development and Leadership and Relationships STANDARDS INDICATORS AND
  • Demonstrate understanding of perimeter of regular and irregular shapes CONT'D
    • Construct different rectangles for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeter
    • Given a perimeter of say 36cm, pupils to draw about three different rectangular shapes for the same perimeter. Combinations may include (6cm, 6cm, 12cm, 12cm; 8cm, 8cm, 10cm, 10cm; 4cm, 4cm, 14cm, 14cm, etc.) Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of area of regular and irregular 2-D shapes
    • Recognise that area is measured in square units
    • Pupils to explore the area of their exercise books. i.e. ask pupils to cut 1cm by 1cm square sheets and tack them on the back of their exercise books until it is covered entirely. Then, count the number of the sheets to obtain the area
    • Pupils to explore the area of graph sheet. Ask pupils to calculate the area of one of the squares on the graph sheet. Then, count the number of squares on the graph sheet to obtain the area of the entire sheet
    • Using floor tiles, ask pupils to measure the area of one of the tiles, then multiply it by the number of tiles to obtain the area of the entire room Note: Help pupils to come out with the understanding that the area of a figure is the number of squares required to cover it completely
    • Select and justify referents for the units cm2 or m2
    • Let pupils explore the area of smaller objects say their exercise books. Then explore the area of larger objects say the entire classroom and compare the results for the two activities. Ask pupils to tell which unit (cm2 or m2) they will use for which activity and why? Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Demonstrate understanding of area of regular and irregular 2-D shapes CONT'D
    • Estimate area by using referents for cm2 or m2
    • Let pupils estimate the area of items in the classroom. Then measure the actual area and compare with their estimates
    • Pupils to measure the area of say their exercise books. With that as a reference point, ask them to estimate the area of the teacher's table
    • Develop and apply a formula for determining area of a rectangle and square
    • Give pupils a standard graph sheet with 1 cm squares and ask them to draw a square of given length on the graph sheet. The area can be measured by counting the number of square units. So, we can count the number of unit units to find the area. In the diagram the area is 16cm2 since there are 36 squares in the shape
    • Ask pupils to count the number of cubic squares on the vertical section of the shape and multiply it by the number on the horizontal section Ask pupils to compare their answer with the first strategy and draw their own conclusions. The area of a square can be given as L L and that of a rectangle is L B
    • Construct different rectangles for a given area (cm2 or m2) in order to demonstrate that many different rectangles may have the same area
    • Given an area of say 24cm2, pupils should draw about three different rectangles for the same area Combinations may include (6cm 4cm; 8cm 3cm; 12cm 2cm, etc.) Thinking; Justification of Ideas; Development and Leadership
Strand 3: GEOMETRY AND MEASUREMENT — Measurement -Time
  • Demonstrate understanding of time taken by events in minutes and hours
    • Tell the time in hours and minutes in analogue and digital watches including 24-hour clocks
    • 1 Use analogue clocks to tell time by keeping the hour hand on 12 and making jumps of 15(quarter past), 30(half past), 45(quarter to), and 60 (12 o'clock)
    • Use analogue clocks to tell time by keeping the hour hand on any number say 3 and move the minutes hand to various numbers for different time (3:12, 3:25, 3:38, 3:50, etc
    • Use analogue clocks to tell time by keeping the minutes hand on 12 and moving the hour hand to tell time at the hour mark
    • 4 Pupils should draw/sketch the face of the clock to tell time given Thinking; Justification of Ideas; Citizenship STANDARDS INDICATORS AND
  • Demonstrate an understanding of time taken by events in minutes and hours CONT'D
    • Pupils to explore the relationship in the units of time (i.e. 60 seconds = 1 minute; 60 minutes = 1hour)
    • Use digital watches to tell time. Pupils to observe the face of the digital watches and tell the time
    • Use clock to measure time to complete simple events in minutes and seconds
    • Use the analogue clock to record the time it takes to say walk from the classroom to the canteen/head teacher's office/library, etc. and back. (mostly minutes)
    • Use the digital watch to record say the time it takes to walk from the teacher's table to the cupboard (mostly seconds)
    • Ask pupils to tell the time it takes to complete activities like bathing, brushing teeth, ironing a shirt cooking rice, etc
    • State dates of events and record calendar dates in a variety of formats
    • Record dates in different formats i. Tuesday, 28th August 2018 ii. 28th August, 2018 iii. 28-Aug-18 iv. 28/08/2018 v. 28.08.18
  • Demonstrate an understanding of time taken by events in minutes and hours CONT'D
    • Ask pupils in groups to state their dates of birth and put this in a table. Guide pupils to draw a time line (or time line-graph) for their birthdays (see Figure below) Thinking; Justification of Ideas; Citizenship
Strand 3: GEOMETRY AND MEASUREMENT — Position/Transformation
  • Describe the position of objects in space using the cardinal points
    • Put pupils in convenient groups a give each group with a worksheet on graph with different labelled coordinates; some with axes labelled and other not etc. Pupils discuss their worksheets in their groups, then with whole class, describing coordinates, axes and pointing out errors on graphs if any
    • Pupils describe the position and motion of objects:
    • E.g. The point P is to the west of point T but to the north of the A
    • Ask learners to locate the coordinates (i.e. ordered pairs of the location) of the Points; e.g. B is (2,-3) and T is (2,2) Thinking; Justification of Ideas; Precision, Global Citizenship
Strand 4: Data — Data Collection, Organization, Presentation, Interpretation and Analysis
  • Demonstrate an understanding of many-to-one correspondence in displaying, and reading or
    • Use an understanding of one-to-one correspondence to read and interpret graphs
    • Give learners graphs that use one-to-one correspondence in displaying data. For example, the graph below shows the favourite fruits of children in a P4 class. Each coloured box in the graph represents a pupil Ask the following questions for children to read and interpret graphs i. How many pupils said they like pawpaw? ii. What is the most favourite food of the class? How many pupils are in the class? Etc. Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Demonstrate an understanding of many-to-one correspondence in displaying, and reading or CONT'D
    • Use an understanding of many-to-one correspondence to display or construct graphs
    • Display a table for of illnesses P4 pupils have had in school last academic year. Discuss with pupils how many objects/cut-outs will be required to display or construct a graph of the illnesses in the table ifrepresents 2 pupils Illness Number of pupils look at pictures or a video of hospital with illnesses Number of objects in graph Diarrhoea 10 5 Fever 16 8 Toothache 4 2 Headache 6 Stomach-ache 8 Cold 14
    • Put a chart with labelled axes on the board; places several card cut-outs of the object ""on the table. Ask pupils to go in turns to construct the graph of the illnesses in the chart by pasting the right number of cut-outs in the columns above each illness as in the figure below Thinking; Justification of Ideas; STANDARDS INDICATORS AND
  • Demonstrate an understanding of many-to-one correspondence in displaying, and reading or CONT'D
    • Ask questions for pupils to read and interpret graphs. Ask pupils also to write questions based on the graph for their friends to answer
    • Give learners tables with data that require the use an understanding of many-to-one correspondence to construct their graphs Number of pupils Diarrhoea Fever Toothache Headache Stomach- ache Cold Thinking; Justification of Ideas; KEY: is 2 pupils STANDARDS INDICATORS AND
  • Demonstrate an understanding of many-to-one correspondence in displaying, and reading or CONT'D
    • Compare graphs in which the same data has been displayed and explain how they are the same and different
    • Give learners several graphs that have used one-to-one correspondence in displaying the same data For instance, the graph below shows the animals at Mr. Wilmot's farm. Ask children to explain how they are the same and different Thinking; Justification of Ideas; STANDARDS INDICATORS AND
  • Demonstrate an understanding of many-to-one correspondence in displaying, and reading or CONT'D
    • Find examples of graphs in which many-to-one correspondence is used in print and electronic media, such as newspapers, magazines and the Internet, and describe the correspondence used
    • Give learners several graphs that have used many-to-one correspondence in displaying the same data. E.g. The graphs below show the number of pupils in a KG to P3 in a school and the time five pupils can take to hold their breath. Ask questions for children to read and interpret graphs How many pupils are in KG and P1? How many pupils more pupils are in P1 than P3? How long did Ben hold his breath? Who can hold her breath longest? Etc. Thinking; Justification of Ideas; STANDARDS INDICATORS AND
  • Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions
    • Identify common features of graphs that use many-to-one correspondence and use that understanding to draw bar graphs or pictographs, complete with title, labelled axes, key or legend, to represent data collected (up to 4 categories of data)
    • Refer to example in B4.4.1.1.4 to common features of graphs that use many-to-one correspondence Examine such features as title, vertical axis and label, hofrizontal axis and label, key or legend
    • Give students data presented in a table to draw bar graph complete with title, labelled axes, key. The table show amount of rainfall recorded in Kumasi in the half of the year. January February March April May June 5mm 10mm 10mm 25mm 40mm 45mm
    • Give pupils data on energy usage by households in a community over a period (e.g. six months) presented in tables for them to draw bar graph complete with title, labelled axes, key. Ask questions for pupils to read and interpret graphs. Thinking; Justification of Ideas; Rainfall in mm STANDARDS INDICATORS AND
  • Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions CONT'D
    • Use understanding of many-to-one correspondence to solve simple problems (how many altogether, comparing, or take apart problems) requiring interpretation of many-to- one bar graphs (up to 4 categories of data)
    • Give learners several graphs that have used many-to-one correspondence in displaying the same data. For example, the graph below on the number of pupils treated for malaria in a school. Ask questions for children to read and interpret graphs. i) How many pupils were treated for malaria in the hospital in April? ii) How many pupils were treated for malaria in the hospital in May and June? iii) How many pupils were treated for malaria in the hospital in the last three months of the year? iv) In which month was the largest number of people treated for malaria in the hospital? of Ideas; Attention to Precision BASIC 5 BASIC 5 Strand 1- Number

Basic 5

12 topics
Strand 4: Data — Counting, Representation & Cardinality
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1000,000
    • Model number quantities up to 1,000,000 using graph sheets and multi-base block
    • Ask pupils to model number quantities up to 1000,000 using graph sheets or multi-base materials. For instance, with multi-base block, a cube = 1000 unit; a rod = 10,000; a flat = 100,000 and a block = 1,000,000; learners model 436,000 with the appropriate materials square represents 1000 units. Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1000,000. CONT'D
    • Read and write numbers in figures and in words up to 1000,000
    • Play the place value number wheel game: Use the million number wheel to generate 7-digit numbers and represent the number generated on a place value frame. Throw a number of pebbles (or stones) onto the number wheel, identify the number of pebbles landing in each place value ring, and state the number generated in the wheel (i.e. 2 landed in the ten-thousands' ring making the number twenty- thousand or 20,000)
    • Ask pupils to write given numbers on the expanded form of the number : 2,524,513=1000,000 2 +100,000 5 + 10,000 2+1000 4+ 100 5 + 10 1+ 1 3 = 2,000,000 + 500,000 + 20,000 + 4,000 + 500 + 10 + 3 Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1000,000. CONT'D
    • Identify numbers in different positions around a given number in a number chart
    • Display a number chart in multiples of 1,500 between 10,000 and 1000,000 and lead learners identify numbers in different positions around a given number. Put learners in pairs and give each group a number grid and have them identify numbers in different positions around a chosen number 10,000 11,500 12,000 13,500 15,000 16,500 20,000 21,500 22,000 23,500 24,000 25,500 30,000 31,500 33,000 34,500 36,000 37,500 40,000 41,500 43,000 44,500 46,000 47,500 50,000 51,500 53,000 54,500 56,000 57,500 60,000 61,500 63,000 64,500 66,000 67,500
    • Compare and order whole numbers up to 100,000 and represent the comparison using ">, <, or ="
    • Learners identify numbers which are 10,000 more or 10,000 less than a given six-digit number. E.g 122,400 is 1,000 less than133,400 Learners use words such as: "equal to" "greater than" "less than" and later use symbols such as "<", "=", ">" to compare numbers up to 10,000 taking into consideration the place value of each digit in the given number. E.g. 251200 = 251,200; 132,734 > 132,635
    • Learners work together in their groups to order a given set of numbers in ascending or descending order verbally and in writing. E.g. 1020, 1025, 2673, 2873, Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1000,000. CONT'D
    • Give two numbers between 10,000 and 100,000 to each group and encourage learners to say as many things as possible about the two numbers. For instance 1022345 and 1022534; 1022345 is less than (smaller than) than1022534 or 1022534 is bigger than (greater than) 1022345, or 1022345 is almost 200 less than 1022534 etc
    • Round (off, up, down) whole numbers up to 100,000 to the nearest ten thousands thousands, hundreds and tens
    • Learners round off numbers to the nearest 10,000, 1000 and 100. For instance; 129,500 is approximately 130,000 and 19100 as approximately 19,000
    • Learners round up and round down to estimate sums and differences NB: To round down learners consider the smaller of the two approximated numbers, while round up considers the bigger of the two numbers. The table below may bring the meaning of these two concepts clearer 214765 Round up Round down Round off to the nearest ten 214770 214760 214770 to the nearest hundred 214800 214700 214800 to the nearest thousand 215000 214000 215000 Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1,000,000
    • Skip count forwards and backwards in 500s 1000s etc. up and from 100,000
    • Put learners into convenient groups. A learner mention a number and another makes skip count in 500s or 1000s to include the fifth count. For instance. Learner 1: Shout out "15290"skip counting up in 500s Learner 2: 15790, 16290, 17290, 17790, 18290, etc. Learner 3; Shout out "31285"skip counting up in 1000s Learner 4; 32285, 33285, 34285, 35285, 36285....etc
    • Skip count forwards and backwards by 50s and between 1000 and 10000 that are multiples of 50s and 100s but make an error or leave out a number. Challenge learners to identify or correct error. Thinking; Justification of Ideas; Precision
  • Demonstrate understanding of Roman Numerals up to C (i.e. 100)
    • Recognize Roman Numerals system up to C (i.e. 100)
    • Display roman numeral charts (1-100) arranged in sequential order and lead learners to identify the numerals. Learners identify the main characters of the roman numerals used to build the table up to 30 i.e. I, II, III, IV, V, X, L and C Call out a numeral and have learners point at it from the chart
    • Have learners match the Roman numerals to the Hindu-Arabic numerals for instance I = 1; V= 5: IX= 9, XV= 15, XXX = 30, XL = 40, LVI = 56, XCIX = 99. Mention some numerals randomly and have learners point at it on the chart
    • Count and convert Hindu Arabic numbers to Roman numerals up to 100 (C) and vice versa
    • Learners read the chart sequentially forwards and backwards, vertically (up and down), zig-zag diagonally and randomly without pointing to the numbers. Invite 2-3 learners to read to the class. Call a Roman numeral and ask learners to write
    • Give learners a numeral in the Hindu Arabic system and have learners convert to roman numeration and vice versa for instance XXIV = 24, LX = 60, XCIV = 94, ETC. Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of factors, multiples of numbers including composite, even odd and prime numbers from 1 to
    • Identify the factors of whole numbers 1 - 100
    • Ask learners to use different arrangements of arrays of objects to find factors of whole numbers 1 100. For instance the factors of 24 can be obtained from the following arrays of objects
    • Ask learner to collect from the arrays, pairs of number as the factors of the given number, 24. Hence the set of factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24} Thinking; Justification of Ideas; Precision
  • Demonstrate an understanding of factors, multiples of numbers including composite, even odd and prime numbers from 1 to
    • Generate and identify prime numbers and composite numbers between 1 and 100
    • Ask learners to use different arrangements of arrays of objects (or the factorization method)to find factors of the first 30 whole numbers and use their results to complete the table below. Have learners identify prime numbers; i.e. number with only two factors, 1 and the number itself; other are composite. Numbers Factors Number of factors 1 1 1 2 1, 2 2 3 1, 3 2 4 1, 2, 4 3 5 1, 5 2 30 1,2, 3, 5, 6, 10, 15, 30
    • In convenient groups, have learners use the "Sieve of Eratosthenes" to identify prime numbers between 1 and 100, i.e. dividing through by whole numbers starting from 2; numbers that cannot be divided by other numbers except the number itself are prime numbers. STANDARDS INDICATORS AND
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 100,000 CONT'D
    • Identify even and odd numbers between 1 and 100 as number that can be arrayed in twos array and those which cannot
    • Ask learners to use arrangements of twos arrays of objects to find even and odd numbers between 1 and 100
    • Ask learner to collect from the arrays, pairs to skip count in twos starting from 1 to generate odd numbers, and skip count in twos starting from 2 to generate even numbers Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate an understanding of factors, multiples of numbers including composite, even, odd and prime numbers from 1 to 100 CONT'D
    • Determine the highest common factor of any 2 or 3 numbers by prime factorisation
    • Have learners use factor tree method to determine prime factors of any given whole number. For example the prime factors of 24 For instance, from the of 24. Ask learners to list the factors of two or more given whole numbers using the factor tree; for 36 and 48 we
    • Learners use the prime factorization to determine the HCF by underlining the common factors in each product
    • Learners use the prime factorization by inspection to determine the LCM by underlining the largest number of factors in each product Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate an understanding of factors, multiples of numbers including composite, even, odd and prime numbers from 1 to 100
    • Learners place factors in a Venn diagrams to find the HCF and LCM of 36 and 48. i.e. the HCF is
    • Learners use the prime factorization to determine the LCM and HCF of three numbers using (i) prime factorization using table and dividing through by prime factors. Example 1, find the LCM and HCF these sets of numbers: 12, 20 and 30. (see method in figure), i.e. HCF = 2, and
    • Recognize relationship between factors and multiples of whole numbers from 1 to 100
    • Investigate even and odd numbers. How do you know a number is even or odd?
    • Investigate numbers that are multiples of 4 and 6. How do you know a number is a multiple of 4? a multiple of 6? (This is also known as the divisibility test)
    • Investigate perfect numbers, that is, numbers whose factors add up to the number; for instance 6 has factors 1, 2, 3 and 6. The sum of factors other than 6 is 1+2+3 =6, and hence 6 is a perfect number. How many more perfect number can we find in the first 100 whole numbers? Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Describe and apply mental mathematics strategies and number properties to determine answers for basic multiplication facts to 81 and related division facts
    • Apply mental mathematics strategies and number properties, such as skip counting from a known fact, using doubling or halving, using patterns in the 9sfacts, using repeated doubling or halving, to determine answers for basic multiplication facts to 81 and related division facts
    • Describe the mental mathematics strategies used to determine a given basic fact, such as skip count up by one or two groups from a known fact (e.g., if 5 7 = 35, then 6 7 is equal to 35 + 7 and 7 7 is equal to 35 + 7 + 7) skip count down by one or two groups from a known fact (e.g., if 8 8 = 64, then 7 8 is equal to 64 8 and 6 8 is equal to 64 8 8) doubling (e.g., for 8 3 think 4 3 = 12, and 8 3 = 12 + 12) patterns when multiplying by 9 (e.g., for 9 6, think 10 6 = 60, and 60 6 = 54; for 7 9, think 7 10 = 70, and 70 7 = 63) repeated doubling (e.g., if 2 6 is equal to 12, then 4 6 is equal to 24 and 8 6 is equal to 48) repeated halving (e.g., for 60 4, think 60 2 = 30 and 30 2 = 15) relating division to multiplication (e.g., for 64 8, think 8... = 64)
    • Recall multiplication facts to 81and related division facts Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Describe and apply mental mathematics strategies and number properties to determine answers for basic multiplication facts to 81 and related division facts
    • Apply mental mathematics strategies for multiplication, such as annexing then adding zero halving and doubling using the distributive property
    • Determine the products when one factor is a multiple of 10, 100, or 1000 by annexing zero or
    • Apply the distributive property to determine a given product involving multiplying factors that can property to determine a given product involving multiplying factors that are close to multiples of 10
    • Explain the property for determining the answer when multiplying numbers by i. one ii. zero. Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Demonstrate an understanding of multiplication of a 2 or 3-digit number by a 2 or 3-digit number
    • Multiply multi digit numbers by 2-digit numbers efficiently
    • Multiplication of whole numbers using the "expand and box" method (partial decomposition method). Lead learners to multiply a 3-digit number by a 1-digit number as shown below, for example 448 2 =? 400 40 8 2 800 80 16 448 2 = (400 2) + (40 2) + (8 2) = 800 + 80 + 16 = 800 + 80 + (10 + 6) = 800 + 90 + 6 = 896 Thinking; Justification of Ideas; Development and Leadership STANDARDS PRACTICES AND
  • Demonstrate an understanding of multiplication of a 2 or 3-digit number by a 2 or 3-digit number CONT'D
    • Multiplication of whole numbers using the lattice method. Have learners draw a 2 by 1 rectangular box for solving 54 3. Thinking; Justification of Ideas; Development and Leadership STANDARDS INDICATORS AND
  • Recall basic division fact up to 100
    • Determine basic division fact up to 81
    • Investigate numbers that are multiples of 3,4, 6, 8 and 9. How do you know a number is divisible by 3, 4, 6, 9? (This is also known as the divisibility test)
    • Draw a 6 by 6 multiplication chart and use it as a game board to play the 3-in-a-line game with a pair of dice or playing cards. Players take turns in throwing a one dice and mark (or cover) a number that can be divided by the results (i.e. a quotient). The winner is the one who obtains three numbers in a line. Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate an understanding of division of a 2 or 3 digit number by a 1 or 2-digit number
    • Divide 3-digit numbers by 1-digit number efficiently
    • Division as repeated subtraction (using the long division method). Explain division as a way of repeatedly subtracting a divisor number from a given dividend until there is none left and then determining the number of times the divisor is taken from the dividend Thinking; Justification of Ideas; Precision
  • Translate word problems into mathematical sentences and solve
    • Solve multi step word problems involving the four basic operations
    • Learners model mathematical statements from a given word problem involving addition and multiplication and solve using the strategies learnt
    • Learners model mathematical statements from a given word problem involving division and subtraction and solve using the strategies learnt
    • Learners role play a given word problem involving addition and multiplication and solve
    • Learners role play a given word problem involving subtraction and division and solve
    • Learners model mathematical statements from a given word problem involving division and multiplication and solve using the strategies learnt. The relationship between operations and the use of calculator and spreadsheet to assess the reasonableness of answers should be stressed. Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of integers
    • Solve simple addition and subtraction problems involving integers
    • Use number line to help learners to do the following types (addition) (1) 9 + -4 = _____ (2) -8 + 4 = _____ (3) -3 + -5 = _____ (4) 1 + -3 = _____ (5) -6 + 5 = _____ (6) 6 + -2 = _____ (7) -6 + 8 = _____ (8) -2 + 9 = ______
    • Use number line to help learners to do the following types (subtraction) (9) -5 1 = ____ (10) -2 1 = ____ (11) 8 7= ____ (12) 2 6 = _____ (13) -1 7 = ____ (14) -5 7= ____ (15) -8 8= ____ (16) 4 6 = _____
    • Solve word problems; e.g. (i) Some number added to 5 is equal to -11. Find the number. (ii) Ben and Cam are diving. Ben is 15.8 meters below the surface of the water. Cam is 4.2 meters above Ben What is Cam's position relative to the surface of the water? Thinking; Justification of Ideas; Precision
Strand 4: Data — Number: Fractions
  • Demonstrate understanding of strategies for comparing, adding subtracting and multiplying fractions
    • Determine equivalent fractions of given fractions
    • To compare, add or subtract the fractions, and, we need find the Lowest Common Denominator (LCD) and use this to express the equivalent fractions. Use the prime factorising strategy to determine the LCD of 4, 6, and 20. Use the LCD work out the equivalent fractions. = ?; = ??; and = ???. [To obtain the numerators, determine how many times the denominator goes into the LCD and multiply this by the numerator to obtain a new numerator.] 24 = 2 x 2 x 2 x 3 so 2 and 3 are prime factors of 24 Thinking; Justification of Ideas; Precision
    • Compare and order fractions
    • Find the Lowest Common Denominator (LCD) of the fractions and use this to express their equivalent fractions and use them for the comparison; e.g. which is larger, and or ?
    • Change the fractions to percentages or decimals and use them for the comparison. i.e. = 0.83, = 0.75, and = 0.66, and compare. STANDARDS INDICATORS AND
  • Demonstrate understanding of strategies for comparing, adding subtracting and multiplying fractions CONT'D
    • Use the concept of equivalent fractions in changing fractions to the same denominator for addition and subtraction of like fractions (one denominator being a multiple of the other)
    • To add or subtract the fractions and, we need find the Lowest Common Denominator (LCD) and use this to express the equivalent fractions. The LCD is 6 and the equivalent fractions are and; their sum is + is 2+2, which is, = = (i.e. its simplest form)
    • To add or subtract the fractions and, we need find the Lowest Common Denominator (LCD) and use this to express the equivalent fractions. The LCD is 15 and the equivalent fractions are and; their difference is
    • 6 = 10 - 6 =
    • Use the concept of equivalent fractions for addition and subtraction of fractions greater than one (improper or mixed fractions)
    • To add like mixed fractions that are larger than 1, i.e. 2 and 3, we write down the sum of the whole numbers and add the fractions; i.e. 2 + 3 = 5 + +, = 5 1+2 = 5 = 6
    • To subtract like-fractions that are larger than 1, i.e. 2 and 3, we change the mixed fractions into improper fractions and subtract; i.e. 3
    • 7 + = 11-7 =. = 1 1
  • Demonstrate understanding of strategies for comparing, adding subtracting and multiplying fractions CONT'D which is 5 ; and difference 3
    • 2 = 1 6-5 = 1 1
    • Use models to explain the result of multiplying a whole number by a fraction
    • Multiplying a whole number by a fraction, e.g. 5 or finding five two-thirds means + 2 + 2 + 2 + = = 3
    • To multiply a whole number by a mixed fraction (e.g. 3 2 ) one can multiply the whole number by the whole number and then whole number by the fraction and add the products or change the mixed fraction to improper fraction and multiply; i.e. 3 2 ) = 6 + + 2 + 2 = 6 = 8 or 3 2 = 2 + 2 + 2 = 6 2+2+2 = 6 = 8
    • To multiply a whole number by a fraction (e.g. 3 2 ) first change all into common fractions, then multiply the numerators separately and multiply the denominators separately and simplify; i.e. 3 2 = = = = 8
    • Use models to explain the result of multiplying a fraction by whole number
    • Multiplying a fraction by a whole number the Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of strategies for comparing, adding subtracting and multiplying fractions CONT'D multiplication is interpreted as "of"; e.g 5 means shade 5 ; i.e. finding two-thirds of each
    • To multiply a mixed fraction by a whole number (e.g. 4 5 ) first change all into common fractions, then multiply the numerators separately and multiply the denominators separately and simplify; i.e. 4 5 = = = = 24 Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of decimals fractions and strategies for comparing, adding and subtracting decimal fraction
    • Describe and represent decimals (up to the thousandths) concretely, pictorially, and symbolically and relate them to fractions
    • Use several pictorial representations or number line to introduce tenths and thousandths and ask pupils to identify the fractions (i.e. A, B, C, D, E, & F)
    • Use the tenth to thousandth place value chart to illustrate how to write the fraction as a base ten number with the introduction of the decimal point "" after ones place in the place value chart Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of decimals fractions and strategies for comparing, adding and subtracting decimal fraction CONT'D
    • Multiply multi-digit numbers by 2-digit numbers efficiently
    • Give pupils several common fractions (including improper fractions) to convert into hundredths and thousandths and write their decimal names; e.g
    • Ask pupils to use graph sheets to model the decimal number 0.133 by shading the graph sheet squares as shown in the figure, where units, units, and 1000 units, Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of decimals fractions and strategies for comparing, adding and subtracting decimal fraction CONT'D
    • Compare and order decimal fractions and a mixture of common and decimal fractions (up to the thousandths) using the symbols <, >, or =
    • To compare and order a mixture of common, decimal and percent fractions, express them in one form (i.e. either common, decimal or percent); e.g. to order 0.758, and 73%; we have = 625 1000 = 62.5%, 0.758 = 758 1000 = 75.8%, and 73% = 73 = 0.73, Hence the order from least to the largest is, 73% and 0.758
    • To compare and order a mixture of common, decimal and percent fractions you can locate the fractions on the number and order them Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of decimals fractions and strategies for comparing, adding and subtracting decimal fraction B5.1. 4.1.3 Round decimals to the nearest tenth and hundredth
    • Explain the rule for of rounding decimals, which is similar to that of rounding whole numbers. That is, rounding to the nearest tenth means that the rounded figure has one digit after the decimal mark. Rounding to the nearest hundredth means that the rounded figure has two digits after the decimal mark
    • Use a table with several decimals fractions and explain the rule for of rounding decimals. Give pupils a table of decimal fractions round to the nearest tenths or hundredths
    • Ask students to change fractions to decimal writing their results to the nearest tenths or hundredths. Fractio n Round to Neares t Result A 0.38 0.4 B 4.085 C 56.584 D 18.096 E 30.084 Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of decimals fractions and strategies for comparing, adding and subtracting decimal fraction CONT'D
    • Use models to explain the result of addition and subtraction of decimals (up to the thousandths)
    • To add 0.645 and 0.39, means sum 1000 + which is 645+390 1000 = 1035 1000 = 1.035. That is, since one is hundredths and other thousandths (i.e. one has 2 decimal places and the other 3 decimal places) we can line up the decimal points to align the place values and add as whole numbers
    • To subtract 0.395 from 0.6 and, one number is in tenths and other is in thousandths (i.e. one has 1 decimal place and the other 3 decimal places) it is important to line up the decimal points to align the place values and add as whole numbers
    • Use models to explain the result of multiplying a decimal (up to the thousandths) by a whole number
    • Review multiplying a fraction by a whole number. e.g 10 means shade 2 (1 10); i.e. 2(2) = 4
    • To multiply a decimal fraction by a whole number, change the decimal number to common fraction and multiply e.g.0.4 10 means( 4 10) = 4.0; Or multiply the whole numbers 4 and 10, and place the decimal point at one decimal place, since 0.4 has one decimal place
    • To multiply a decimal fraction (up to thousandths) by a whole number, first ignore the decimal point and multiply the whole numbers, check the number of decimal places and place the decimal point Thinking; Justification of Ideas; Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of percentage of a given number
    • Determine the percentage of a given quantity (limit to 2-digit whole number) and vice versa
    • Review multiplying a fraction by a whole number. e.g 10 means shade 2 (1 10); i.e. 2(2) = 4
    • To multiply a percent fraction by a whole number, change the percentage to common fraction and multiply and simplify e.g.40% 10 means ( 40 10) = 4
    • Ask learners to find given percentage of given quantities; e.g. What is 20% of 45? of Ideas; Collaborative Learning
  • Demonstrate understanding of percentage of a given number CONT'D
    • Determine the benchmark percentages from their common fractions and use these to estimate percentages of quantities
    • Use pictorial representations and chart to display common or benchmarks percentages and ask pupils to determine these from their equivalent common fractions
    • Give learners practice through drills and games to learn the equivalences of the benchmark fractions
    • Ask pupils to use the benchmarks for estimating percentages of given quantities. E.g. for "what is 60% of 45?" using the nearest benchmark fraction (i.e. 50%) the learner will know the expected result is close to 30;the learner can use benchmark fractions to determine the result mentally by finding which can easily multiply 45, and in this case to give 9. Since is 20%, then the 60% required will be 3 times 9 which is 27
    • Ask pupils to use the benchmarks for estimating and determining the results of finding percentages of given quantities and then verify by working; that is, changing the percentage to common fraction and multiplying by the quantity Precision STANDARDS INDICATORS AND
  • Demonstrate understanding of percentage of a given number CONT'D
    • Identify and describe percent from real-life contexts and solve problems using percent
    • Discuss the contexts below in which fractions are used in real life and provide materials for pupils to act them out In shops discounts, reduction to clear 50%, etc. In exams expressing marks as percentages Phone battery power used etc
    • Drawing circle graphs that represent that represent various percentages of halves, fourths and eighths The graph shows the ages of pupils in Primary 4. If there are 40 pupils in the class, ask questions for pupils to interpret the graph
Strand 2. ALGEBRA — Patterns and Relationships
  • Determine the pattern rule to make predictions about subsequent elements
    • Extend a given pattern with and without concrete materials, and explain how each element differs from the preceding one
    • Skip count in multiples of 20, 50, 500, etc. is one way to introduce patterns
    • Provide students with a thousand number chart or number line with missing numbers and help use the strategy of skip counting to find missing numbers Precision STANDARDS INDICATORS AND
  • Determine the pattern rule to make predictions about subsequent elements CONT'D
    • Describe, orally or in writing, a given pattern, using mathematical language, such as one more, one less, five more, one more than or less than twice, etc
    • Lines are drawn to intersect two lines in each diagram and the number of points of intersection are counted to form a sequence. Ask learners to tabulate your results for the next four terms in the sequence and complete the table Find the rule for lines Number of lines 1 2 3 4 5 6 Intersections 2 4 Guide learners to describe the relationship as "intersection is one less number of lines"
    • Consider a design on the wall is being made using square tiles of size 10cm by 10cm Ask learners to find the number of joints made by the tiles if one, two, three, four, etc. of the squares tiles are used, and use it to complete the following table and describe the relationships. Number of tiles 1 2 3 4 5 Number of joints 0 1 Precision STANDARDS INDICATORS AND
  • Determine the pattern rule to make predictions about subsequent elements CONT'D
    • Predict subsequent elements in a given pattern
    • Ask students to respond to find the next two terms in a pattern and state the rule for the pattern
    • Ask learners to complete the table below for the number of match sticks used in this geometric pattern Guide learners to describe the relationship
    • Ask learners to write questions based on number or geometric patterns for their friends to find answers to; e.g. how many match sticks will be used for the 9th geometric pattern? Number of triangles 1 2 3 4 5 n Number of match sticks 3 6 Precision STANDARDS INDICATORS AND
  • Determine the pattern rule to make predictions about subsequent elements CONT'D
    • Represent a given pattern visually to verify predictions
    • Ask learners to examine the pattern in the table below which shows the number of match sticks used in making a pattern of triangles. Pattern Number (sticks in side) 1 2 3 4 5 6 7 8 9 Number of match sticks 3 9 18 Ask learners to use match sticks to make the patterns of triangles and complete the table. Guide learners to describe the relationship
    • Ask learners to examine the pattern in the table below which shows the number of match sticks used in making a pattern of squares Ask learners to use match sticks to make the patterns of triangles and complete the table. Guide learners to describe the relationship Pattern Number (sticks in side) 1 2 3 4 5 6 7 8 9 Number of Pattern 1 triangles 1 4 9
    • Ask learners to write questions based on number or geometric patterns for their friends to find answers to; e.g. how many match sticks will be used for the 9th pattern of squares? How many match sticks will be used for the 8th pattern of squares? Precision STANDARDS INDICATORS AND
  • Determine the pattern rule to make predictions about subsequent elements CONT'D
    • Solve a given problem by using a pattern rule to determine subsequent elements
    • Ask learners to describe the pattern rule for each example and determine the next three elements of each: (i) 1, 10, 7, 70, 67, 670,... (ii) 10, 12, 16, 22, 30... (iii) 50, 48, 47, 45, 44
    • Ask learners to describe the pattern rule for each of the patterns and determine the next three elements: (i).25,.5,.75, ___, ___, ___, (ii) 2.50, 5, 7.50, ___, ___, ___, (iii) 64, 32, 16,, ___, ___, ___, (iv) 900, 450, 225,, ___, ___, ___
    • Determine and explain why a given number is or is not the next element in a pattern
    • Ask students to respond to the following prompt: Shika filled bags with marbles. She placed two marbles in the first bag, four marbles in the second bag, six marbles in the third bag, eight marbles in the fourth bag and twelve in the fifth bag. Her friend Ayerko noticed an error in the pattern. Can you identify and describe the error? Bags 1 2 3 4 5 6 7 Marbles 2 4
    • Write a rule in words and in algebra to represent a given pattern
    • Ask learners to state the rules in words and in algebra to represent a given increasing linear patterns. Precision STANDARDS INDICATORS AND
  • Determine the pattern rule to make predictions about subsequent elements CONT'D Term/Input 1 2 3 4 5 6 Rule for n in words Rule for n in Algebra Result/Output A 7 14 21 7 times n 7n Result/Output B 0
    • Describe the relationship in a given table or chart, using a mathematical expression
    • This table shows the pattern of cost of boxed lunches for students on a look at pictures or a short video (or look outside from a window with a grown-up) to. Ask learners to: (i) explain the pattern of how the cost of lunches changes as more students go on the trip; (ii) use the pattern to determine how many students went on the trip if the cost of lunches is GHC90. Number of students 1 2 3 4 5 ? Cost of lunch in cedis 3 6 9 12 15 90
    • Ask learners to write questions based on the pattern for their friends to find answers Precision
Strand 2. ALGEBRA — Algebraic Expressions
  • Demonstrate understanding of algebraic expressions
    • Demonstrate understanding of algebraic expressions as mathematical phrases that can contain letters which represent ordinary numbers and operators (like add, subtract, multiply, and divide)
    • Write algebraic expressions for word problems: 1) Sum of 8 and s 2) 8 times the sum of c and 7 3) Take away 4 from m 4) Subtract 4 from 7 times g
    • Write algebraic expressions for the perimeter of the following shapes: Precision STANDARDS INDICATORS AND
    • Simplify basic algebraic expressions by grouping like terms. E.g 1) m + 5 m 4) 9 w 4 10 w 5) 8 w + 5 w 6) m + 9 5 m
    • Substitute a value for an unknown into an expression and correctly calculate the answer. E.g. Find the values of these algebraic expressions using the values given in the following: 1) z + 7d use z = 7 and d = 4 2) 4 - 5s + 3b use s = 6 and b = 2 3) 8k + d use k = 2 and d = 3 4) -7 - 2b + 6 - 3r use b = 3 and r = 4 5) 7(5f - 3n) - 8 use n = 3 and f = 7 6) -5d - k 7 _ use k = 14 and d = 5
Strand 2. ALGEBRA — Variables and Equations
  • Solve problems involving single variable, one-step equations with whole number coefficients
    • Express a given problem as an equation where the unknown is represented by a letter to variable
    • Ask learners solve word problems; e.g ii. The product of two numbers is 120. If one of the numbers is 24, what is the other number?
    • Ask learners to read Ama's problem below, complete the table and solve the problem Ama is tracking the progress of her plant's growth. Today the plant is 5cm tall. The plant grows 2cm a day (i) Write a mathematical sentence that represents the height of the plant after d days; (ii) What will the height of the plant be after 20 days? (iii) How many days will the height take to reach 75cm? Days (d) Days 1 2 3 4 5 Height (h) Height 5cm 7cm of Ideas; Collaborative Learning
  • Perform a single transformation (translation and reflection) of a 2D shape
    • Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially or symbolically
    • Learners use concrete materials, such as blocks or counters and the balance scales, to find the value of p in the following equations. If necessary, model the use of guess and test as one strategy. By observing patterns in their results, students become more systematic in the guesses they make B5.2.3.1.3Create a problem for a given equation
    • Ask students to describe two different stories that the equation 5 + k = 9 could represent
    • Ask learners to solve puzzle in the figure, by solving the equations in each line 1. 3 + p =11 2. 14 - p = 8 3. p - 9 = 16 4. 3p = 12 5. p + 5 = 17 6. 24 = p + 9 7. 25 = 35 - p of Ideas; Collaborative Learning Look for Patterns and Relationships
Strand 3: GEOMETRY AND MEASUREMENT — Lines and Shapes
  • Identify and sort quadrilaterals including rectangles squares, trapezoids parallelograms, and rhombuses according to their attributes
    • Demonstrate an understanding of the properties (e.g. sides, angles, and diagonals) of squares and rectangles
    • Give learners photocopied worksheets with shapes to identify squares and rectangles and give reasons. (Or Draw on the chalk board) of Ideas; Collaborative learning Look for Patterns and Relationships
Strand 3: GEOMETRY AND MEASUREMENT — Measurement Perimeter, Area, Capacity/Volume and Angle
  • Identify and sort quadrilaterals including rectangles squares, trapezoids parallelograms, and rhombuses, according to their attributes CONT'D
    • Use paper folding with cut-out squares and rectangles to investigate sides, angles and diagonals properties
    • Give learners foldable cut-out 2D squares and rectangles to investigate the properties in terms of sides, angles, and diagonals and complete the table Properties Rectangle Square Sides All sides are congruent No Yes Opposite sides are congruent Opposite sides are parallel Angle Opposite angles are congruent All angles are right angles Diagonals Diagonals bisect each other Diagonals are congruent Diagonals meet at right angles and Leadership Attention to Precision STANDARDS INDICATORS AND
  • Identify and sort quadrilaterals including rectangles squares trapezoids parallelograms and rhombuses according to their attributes CONT'D
    • Prove that a polygon is regular by measuring the sides and angles or by folding and superimposing
    • Give learners foldable cut-out 2D quadrilaterals - rectangles, squares, trapezoids, parallelograms, and rhombuses - to investigate the properties in terms of sides, angles, and diagonals and complete the table Properties Rectangle Square rhombuses trapezoids parallelograms Sides All sides are congruent No Yes Opposite sides are congruent Opposite sides are parallel Angle Opposite angles are congruent All angles are right angles Diagonals Diagonals bisect each other Diagonals are congruent Diagonals meet at right angles of Ideas; Collaborative Learning
Strand 3: GEOMETRY AND MEASUREMENT — Measurement
  • Estimate and measure perimeter and surface area of 2-D shapes using centimetre and metre
    • Estimate perimeter using referents for centimetre and metre, and calculate the actual perimeter and compare
    • Using pupils' referents for centimetre (hand span and thumb width) or metre (two strides or pace steps) estimate and calculate perimeter of any object in the classroom (e.g. exercise book, floor tiles, math set, teacher's table, classroom floor, etc.) then measure with a ruler of tape and calculate the actual perimeter and compare the answers. of Ideas; Collaborative Learning
  • Estimate and measure perimeter and surface area of 2-D shapes using centimetre and metre CONT'D
    • Calculate perimeter of given shapes in centimetres and metres
    • Give learners 2D shapes with given dimensions to find the perimeter by adding the distance around the shapes of Ideas; Collaborative Learning
  • Estimate and measure perimeter and surface area of 2-D shapes using centimetre and metre CONT'D
    • Calculate surface area of given shapes in centimetres and metres
    • Give learners compound 2D shapes that can be spilt to many rectangles with given dimensions to find the surface area by adding areas of the various rectangles of Ideas; Collaborative Learning
  • Demonstrate an understanding of volume of common 3D shapes
    • Select and justify referents for cm3 or m3 units
    • Show learners an object which is a cubic centimetre (or 1 cm3) and another object which is a cubic metre (or 1 m3)
    • Let learners explore the classroom and compound to find that can be used as referents for the cubic centimetre (1cm3) and cubic metre (1m3). Example of 1m3is polytank; and 1cm3is cube sugar
    • Ask learners identify containers in the classroom and compound that can be measured using cubic centimetre (cm3) and cubic metre (m3)
    • Ask learners to explore and state the relationship between 1cm3 and 1m3; that is, a cubic is the volume of a cube with measurements of Ideas; Collaborative Learning
  • Demonstrate an understanding of volume of common 3D shapes CONT'D
    • Determine the volume of boxes by finding how many cubes of sizes 1cm3 each contains
    • Ask learners to determine the volume of different sizes of boxes by investigating how many cubes of sizes 1cm3 can fill the containers. i.e. for box A, the base can take 2 by 7 1cm3, and to fill it this arrangement will done 3 times, hence Volume of A is base area height =
    • Ask learners to determine the volume of the boxes B C, D and E
    • Guide learners to deduce the rule for volume of a box, and use is to calculate volumes of given boxes F, G and H. That is, if the base area is and the height is, then the. Volume of box is given by of Ideas; Collaborative Learning
  • Demonstrate an understanding of volume of common 3D shapes. CONT'D B5.3.2.2.3Determine different sizes of boxes that have the same volume
    • Given 12 centimetre cubes, ask learners to find the different dimensions of boxes that can take the cubes. For 12 cubes the boxes can be of drawings
    • Ask learners to investigate with 20, 24, 30 and 48 centimetre cubes and draw all possible boxes of Ideas; Collaborative learning
    • Demonstrate an understanding of capacity by describing the relationship between capacity and volume as well as litre and 10cm3 to fill one with water and empty it into the other; and ask them to explore and state the relationship between 1cm3 and 1m3i.e. [see B5.3.2.2.1 i.e. 1000litres is 1m3] Note: the volume is the actual amount of something which covers a definite space. Capacity is the potential amount of a substance which an object is able to hold (units are litres and millilitres, gallons, etc)
Strand 3: GEOMETRY AND MEASUREMENT — Measurement - Angles
  • Demonstrate an understanding of angles
    • Identify examples of angles in the environment that are equal to, less than or larger than, a right angle
    • Review the definition of angles: angles as the region formed in a plane when two lines meet or cross, they form an Angle. And ask learners to identified angles in the classroom and compound. E.g. opening laptop, door, window, pair of scissors, pavement floor, etc
    • Guide learners to see right angles and fold right angles from paper. Ask learners to identify examples of angles in the classroom and compound that are equal to, less than or larger than, a right angle of Ideas; Collaborative Learning; Attention to Precision; Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Demonstrate an understanding of angles CONT'D
    • Measure given angles with a protractor and classify them according to their measured sizes right, acute, obtuse and reflex
    • Review with learners how to use the protractor to measure angles
    • Give learners photocopied worksheets with protractor in position measuring angles; ask them to read the angles or place their protractors on it and read it
    • Give learners photocopied worksheets with several angles to measure and sort into those which are right, acute obtuse angles
    • Ask learners to draw various angles such as 30o 45o,60o, 75o, 90o, 120o, 150o,270o, etc. of Ideas; Collaborative Learning; Attention to Precision; Look for Patterns and Relationships
Strand 3: GEOMETRY AND MEASUREMENT — Geometric Reasoning
  • Describe the position of objects in space using the cardinal points B5.3.4.1.1Tell the position and motion of objects in space using the cardinal points north, south east and west
    • Pupils describe the position and motion of objects from one point to another using the 4 main cardinal points: e.g. The point P is to the west of point T but to the north of the A
    • Pupils describe the position of places in a grid from a given location. E.g. from Kofi's house - the school is East of Kofi's house; the hospital is North of Kofi's house
    • Ask learners to give directions from Kofi's house the various locations. E.g. Move 2 squares to the east and 2 squares to the north to get to the church of Ideas; Collaborative Learning; Attention to Precision; Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Perform a single transformation (i.e. reflection) on a 2D shape
    • Identify images of a single transformation (i.e. reflection) of a 2D shapes in a plane
    • Ask learners to identify images of reflections of given 2D shapes in a given plane. Ask learners to study the shapes and the mirror line and state which are objects and their images in the given four mirror lines. Shape E is the image of Shape B in mirror line 2 or the line = 0; shape A is a reflection of shape E in the line =. of Ideas; Collaborative learning; Attention to Precision; Look for Patterns and Relationships
Strand 4: Data — Data Collection, Organisation, Presentation, Interpretation and Analysis
  • Differentiate between first-hand and second hand data B5.4.1.1.1Explain the difference between first-hand and second-hand data
    • Explain first-hand data as data that you collect on your own; and second-hand data is data that has been collected and organized by somebody else
    • Mrs. Acquaye's class studied the weather. The learners measured the rainfall for 5 days (Monday to Friday). For her class these results are first-hand data. But for another class these results are second-hand data
    • Find examples of second-hand data in print and electronic media, such as newspapers, magazines, and the internet
    • Look for examples of second-hand data in the newspaper or website; You can find data on league table, price list, sales, rainfall, etc
    • Ask learners to study the second-hand data on the league table and write questions for their friends to read and interpret the data. E.g. Which team has not lost in a match? Which team has won only one match? of Ideas; Collaborative Learning
  • Differentiate between first-hand and second hand data. CONT'D
    • Ask learners to study the second-hand data on suggested number of 30 minutes periods that Ghanaian primary school children learn certain subjects every week. Ask them to write questions for their friends to read and interpret the data. of Ideas; Collaborative Learning
  • Construct and interpret double bar graphs to draw conclusions
    • Draw double bar graphs, complete with title, labelled axes, key or legend, to represent data collected (up to 3 pairs of categories of data and use it to solve problems
    • Give students data presented in a table on rainfall in mm for two towns to draw a double bar graph complete with title, labelled axes, key January February March April May June Kumasi 5 10 15 20 50 45 Oda 3 10 13 25 40 50 of Ideas; Collaborative Learning Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Construct and interpret double bar graphs to draw conclusions CONT'D
    • Give students more paired data presented in a tables. Ask them to study the paired data in the tables and ask them questions based on them. Also ask them to write questions for their friends to read and interpret the data. For instance some questions can be (i) In which subject was Fusena's worse performance? (ii) How many pupils are in the upper primary classes in Presby? (iii) When was the best day for Senasco shop?
    • Ask learners to draw double bar graphs complete with title, labelled axes, key for the paired data presented in the tables on (i) percentage test scores of 2 students; (ii) enrolment in 2 schools in a town; sales of two of bread in two shops in a week; etc. of Ideas; Collaborative Learning Look for Patterns and Relationships STANDARDS INDICATORS AND
  • Construct and interpret double bar graphs to draw conclusions CONT'D
    • Identify examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines, and the internet
    • Provide opportunities for learners to access, read and interpret examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines and the internet of Ideas; Collaborative Learning
Strand 4: Data — Chance (Probability)
  • Describe the likelihood of a single outcome occurring using words such as impossible possible, and certain
    • Classify the likelihood of a single outcome occurring in a probability experiment as impossible, possible, or certain
    • In a Ludo competition with a die, the event of "obtaining the number 1" is possible; the event of "obtaining the number 7" is impossible; the event of "obtaining the number 1 or 2 or 3 or 4 or 5 or 6" is certain
    • Design and conduct an experiment in which the likelihood of a single outcome occurring is impossible, possible (likely or unlikely), certain
    • In a bag containing 10 red, 4 green and 1 pink bottle tops, let a learner pick one bottle top from the bag. 1. Picking a black bottle top is impossible 2. Picking a red bottle top is possible (likely) 3. Picking a pink bottle top is possible (unlikely) 4. Picking a red or green or pink bottle top is certain. Explain each of the four outcomes
    • Conduct a given probability experiment a number of times, recording the outcomes, and explaining the results
    • Ask 5 learners of their expectations/predictions about the outcome of tossing a coin three times Teacher tosses a coin three times and records the outcome. (e.g. head, head, tail) Does the outcome match their expectation? Either way the teacher should explain. In pairs, learners should repeat the experiment several times, record the outcomes and compare the number of heads turning up of Ideas; Collaborative Learning

Basic 6

11 topics
Strand 1: Number — Counting, Representation, Cardinality & Ordinality
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1,000, 000,000 or 1 billion
    • Model number quantities up to 1,000,000 using graph sheets and multi-base block
    • Ask pupils to model number quantities up to 1000,000 using graph sheets or multi-base materials For instance, with multi-base block, a cube = 1000 unit; a rod = 10,000; a flat = 100,000 and a block = 1,000,000; learners model 436,000 with the appropriate materials
    • Ask pupils to model the number 137,000 shading graph sheet square as shown below of Ideas; Collaborative learning
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1,000, 000,000 or 1 billion CONT'D
    • Read and write numbers in figures and in words up to 1,000,000,000
    • Play the place value number wheel game: Use the million number wheel to generate 7-digit numbers and represent the number generated on a place value frame. Throw a number of pebbles (or stones) onto the number wheel, identify the number of pebbles landing in each place value ring, and state the number generated in the wheel (i.e. 5 landed in the hundred-thousands' ring making the number twenty-thousand or 500,000). NB: The representations to use also include verbal, and numerals. Learners must match number word cards to the figures
    • Ask pupils to write given numbers on the expanded form of the number : 1,362,524,513 = 1,000,000,000 1 + 100,000,000 3 +10,000,000 6 1,000,000 2 + 100,000 5 +10,000 2 + 1,000 4 +100 5 + 10 1 + 1 3 = 1,000,000,000 + 300,000,000 + 60,000,000 + 2,000,000 + 500,000 + 20,000 + 4000 + 500 + 10 + 3 of Ideas; Collaborative learning
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1,000, 000,000 or 1 billion CONT'D
    • Identify numbers in different positions around a given number in a number chart
    • Display a number chart in multiples of 1,500 between 10,000 and 50,000 and lead learners identify numbers in different positions around a given number. Put learners in pairs and give each group a number grid and have them identify numbers in different positions around a chosen number 10,000 11,500 12,000 13,500 15,000 16,500 20,000 21,500 22,000 23,500 24,000 25,500 30,000 31,500 33,000 34,500 36,000 37,500 40,000 41,500 43,000 44,500 46,000 47,500 50,000 51,500 53,000 54,500 56,000 57,500 60,000 61,500 63,000 64,500 66,000 67,500 of Ideas; Collaborative Learning
  • Demonstrate understanding of quantities and place value for multi-digit numerals up to 1,000, 000,000 or 1 billion CONT'D
    • Compare and order whole numbers up to 100,000 and represent the comparison using ">, <, or ="
    • Learners identify numbers which are 10,000 more or 10,000 less than a given six-digit number
    • 400 is 10,000 less than133,400 Learners use words such as: "equal to" "greater than" "less than" and later use symbols such as "<", "=", ">" to compare numbers up to 10,000 taking into consideration the place value of each digit in the given number. E.g. 100200 = 100200, 2746794 > 2646796
    • Learners work together in their groups to order a given set of numbers in ascending or descending order verbally and in writing. E.g. For instance; 140230,17025,75 267389, 287368
    • Give two numbers between 10,000 and 100,000 to each group and encourage learners to say as many things as possible about the two numbers. For instance 234675 and 253874; 234675 is less than (smaller than) than 253874 or 253874 is bigger than (greater than) 234675, or 234675 is almost 20000 less than 253874 etc. of Ideas; Collaborative Learning
  • Demonstrate an understanding of quantities and place value for multi-digit numerals up to 1,000, 000,000 or 1 billion CONT'D
    • Round (off, up, down) whole numbers up to 100,000 to the nearest ten thousands thousands, hundreds and tens
    • Learners round off numbers to the nearest 100,000, 10,000 and 1000. For instance; 129,500 is approximately 130,000 and 19100 as approximately 19,000
    • Learners round up and round down to estimate sums and differences NB: To round down learners consider the smaller of the two approximated numbers, while round up considers the bigger of the two numbers. The table below may bring the meaning of these two concepts clearer 214765 Round up Round down Round off to the nearest ten 214770 214760 214970 to the nearest hundred 214800 214700 214800 to the nearest thousand 215000 214000 215000
    • Give two numbers between 10,000 and 1000,000 to each group and encourage learners to compare and say as many things as possible about the two numbers. For instance 234675 and 253874; 234675 is less than (smaller than) than 253874 or 253874 is bigger than (greater than) 234675, or 234675 is almost 20000 less than 253874 etc
    • Ask learners to work together round up and round down to estimate sums and differences of Ideas; Collaborative learning
  • Demonstrate understanding of quantities and place value for multi-digit numerals up to 1,000, 000,000 or 1 billion CONT'D
    • Skip count forwards and backwards in 5000s, 10,000s etc. up and from 1,000,000
    • Put learners into convenient groups. A learner mentions a number and another makes skip count in 5000s or 10000s to include the fifth count. For instance. Learner 1: Shout out "287940" Learner 2: 292940, 297940, 312940, 317940, etc. Learner 3; Shout out "827685" Learner 4; 817685, 807685, 797685, 787685, 777685....etc
    • 2 Skip count forwards and backwards by 5000s and between 10000 and 100000, but make an error or leave out a number. Challenge learners to identify or correct error of Ideas; Collaborative Learning
  • Demonstrate
    • Recognise Roman Numerals system up to C (i.e. 100)
    • Display roman numeral charts (1-100) arranged in sequential order and lead learners to identify the numerals. Learners identify the main characters of the roman numerals used to build the table up to 30 i.e. I, II, III, IV, V, X, L and C Call out a numeral and have learners point at it from the chart
    • Have learners match the Roman numerals to the Hindu-Arabic numerals for instance I = 1; V= 5: IX= 9, XV= 15, XXX = 30, XL = 40, LVI = 56, XCIX = 99. Mention some numerals randomly and have learners point at it on the chart. of Ideas; Collaborative Learning
  • Demonstrate
    • Count and convert Hindu Arabic numbers to Roman numerals up to 100 (C) and vice versa
    • Learners read the chart sequentially forwards and backwards, vertically (up and down), zig-zag diagonally and randomly without pointing to the numbers. Invite 2-3 learners to read to the class. Call a Roman numeral and ask learners to write
    • Give learners a numeral in the Hindu Arabic system and have learners convert to roman numeration and vice versa for instance XXIV = 24, LX = 60, XCIV = 94, CCCXXXIII = 333, etc
    • Challenge learner to find missing numbers in addition and subtraction sentences involving roman numerals. Ask learners to write similar puzzles for their friends to solve. of Ideas; Collaborative learning
  • Demonstrate understanding of factors multiples and prime numbers from 1 to 100 CONT'D
    • Determine the HCF and the LCM of two or three numbers using prime factors
    • Have learners revise the use of the factor tree method to determine prime factors of any given whole number. For example the prime factors of so 2 and 3 are the prime factors of 24. Ask learners to list the factors of two or more given whole numbers using the factor tree; for 36 and 48
    • Learners use the prime factorization by inspection to determine the HCF by underlining the common factors in each product
    • Learners use the prime factorization by inspection to determine the LCM and underlining the largest number of factors in each product
    • Learners place factors in a Venn diagrams to find the HCF and LCM of 36 and 48. i.e. the HCF is product =144 of Ideas; Collaborative Learning
  • Demonstrate understanding of factors multiples and prime numbers from 1 to 100 CONT'D
    • Learners use the prime factorisation to determine the LCM and HCF of three numbers using table and dividing through by prime factors. Example 1, find the LCM and HCF these sets of numbers: 18, 24 and 30. Using prime factorization table (see method in of Ideas; Collaborative Learning
Strand 1: Number — Number Operations
  • Describe and
    • Apply mental mathematics strategies and number properties, such as skip counting from a known fact, using doubling or halving, using patterns in the 9s and 11s facts, using repeated doubling or halving, to determine answers for basic multiplication facts to 81 and related division facts
    • Describe the mental Mathematics strategies used to determine a given basic fact, such as skip count up by one or two groups from a known fact (e.g., if 5 7 = 35, then 6 7 is equal to 35 + 7 and 7 7 is equal to 35 + 7 + 7) skip count down by one or two groups from a known fact (e.g., if 8 8 = 64, then 7 8 is equal to 64 8 and 6 8 is equal to 64 8 8) doubling (e.g., for 8 3 think 4 3 = 12, and 8 3 = 12 + 12) patterns when multiplying by 9 (e.g., for 9 6, think 10 6 = 60, and 60 6 = 54; for 7 9, think 7 10 = 70, and 70 7 = 63) repeated doubling (e.g., if 2 6 is equal to 12, then 4 6 is equal to 24 and 8 6 is equal to 48) repeated halving (e.g., for 60 4, think 60 2 = 30 and 30 2 = 15) relating division to multiplication (e.g., for 64 8, think 8... = 64)
    • Recall multiplication facts to 81and related division facts of Ideas; Collaborative learning
  • Describe and
    • Apply mental mathematics strategies for multiplication, such as annexing then adding zero halving and doubling using the distributive property
    • Determine the products when one factor is a multiple of 10, 100, or 1000 by annexing zero or
    • Apply the distributive property to determine a given product involving multiplying factors that can be written in the expanded form 108. Or apply distributive property to determine a given product involving multiplying factors that are close to = 203
    • Explain the property for determining the answer when multiplying numbers by iii. one iv. zero. of Ideas; Collaborative Learning
  • Demonstrate understanding of multiplication of a 2 or 3-digit number by a 2 or 3-digit number
    • Multiply multi digit numbers by 2 or 3-digit numbers efficiently
    • Multiplication of whole numbers using the "expand and box" method (partial decomposition method). Lead learners to multiply a 3-digit number by a 1-digit number as shown below, for example 448 2 =? 400 40 8 2 800 80 16 448 2 = (400 2) + (40 2) + (8 2) = 800 + 80 + 16 = 800 + 80 + (10 + 6) = 800 + 90 + 6 = 896
    • Multiplication of whole numbers using the Column or vertical
    • Multiplication of whole numbers using the Distributive property
    • Multiplication of whole numbers using the lattice method. Have learners draw a 2 by 3 lattice for solving 345 27; and 3 by 3 and 3 by 3 lattice for solving 382 856. of Ideas; Collaborative Learning
  • Manipulate numbers using basic division fact up to 144
    • Determine basic division fact up to 81
    • Investigate numbers that are multiples of 6, 8, 9 and 11. How do you know a number is divisible by 6, 8, 9 and 11? (This is also known as the divisibility test)
    • Draw a 6 by 6 multiplication chart and use it as a game board to play the 3-in-a-line game with a pair of dice or playing cards. Players take turns in throwing a one dice and mark (or cover) a number that can be divided by the results (i.e. a quotient). The winner is the one who obtains three numbers in a line. of Ideas; Collaborative learning
  • Demonstrate understanding of division of a 2 or 3-digit number by a 1 or 2-digit number
    • Divide 3-digit numbers by 1-digit number efficiently
    • Division as repeated subtraction (using the long division method). Explain division as a way of repeatedly subtracting a divisor number from a given dividend until there is none left and then determining the number of times the divisor is taken from the dividend. of Ideas; Collaborative Learning
  • Translate word problems into mathematical sentences and solve
    • Solve multi step word problems involving the four basic operations
    • Learners model mathematical statements from a given word problem involving addition and multiplication and solve using the strategies learnt
    • Learners model mathematical statements from a given word problem involving division and subtraction and solve using the strategies learnt
    • Learners role play a given word problem involving addition and multiplication and solve
    • Learners role play a given word problem involving subtraction and division and solve
    • Learners model mathematical statements from a given word problem involving division and multiplication and solve using the strategies learnt. The relationship between operations and the use of calculator and spreadsheet to assess the reasonableness of answers should be stressed. of Ideas; Collaborative Learning
  • Demonstrate an understanding of integers
    • Locate, compare and order sets of integers using the number line and symbols "< or >"
    • Use number line to help learners to identify integers as opposites of whole numbers by answering the following questions: i. Which integer is at the point marked B1? ii. Which integer is larger than B1 and which is smaller? iii. How many steps away from B is B1? of Ideas; Collaborative Learning
  • Demonstrate understanding of integers CONT'D
    • Solve simple addition and subtraction problems involving integers (excluding subtraction of negative numbers)
    • Use number line to help learners to do the following types (addition) (1) 9 + -4 = _____ (2) -8 + 4 = _____ (3) -3 + -5 = _____ (4) 1 + -3 = _____ (5) -6 + 5 = _____ (6) 6 + -2 = _____ (7) -6 + 8 = _____ (8) -2 + 9 = ______
    • Learners do the following types (subtraction) (9) -5 1 = ___ (10) -2 1 = ___ (11) 8 7) = ___ (12) 2 6) = _____ (13) -1 7 = ___ (14) -5 7) = ___ (15) -8 8 = ___ (16) 4 6 = ____
    • Solve word problems; e.g. (i) Some number added to 5 is equal to -11. Find the number. (ii) Ben and Cam are diving. Ben is 15.8 meters below the surface of the water. Cam is 4.2 meters above Ben. What is Cam's position relative to the surface of the water? of Ideas; Collaborative learning
  • Demonstrate an understanding of integers CONT'D
    • Perform simple multiplication with integers
    • Use number line to help learners to multiply integers; learners should always start from zero and skip/hop to the left or write on the number line. For instance, to multiply 3 by (-2), have learners start from zero and hop to the left 3times in an interval of 2. of Ideas; Collaborative Learning
Strand 1: Number — Fractions
  • Demonstrate an understanding of strategies for comparing adding, subtracting multiplying and dividing common, decimal and percent fractions
    • Compare and order a mixture of fractions: common, percent and decimal fractions (up to thousandths)
    • To compare and order a mixture of common, decimal and percent fractions, express them in one form (i.e. either common, decimal or percent); e.g. to order 0.758, 5 and 73%; we have 5 = 625 1000 = 62.5%, 0.758 758 1000 = 75.8%, and 73% 73 = 0.73, Hence the order from least to the largest is 5, 73% and 0.758
    • To compare and order a mixture of common, decimal and percent fractions you can locate the fractions on the number and order them of Ideas; Collaborative Learning
  • Demonstrate understanding of strategies for comparing, adding subtracting multiplying and dividing common decimal and percent fractions. CONT'D
    • Add and subtract unlike and mixed fractions
    • To add like mixed fractions that are larger than 1, i.e. 2 1/3 and 32/3 we write down the sum of the whole numbers and add the fractions; i.e. 2 1/3 + 32/3 = 5 + 1/3 + 2/3, = 5 (1+2)/3 = 53/3= 6
    • To subtract like-fractions that are larger than 1, i.e. 2 1/3 and 32/3, we change the mixed fractions into improper fractions and subtract; i.e. 32/3 - 2 1/3 + = 11/3- 7/3 + = (11-7)/3 = 4/3. = 1 1/3
    • To add or subtract improper fractions with different denominators, (2 1/3 and 32/5 ) we need find the Lowest Common Denominator (LCD) and use this to express the equivalent fractions. The LCD is 15 and the equivalent fractions are 2 5/15 and 3 6/15; their sum is 2 1/3 + 32/5 =2 5/15+ 3 6/15 = 5 (5+6)/15 which is 5 11/15; and difference 32/5 -2 1/3 = 1 (6- 5)/15 = 1 1/15 of Ideas; Collaborative Learning
  • Demonstrate understanding of strategies for comparing, adding subtracting multiplying and dividing common decimal and percent fractions. CONT'D
    • Use models to explain the result of multiplying a fraction by whole number, a whole number by a fraction and a fraction by fraction
    • To multiply a whole number by a mixed fraction (e.g. 3 2 2/3) one can multiply the whole number by the whole number and then whole number by the fraction and add the products or change the mixed fraction to improper fraction and multiply; 3 2 2/3 = 2 2/3+2 2/3+2 2/3 = 6 (2+2+2)/3 = 66/3 = 8
    • To multiply a fraction by a whole number the multiplication is interpreted as "of"; e.g
    • To multiply a fraction (i.e. common or mixed) by a whole number (e.g. 4 2/5 5 ) first change all into common fractions, then multiply the numerators separately and multiply the = 24. [Note, the product can be simplified before multiplying the numerators separately and multiplying the denominators separately]. of Ideas; Collaborative Learning
Strand 1: Number — Ratios and Proportion
  • Demonstrate understanding of the concept of ratios and its relationship to fractions and to the multiplication and division of whole numbers
    • Use concrete models and pictorial representations to explain a ratio as a concept that shows the number of times one quantity can be obtained in another and write this symbolically and in its simplest form
    • Use concrete objects and/or pictorial representations to explain ratio as a number which tells the number of times a quantity can be obtained in another. In the figures, the area of the shape A is 1 of the area of the shape B; so they are in the ratio 1:4. Shape C is three times the size of A so the ratio of C to A is 3:1
    • Use concrete objects and/or pictorial representations to explain simplest form of a ratio. Shape C is made up of 6 squares and shape A is made up of 2 squares, the areas of the shapes C and A are in the ratio 6:2; and since C is three times A, the ratio 3:1 is the simplest form of 6:2. The simplest form of a ratio is obtained by dividing through by the highest common factor. The ratio of C to B is 6:8 and its simplest form is 3:4. E.g. Simplify (i) 10m : 1000km (ii) Write 4 : 12 in the form 1 : n (iii) Express 15 : 20 in the form n : 1
    • Solve simple problems that involve ratios and finding total ratios. E.g. (i) Out of 24 students in a class, 10 are girls. Find its simplest form the ratio of boys to girls. (ii) A boy's mass is 50kgs, and his sister's is 45kg. Find the ratio of their masses. (iii) If an orange drink is made from concentrate and water in the ratio 3:8, what fraction of the mixture is concentrate? of Ideas; Collaborative Learning
  • Demonstrate
    • Express ratios in equivalent forms, compare and order ratios
    • Use the concept of ratio as a fraction to find equivalent ratios that can be easily compared. The ratio 2:3 can be expressed as 2/3; to determine which ratio is larger/largest change to equivalent ratios with same denominator and compare or order. E.g. Afia, Bedu and Caro each mix orange squash (S) and water (W) in the ratio 3:14, 2:7 and 1:4 respectively. Whose drink tastes strongest of squash? To determine the one Whose drink tastes strongest of squash we need to have the same unit of water, hence Bedu's
    • Solve simple problems that involve simplifying, comparing, finding missing and total ratios. E.g. (i) Given that 10: q = 2 : 3, find q. (ii) The ratio of boys to girls in a class room is 7 to 11. If there are a total of 49 boys in the classroom, then how many boys and girls are there altogether?
    • Solve simple problems that involve ratios and finding total ratios. E.g. (i) Out of 24 students in a class, 10 are girls. Find its simplest form the ratio of boys to girls. (ii) A boy's mass is 50kgs, and his sister's is 45kg. Find the ratio of their masses. (iii) If an orange drink is made from concentrate and water in the ratio 3:8, what fraction of the mixture is concentrate? of Ideas; Collaborative Learning
  • Understand the concept of proportion and its relationship to ratios and rates. Use proportional reasoning and rates to solve real world and mathematical problems
    • Use models to explain proportion as a comparison between quantities with equal ratios
    • Use mapping diagram to explain the concept of proportion as equal fractions or equivalent ratios. The mapping diagram shows that the ratio of number of goats to number of legs are equal, hence the number of goats is proportional to the number of legs. The proportion can be written as equal fractions or ratios, i.e. 3/12 = 4/16 or 3:12 = 4:16
    • Give learners mappings to identify those that are proportional and those that are not
    • Work out proportion in given contexts and use them in solving problems; e.g. 200 bottles of equal capacity hold 350 litres of water. How much water does each bottle hold? of Ideas; Collaborative Learning
  • Understand the concept of proportion and its relationship to ratios and rates. Use proportional reasoning and rates to solve real world and mathematical problems. CONT'D
    • Use various strategies to solve proportional reasoning problems involving rates and scales
    • Use diagrams to explain the concept of rate a ratio that compares two different quantities measured in different units; e.g. the ratio cost : weight = 8:2 = 4:1. This ratio is the unit ratio and show the rate for selling a unit or 1kg of the meat
    • Work out rates and use them in solving problems. E.g. A litre of sachet water costs 40p. Find the cost of (i) 1 litre (ii) 7 litres (iii) 9 litres
    • Use diagrams to explain the concept of scale as a ratio that compares two different sizes an object and its model; e.g. plan of a house or room. [Here is the plan of a bedroom. The scale is 1:100, which means that 1cm in the drawing represents 100 cm in the actual room. What is the actual length of (i) the room if it measures 41 cm; (ii) the bed if it measures 1.8cm?]
    • Work out scales and use them in solving problems; e.g. If 10cm on a map stands for 10km, what distances on the map stands for (i) 1km (ii) 7km (iii) 41km? of Ideas; Collaborative learning
Strand 2: Algebra — Pattern and Relationships
  • Represent a given pattern visually to verify predictions
    • Represent a given pattern visually to verify predictions
    • Ask learners to examine the pattern made with match sticks below
    • Ask learners to examine the pattern in the table below which shows the number of match sticks used in making a pattern of squares. Ask learners to use match sticks to make the patterns of triangles and complete the table. Guide learners to describe the relationship Pattern Number 1 2 3 4 5 6 7 8 9 Match sticks in the perimeter 3 6 Match sticks enclosed in the pattern 0 3 Thinking; Justification of Ideas
  • Determine the pattern rule to make predictions about subsequent elements. CONT'D PRACTICES AND
    • Ask learners to write questions based on number or geometric patterns for their friends to find answers to; e.g. how many match sticks will be used for the 9th pattern of triangles? How many match sticks will be used for the 8th pattern of squares? Number of triangles 1 2 3 4 5 6 7 8 9 Match sticks 7 12 of Ideas; Collaborative Learning
  • Determine the pattern rule to make predictions about subsequent elements. CONT'D
    • Write a rule in words and in algebra to represent a given pattern
    • Ask learners to state the rules in words and in algebra to represent a given linear patterns Term/Input 1 2 3 4 5 Rule for n in words Rule for n in Algebra Result/Output A 9 18 27 9 times n 9n Result/Output B 0 4 8 12 4 times 1 less than n 4(n-1) Result/Output C 4 7 10 1 more than 3 times n 1 +3n Result/Output D 20 18 16 20 minus 2 times 1 less than n 20-2(n-1) Result/Output E 15 19 23 Result/Output F 12 17 22 100 85 70
    • Describe the relationship in a given table or chart, using a mathematical expression
    • This table shows the pattern of cost of boxed lunches for students on a look at pictures or a short video (or look outside from a window with a grown-up) to. Ask learners to: (i) explain the pattern of how the cost of lunches changes as more students go on the trip; (ii) use the pattern to determine how many students went on the trip if the cost of lunches is GHC90. Number of students 1 2 3 4 5 ? Cost of lunch in Cedis 3 6 9 12 15 90
    • Ask learners to write questions based on the pattern for their friends to find answers Precision
Strand 2: Algebra — Algebraic Expressions
  • Demonstrate understanding of algebraic expressions
    • Write algebraic expressions for word problems: 1) Sum of 8 and s 2) Take away 4 from m 3) 9 times the sum of 8 and q 4) Subtract 4 from 7 times g 5) One-sixth of n is added to the product of 9 and y 6) Three-fourths of the sum of c and 2 7) 8 divided by r 8) 8 times the sum of c and 7
    • Write algebraic expressions for the perimeter of the following shapes: Precision
  • Demonstrate understanding of algebraic expressions CONT'D
    • Write algebraic expressions for the area of the following shapes:
    • Simplify basic algebraic expressions by grouping like terms. E.g 1) 5 + 4 z 1 + 2 z 2) 10s 1 + 3 5 s
    • Substitute a value for an unknown into an expression and correctly calculate the answer. E.g. Find the values of these algebraic expressions using the values given in the following: 1) z + 7d use z = 7 and d = 4 2) 8k + d use k = 2 and d = 3 3) 7(5f - 3n) - 8 use n = 3 and f = 7 4) 7d - 2f + 9 use d = 2 and f = 5 5) -5f + 8b + 4 - 9 use f = 9 and b = 3 6) -6(2x - 7h) use h = 2 and x = 4 (i) (ii) If Sena used 13 match sticks in making next pattern squares, (i) write a mathematical sentence that represents the matchsticks. (ii) how may match sticks will she need to make the pattern with 10 squares? how may squares did she make if she used 64 match sticks? Precision
Strand 2: Algebra — Variables and Equations
  • Solve problems involving single-variable, one-step equations with whole number coefficients CONT'D
    • Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially or symbolically
    • Learners find the value of x in equations 8. 4 + = 11 9. - 3 = 10 10. 4 = 12 11. 24 = 3 12. = 5
    • Create a problem for a given equation
    • Ask students to describe two different stories that the equation 4 - x = 9 could represent
    • Ask learners to solve puzzle in the figure, by solving the equations in each line of Ideas; Collaborative Learning
Strand 3: Geometry and Measurement
  • Demonstrate understanding of prisms
    • Identify examples of rectangular and triangular prisms in the classroom and the community
    • Give learners models of 3-D shapes made from cardboard to examine and describe their cross sections (i.e. the surface or shape exposed by making a straight cut through something, especially at right angles to an axis). Ask learners to draw and complete the table for the description of the cross sections of the 3-D objects
    • Ask learners to sort 3-D shapes with uniform cross sections; these are prisms and they are named after their uniform cross sections. Ask them to identify and name the following prisms of Ideas; Collaborative Learning
  • Demonstrate an understanding of prisms CONT'D
    • Construct rectangular and triangular prisms from their nets
    • Give the learners rectangular and triangular prisms made from cardboard by yourself (or cardboard packing cases from shops) to open and examine their nets
    • Give the learners some cardboard or manila card to draw a net of a square prism whose cross section is a square with sides 10cm by 10cm and height 10cm. After drawing add tabs so that it can be folded so that the tabs are glued inside
    • Give the learners some cardboard or manila card to draw a net of a rectangular prism whose cross section is a square with sides 10cm by 10cm and height 15cm. After drawing add tabs so that it can be folded so that the tabs are glued inside
    • Give the learners some cardboard or manila card to draw a net of a triangular prism whose cross section is an equilateral triangle with side 10cm and height 10 cm. After drawing add tabs so that it can be folded so that the tabs are glued inside of Ideas; Collaborative Learning
Strand 3: Geometry and Measurement — Geometric Reasoning
  • Describe the position of objects in space using the cardinal points
    • Tell the position and motion of objects in space using the cardinal points north east, north-west, south-east and south-west
    • Pupils describe the position and motion of objects from one point to another using the 4 main cardinal points and the half-betweens: e.g. The point P is north of the point P X but north-west of point C. Y is south of T but south-west of C
    • Pupils describe the position of places in a grid from a given location. E.g. the church is north-east from Kofi's house; the hospital is north-west from Kofi's house
    • Ask learners to give directions from Kofi's house the various locations. E.g. Move 2 squares to the east and 2 squares to the north to get to the church. of Ideas; Collaborative Learning
  • Perform a single transformation (i.e reflection translation) on a 2D shape
    • Perform and identify images of a single transformation (i.e. reflection) on 2D shapes in a plane
    • Give learners photocopied worksheets with several incomplete 2D shapes to review the drawing of images of objects when reflected in the line of symmetry which is outside the object
    • Review the properties of images under reflection, i.e. object and image sizes and shape, distances from mirror line and shape
    • Use a grid or graph board to demonstrate the `horizontal followed by vertical' movements called translation. E.g. In the figure is `the movement which takes each point four units horizontally to the right and one unit vertically down' or 4 right, one down', is a vector or translation vector (2, 1) and written as (
    • 1 ). Q is the image of P under the translation by the vector (
    • 1 ) of Ideas; Collaborative Learning
  • Perform a single transformation (i.e reflection translation) on a 2D shape. CONT'D
    • Discuss the properties of images under translations, i.e. object and image sizes and shape
    • Give learners photocopied worksheets with several 2D shapes and ask them to draw images of each under the translation vector given Note: Diagram is on the next page of Ideas; Collaborative Learning
  • Perform a single transformation (i.e reflection translation) on a 2D shape CONT'D
    • Identify images of a single transformation (i.e. reflection and translation) of a 2D shapes in a plane
    • Ask learners to identify images of reflections of 2D shapes in the figure. Ask learners to study the shapes, identify their images. E.g. shape D is a reflection of shape E in the line y = 0 or x-axis; shape A is a reflection of shape B in the line = -1; and Shape X is a reflection of shape W in the line = 0
    • Ask learners to identify images of translations of given 2D shapes in a given plane. Ask learners to study the shapes, identify their images and the translation vectors. E.g. shape F is a translation of shape A by the translation vector (
    • 3 ) (or 2 right, 3 three down); and Shape X is a translation of shape W by the translation vector ( ) (or 0 right, 6 up) of Ideas; Collaborative Learning
Strand 4: Data — Data Collection, Organization, Presentation, Interpretation and Analysis
  • Create, label, and interpret line graphs to draw conclusions CONT'D
    • Draw a line graph by determining the common attributes (title, axes and intervals) and draw the graph for a given table of values
    • Give learners the data presented in tables and ask them to determine the common attributes (title axes and intervals) and draw a line graph. Let them understand line graphs are used when we want to show how something changes over time in relation to something else
    • Ask learners to draw a line graph by determining the common attributes (title, axes and intervals) and completing the drawing with title and labelled axes for the data below on how temperature of water increases with time when it is heated
    • Ask learners to study the line graph and answer questions based on them. For instance, after what time will the water temperature reach 70oC? What is the water temperature after 5 minutes? Time (minutes) 0 1 2 3 4 5 6 7 8 9 10 11 Temperature (oC) 15 25 35 45 53 60 70 75 80 85 90 95 Thinking; Justification of Ideas; Precision PRACTICES AND
  • Create, label, and interpret line graphs to draw conclusions CONT'D
    • Determine whether a given set of data can be represented by a line graph (continuous data) or a series of points (discrete data) and explain why
    • Through discussion, guide learners to understand the difference between discrete and continuous data. Ask them to sort the following tables of values into the two categories those with discrete data and those with continuous data [Discrete data take particular values, while continuous data are not restricted to separate values. Discrete data can take on only integer values whereas continuous data can take on any value. For instance the number of malaria patients treated by a hospital each year is discrete but your weight recorded of over a year is continuous] (i) The number of match sticks Sena used in making a pattern of squares Number of Squares (n) 1 2 3 4 5 6 7 8 Matchsticks (s) 4 7 10 13 16 19 22 25 (ii) Progress of plant's growth recorded by Kofi over a week Days (d) 1 2 3 4 5 6 7 8 Height (h) (cm) 5 6.5 8 9.5 11 12.5 14 15.5 (iii) Number of people in the immediate family of P6 students in a school Number of people in family 1 2 3 4 5 6 7 8 9 Number of students 0 4 9 11 6 5 3 3 1 (iv) Abu travelled on a bicycle to buy food, the table shows how far (in kilometres) he was away from the house. Time (minutes) 0 5 10 15 20 25 30 Distance (km) 0 3 3.5 4 4 2 0
    • Ask learners to write questions for their friends to read and interpret the tables Thinking; Justification of Ideas; Development and Leadership PRACTICES AND
  • Create, label, and interpret line graphs to draw conclusions CONT'D
    • Apply understanding of how to create a line graph by using a given table of values (or set of data) to draw a line graph and answer questions based on them to interpret and draw conclusions
    • Ask learners to draw more line graphs for given data values by determining the common attributes (title, axes and intervals) and pose, as well as answer, questions based on them to interpret the line graphs to draw conclusions (i) Progress of plant's growth recorded by Kofi over a week Days (d) 1 2 3 4 5 6 7 8 Height (h) (cm) 5 6.5 8 9.5 11 12.5 14 15.5 (ii) Cost of boxed lunches for students on a look at pictures or a short video (or look outside from a window with a grown-up) to. Number of students 1 2 3 4 5 6 7 8 Cost of lunch () 3 6 9 12 15 18 21 24 (iii) Abu travelled on a bicycle to buy food, the table shows how far (in kilometers) he was away from the house. Time (minutes) 0 5 10 15 20 25 30 Distance (km) 0 3 3.5 4 4 2 0 (iv) Average monthly rainfall in mm recorded for two towns in a year
    • Ask learners to write questions for their friends to read and interpret the line graphs J F M A M J J A S O N D Kumasi 5 10 15 20 50 45 55 35 40 50 35 10 Oda 3 10 13 25 40 50 60 50 40 45 35 8 and Leadership Attention to Precision PRACTICES AND
  • Select, justify, and use appropriate methods of collecting data, including questionnaires, interview databases, electronic media, etc
    • Select a method for collecting data to answer a given question and justify the choice
    • Lead learners (in small groups) to discuss and write down how they would make decisions in the following situations, what facts they would take into account and how they would collect these `facts'. (a) The type of drinks to buy for a class party (b) The make of sport shoes to buy for all P6 students (c) The make of school bag to buy for all P6 students (d) The number of desks in each classroom (e) How much money P6 students spend on bus fare to school every month? (f) To buy drinks for people in the immediate family of all P6 students at a party. (g) Buy a mobile phone from an online shop
    • Lead a discussion on the methods of data collection below and ask them to identify which method they will use to gather the facts for each situation (i.e. in E.g. 1. above) questionnaires interview experiments databases electronic media or internet of Ideas; Collaborative Learning
  • Design and administer a questionnaire for collecting data to answer a given question
    • Guide learners (in small groups) to do surveys; as surveys are useful ways of getting them to interact, produce question forms and collect real information. Ask them to use Question Form below for collecting the class data Class Survey Question Form 1) Hello, What is your name? _________________ 2) How old are you? _________________ 3) What is your favourite school subject? _________________ 4) What is your worst subject? _________________ 5) What is the most important school subject? _________________ 6) The size of your shoe? _________________ 7) What is your favourite drink? _________________ 8) How much do you spend on bus fare to school every day? _________________ Precision PRACTICES AND
  • Select, justify, and use appropriate methods of collecting data, including questionnaires, interviews experiments, databases electronic media, etc CONT'D
    • Guide learners in each group to use a table (like the one below) to organize the data obtained with the question form Name Age Favourite subject Worst subject Important subject Shoe size Favourite mineral Daily bus fare (cedis) Kojo 12 English Maths English 6 Coke 2 Aku 11 Science P.E. English 6 Coke 1 Ami 11 Maths Art Maths 6 Fanta 3 Abu 13 Maths Art Maths 7 Sprite 1 Ama 12 Science Art Maths 7 Fanta 2 Paapa 11 Maths P.E. Science 6 Fanta 1 Precision PRACTICES AND
  • Select, justify, and use appropriate methods of collecting data, including questionnaires, interview databases, electronic media etc. CONT'D
    • Design and administer a questionnaire for collecting data to answer given question(s), record the data, analyse and graph the results to solve problems
    • Guide learners (in each small group) to use tallies and count the results obtained in the organized data table (see P6.5.2.2.3 above) to do a frequency table for each question
    • Ask learners to study the results in the frequency tables to draw bar or line graphs and write their conclusion
    • Ask learners to identify questions for a survey, do a question form and collect real data organize the data obtained into frequency tables and graph it using bar or line graphs and the results to solve problems. They may do surveys on the following situations or issues: (a) The type of drinks to buy for a class party. (b) The make of sport shoes to buy for all P6 students. (c) The make of school bag to buy for all P6 students. Thinking; Justification of Ideas; Development and Leadership
Strand 4: Data — Chance or Probability
  • Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment determining the theoretical and experimental probability of outcomes in a probability exper
    • List the possible outcomes of a probability experiment, such as tossing a coin, rolling a die with a given number of sides, spinning a spinner with a given number of sectors and determine the theoretical probability of an outcome occurring for a given probability experiment
    • Through discussion guide learners to understand that theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. The both probabilities are calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes
    • Guide learners (in each small group) to carry out the following experiments 100 times use tallies to record their results, and transfer it to frequency tables: (i) tossing a coin 100 times; (ii) throwing a dice 100 times Thinking; Justification of Ideas; Development and Leadership PRACTICES AND
  • Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment, determining the theoretical and experimental probability of outcomes in a probability expe
    • Guide learners (in each small group) to use the results of the experiments above (recorded in the tables above) to work out the experimental probability and compare to the theoretical probability. E.g. the experiment probability of a head showing up out of the hundred outcomes is given by 42 =0.42; and the theatrical probability is 50 = 0.5
    • Ask learners (in each small group) use the results of the experiments above (recorded in the tables above) to work out the experimental probability and compare to the theoretical probability of the following events (i.e. second table) i. rolling a 2 ii. rolling a number greater than 4 iii. rolling a 1 or a 3
    • Put the results from all the small groups together ask the class to work out the experimental probabilities and compare to the theoretical probabilities of the events i. rolling a 2 ii. rolling a number greater than 4 iii. rolling a 1 or a 3
    • Ask the learners their observations on whether or not the experimental probability is getting closer to the theoretical probability of Ideas; Collaborative Learning
  • Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment, determining the theoretical and experimental probability of outcomes in a probability expe
    • Predict the probability of a given outcome occurring for a given probability experiment by using theoretical probability
    • Guide learners (in each small group) to carry out the following experiments 100 times, use tallies to record their results, and transfer it to frequency tables: (i) spinning a 5-sector spinner 100 times; (ii) spinning an 8-sector spinner 100 times
    • Ask learners (in each small group) to use the results of the experiments above (recorded in the tables above) to work out the experimental probability and compare to the theoretical probability of the following events with each of the spinners (i.e. table above) i. pinning a 2 ii. pinning a number greater than 4 iii. pinning a 1 or a 3 Thinking; Justification of Ideas; Development and Leadership PRACTICES AND
  • Demonstrate an understanding of probability by identifying all possible outcomes of a probability experiment, determining the theoretical and experimental probability of outcomes in a probability expe
    • Put the results from all the small groups for (a) spinning the 5-sector spinner, (b) spinning the 8-sector spinner, together. Ask the class to work out the experimental probabilities and compare to the theoretical probabilities of the events i. pinning a 2 ii. pinning a number greater than 4 iii. pinning a 1 or a 3
    • Ask learners their observations as to whether or not the experimental probability is getting closer to the theoretical probability. Ask them to explain the difference between theoretical probability and experimental probability Thinking; Justification of Ideas; Development and Leadership MATHEMATICS SUBJECT PANEL MEMBERS AND REVIEWERS NAME INSTITUTION Writing panels Prof. Eric Magnus Wilmot University of Cape Coast Dr. Prince H. Armah University of Education, Winneba Dr. Forster Ntow University of Cape Coast Prof. Douglas D. Agyei University of Cape Coast Mr. Emmanuel Acquaye Consultant, NEWAGE Strategies, Koforidua Mr. Miracule Gavor USAID Learning Numeracy Project Mr. Stephen Nukpofe Abetifi College of Education Mr. Charles B. Ampofo Kibi Presbyterian College of Education Mr. Edward Dadson Mills Methodist B Junior High School, Winneba Expert Reviewers Prof. Damian Kofi Mereku University of Education, Winneba Prof. Olivier M. Pamen African Institute of Mathematical Sciences (AIMS) Prof. S.K. Amponsah Kwame Nkrumah University of Science and Technology Curriculum Adviser Dr. Sam K. Awuku OPM (Oxford Policy Management) Supervisor
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