STRAND 4: HANDLING DATA
                                           Sub-strand 2: Chance or Probability

CONTENT STANDARDS     INDICATORS AND EXEMPLARS                            CORE COMPETENCIES

B8.4.2.1 Identify the sample  B8.4.2.1.1.Perform a probability experiment involving two independent    Critical Thinking and
space for a probability             events such as drawing coloured bottle tops from a bag with     Problem solving (CP)
experiment involving two          replacement and list the elements of the sample space
independent events and                                                                 Communication and
express the probabilities of   E.g. 1In an experiment, Emmanuel was asked to pick one bottle top from a    Collaboration (CC)
given events as fractions,       bag, three times, which contains 3 red, 2 green and 1 pink bottle tops.
decimals, percentages                                                                                  Cultural Identity and                                                              i.    List the elements of the sample space of the events.and/or ratios to solve                                                                            Global Citizenship (CG)
problems.                                            ii.   The sample space of the event of picking a red bottle top, R, with
                                   replacement is?                                               Personal Development
                                                                                   and Leadership (PL)                                                                iii.   The probability of picking a red bottle top is ………….

                                E.g. 2 Consider the following two events: (a) throwing of a fair six-sided die
                             and (b) tossing a fair coin
                                                              i.   What is the sample space for (a) and for (b)?
                                                                ii.   Does the occurrence of event (a) affect the occurrence of event (b)?
                                                                iii.   What is the probability of an even number showing up in (a)? What is
                                      the probability of a head showing up in (b)?
                                             iv.   What is the relationship between the two events?

                                E.g. 3 Ampofo and Serwa are two learners from a school. Ampofo walks to
                                  school daily and Serwa travels to school on a bus daily.
                                                              i.   Does the event of Ampofo affect that of Serwa?
                                                                ii.   Can the two events occur together?





                                                                   161

1. B7 • Model number quantities more than 1,000,000,000 using graph sheets, isometric papers and multi-base — Curriculum p. 2
2. B7 • Compare and order whole numbers more than1,000,000,000 and represent the comparison using ">, <, — Curriculum p. 3
3. B7 • Round (off, up, down) whole numbers more than 1,000,000,000 to the nearest hundred-thousand, — Curriculum p. 4
4. B7 • Round decimals to the nearest tenth, hundredth, thousandths, etc — Curriculum p. 5
5. B7 • Express decimal numerals to given significant and decimal places — Curriculum p. 6
6. B8 • Apply the understanding of place value to read and write in number quantities over 1,000,000,000 — Curriculum p. 90
7. B8 • Express integers of any size into standard form — Curriculum p. 91
8. B8 • Create and solve word or real-life problems on place values — Curriculum p. 92
9. B8 • Use the knowledge on sets and sets of factors of numbers to solve real life problems involving — Curriculum p. 93
10. B9 • Express integers to a given number of significant and decimal places — Curriculum p. 165
11. B9 • Solve problems on relationship between members of the rational number system using knowledge and — Curriculum p. 166
12. B9 • Apply the concept of sets to solve problems on relationship between members of rational number — Curriculum p. 167

1. B7 • Multiply and divide given numbers by powers of 10 including decimals and benchmark fractions — Curriculum p. 7
2. B7 • Apply mental mathematics strategies to solve word problems — Curriculum p. 8
3. B7 • Add and subtract up to four-digit numbers — Curriculum p. 9
4. B7 • Add and subtract up to four-digit numbers — Curriculum p. 10
5. B7 • Create and solve story problems involving decimals on the four basic operations — Curriculum p. 11
6. B7 • Create and solve story problems involving decimals on the four basic operations — Curriculum p. 12
7. B7 • Illustrate with examples the meaning of repeated factors using counting objects such as bottle tops — Curriculum p. 13
8. B7 • Show that the value of any natural number with zero as its exponent or index is 1 and use it to — Curriculum p. 14
9. B7 • Apply the concept of powers of numbers (product of prime) to find Highest Common Factor (HCF) — Curriculum p. 15
10. B7 • Apply the concept of powers of numbers (product of prime) to find Highest Common Factor (HCF) — Curriculum p. 16
11. B8 • Multiply and divide by power of 10 including decimals and the benchmark fractions — Curriculum p. 94
12. B8 • Add and subtract more than four-digit numbers — Curriculum p. 95
13. B8 • Multiply or divide multi-digit numbers by 2- and 3-digit numbers — Curriculum p. 96
14. B8 • Multiply or divide multi-digit numbers by 2- and 3-digit numbers — Curriculum p. 97
15. B8 • Create and solve story problems involving decimals on the four basic operations — Curriculum p. 98
16. B8 • Create and solve story problems involving decimals on the four basic operations — Curriculum p. 99
17. B8 • Identify and explain the laws of indices — Curriculum p. 100
18. B8 • Solve exponential equations — Curriculum p. 101
19. B9 • Multiply and divide given numbers by powers of 10 including decimals and benchmark fractions — Curriculum p. 168
20. B9 • Use the distributive property in solving problems — Curriculum p. 169
21. B9 • Identify simple and compound surds — Curriculum p. 170
22. B9 • Approximate the square roots of non-perfect squares with calculators/tables — Curriculum p. 171

1. B7 • Determine and recall the percentages and decimals of given benchmark fractions (i.e. tenths, — Curriculum p. 17
2. B7 • Determine and recall the percentages and decimals of given benchmark fractions (i.e. tenths, — Curriculum p. 18
3. B7 • Compare and order fractions (i.e. common, percent and decimal fractions up to thousandths) limit to — Curriculum p. 19
4. B7 • Solve problems involving addition or subtraction of fractions — Curriculum p. 20
5. B7 • Find a fraction of given quantity (i.e. money or given quantity of objects) — Curriculum p. 21
6. B7 • Explain the process of dividing a fraction (i.e. common, percent and decimal fractions up to — Curriculum p. 22
7. B7 • Determine the result of dividing a quantity (i.e. money or objects) or a fraction by a fraction — Curriculum p. 23
8. B8 • Review fractions and solve problems involving basic operations on fractions — Curriculum p. 102
9. B8 • Add and/or subtract, multiply and/or divide given fractions, by using the principle of the order of — Curriculum p. 103
10. B8 • Add and/or subtract, multiply and/or divide given fractions, by using the principle of the order of — Curriculum p. 104
11. B9 • Review fractions and solve problems involving basic operations on fractions — Curriculum p. 172
12. B9 • Add and/or subtract, multiply and/or divide given fractions, using the principle of order of — Curriculum p. 173
13. B9 • Review word problems involving basic operations on fractions — Curriculum p. 174

1. B7 • Find ratio and use ratio language to describe relationship between two quantities — Curriculum p. 24
2. B7 • Make tables of equivalent ratios (written as common fractions) relating quantities that are — Curriculum p. 25
3. B7 • Use the proportional reasoning to find missing values in the tables, and plot pairs of values on — Curriculum p. 26
4. B8 • Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when — Curriculum p. 105
5. B8 • Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when — Curriculum p. 106
6. B8 • Apply the knowledge of speed to draw and interpret travel graphs or distance-time graphs — Curriculum p. 107
7. B8 • Apply the knowledge of speed to draw and interpret travel graphs or distance-time graphs — Curriculum p. 108
8. B8 • Recognise and represent proportional relationships between quantities by deciding whether two — Curriculum p. 109
9. B8 • Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and — Curriculum p. 110
10. B8 • Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and — Curriculum p. 111
11. B9 • Represent proportional relationships by equations — Curriculum p. 175
12. B9 • Use knowledge of rates and proportional reasoning to solve problems involving SSNIT benefits and — Curriculum p. 176
13. B9 • Use knowledge of rates and proportional reasoning to solve problems involving SSNIT benefits and — Curriculum p. 177
14. B9 • Use knowledge of rates and proportional reasoning to solve problems involving SSNIT benefits and — Curriculum p. 178
15. B9 • Recognise and graph proportional relationships, interpreting the unit rate as the slope of the — Curriculum p. 179

1. B7 • Extend a given relation presented with and without symbolic materials and explain how each element — Curriculum p. 27
2. B7 • Describe the rule for a given relation using mathematical language such as one more, one less, one — Curriculum p. 28
3. B7 • Describe the rule for a given relation using mathematical language such as one more, one less, one — Curriculum p. 29
4. B7 • Identify the relation or rule in a pattern/mapping presented numerically or symbolically and — Curriculum p. 30
5. B7 • Locate points on the number plane, draw a table of values of a given relation, draw graphs for — Curriculum p. 31
6. B7 • Locate points on the number plane, draw a table of values of a given relation, draw graphs for — Curriculum p. 32
7. B7 • Locate points on the number plane, draw a table of values of a given relation, draw graphs for — Curriculum p. 33
8. B7 • Locate points on the number plane, draw a table of values of a given relation, draw graphs for — Curriculum p. 34
9. B8 • Calculate the gradient of a line and use it to write equation of a line of the form y = mx + c — Curriculum p. 112
10. B8 • Calculate the gradient of a line and use it to write equation of a line of the form y = mx + c — Curriculum p. 113
11. B8 • Calculate the gradient of a line and use it to write equation of a line of the form y = mx + c — Curriculum p. 114
12. B8 • Use graph of a linear relation to determine subsequent missing elements in the ordered pairs of the — Curriculum p. 115
13. B8 • Use graphs of linear relations to solve real life problems — Curriculum p. 116
14. B8 • Use graphs of linear relations to solve real life problems — Curriculum p. 117
15. B9 • Construct a table of values for two linear relations and graph the relation — Curriculum p. 180
16. B9 • Use graphs of two linear relations to determine subsequent missing elements in ordered pairs of the — Curriculum p. 181
17. B9 • Use graphs to solve equations involving two linear relations — Curriculum p. 182

1. B7 • Create simple algebraic expressions using simple logic to translate a set of instructions into an — Curriculum p. 35
2. B7 • Perform addition and subtraction of algebraic expressions with rational coefficients — Curriculum p. 36
3. B7 • Perform addition and subtraction of algebraic expressions with rational coefficients — Curriculum p. 37
4. B7 • Perform multiplication and division of algebraic expressions with rational coefficients — Curriculum p. 38
5. B7 • Substitute values to evaluate algebraic expressions — Curriculum p. 39
6. B7 • Substitute values to evaluate algebraic expressions — Curriculum p. 40
7. B8 • Use the distributive property to remove brackets and solve multiplication of binomial expression — Curriculum p. 118
8. B8 • Substitute values to evaluate algebraic expressions including fractions and use these to solve — Curriculum p. 119
9. B8 • Factorise given expressions involving the four operations and use the experiences gained to solve — Curriculum p. 120
10. B9 • Perform change of subject of a given formula and use it to solve problems — Curriculum p. 183
11. B9 • Perform change of subject of a given formula and use it to solve problems — Curriculum p. 184
12. B9 • Substitute values into given formulae to evaluate it and use it to solve problems — Curriculum p. 185
13. B9 • Factorise expressions that have simple binomial — Curriculum p. 186
14. B9 • Use the knowledge of simplifying and factorising expressions to solve real world problems — Curriculum p. 187
15. B9 • Use the knowledge of simplifying and factorising expressions to solve real world problems — Curriculum p. 188
16. B9 • Use the knowledge of simplifying and factorising expressions to solve real world problems — Curriculum p. 189

1. B7 • Translate word problems to linear equations in one variable and vice versa — Curriculum p. 41
2. B7 • Translate word problems to linear equations in one variable and vice versa — Curriculum p. 42
3. B7 • Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and — Curriculum p. 43
4. B7 • Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and — Curriculum p. 44
5. B7 • Model linear equations, then write mathematical expressions and describe the process of solving the — Curriculum p. 45
6. B7 • Solve linear equations in one variable — Curriculum p. 46
7. B8 • Translate word problems into linear inequalities in one variable and vice versa — Curriculum p. 121
8. B8 • Determine solution sets of simple linear inequalities in given domains — Curriculum p. 122
9. B9 • Solve single variable linear inequalities with rational coefficients. i — Curriculum p. 190
10. B9 • Solve single variable linear inequalities with rational coefficients. i — Curriculum p. 191
11. B9 • Solve single variable linear inequalities with rational coefficients. i — Curriculum p. 192
12. B9 • Solve real-life problems involving linear equations and inequalities — Curriculum p. 193
13. B9 • Solve real-life problems involving linear equations and inequalities — Curriculum p. 194
14. B9 • Solve real-life problems involving linear equations and inequalities — Curriculum p. 195

1. B7 • Measure and classify angles according to their measured sizes – right, acute, obtuse and reflex — Curriculum p. 47
2. B7 • Apply the fact that (i) complementary angles are two angles that have a sum of 90°, and (ii) — Curriculum p. 48
3. B7 • Use adjacent, supplementary and vertically opposite angles to solve problems — Curriculum p. 49
4. B7 • Use adjacent, supplementary and vertically opposite angles to solve problems — Curriculum p. 50
5. B7 • Construct a line segment perpendicular to another line segment — Curriculum p. 51
6. B7 • Construct the perpendicular bisector of a line segment — Curriculum p. 52
7. B7 • Copy and bisect angles — Curriculum p. 53
8. B7 • Copy and bisect angles — Curriculum p. 54
9. B7 • Copy and bisect angles — Curriculum p. 55
10. B7 • Copy and bisect angles — Curriculum p. 56
11. B7 • Copy and bisect angles — Curriculum p. 57
12. B7 • Describe examples of perpendicular line segments, perpendicular bisectors and angle bisectors in — Curriculum p. 58
13. B8 • Draw and determine the values of alternate and corresponding angles — Curriculum p. 123
14. B8 • Determine the values of angles in a triangle using knowledge of the sum of interior angles in a — Curriculum p. 124
15. B8 • Construct and bisect angles of 120˚, 105˚, 135˚ and 150˚ — Curriculum p. 125
16. B8 • Construct and bisect angles of 120˚, 105˚, 135˚ and 150˚ — Curriculum p. 126
17. B8 • Construct scalene triangles, isosceles triangles, equilateral triangles, obtuse-angled triangle, — Curriculum p. 127
18. B8 • Construct scalene triangles, isosceles triangles, equilateral triangles, obtuse-angled triangle, — Curriculum p. 128
19. B8 • Construct scalene triangles, isosceles triangles, equilateral triangles, obtuse-angled triangle, — Curriculum p. 129
20. B8 • Construct scalene triangles, isosceles triangles, equilateral triangles, obtuse-angled triangle, — Curriculum p. 130
21. B8 • Construct scalene triangles, isosceles triangles, equilateral triangles, obtuse-angled triangle, — Curriculum p. 131
22. B8 • Construct scalene triangles, isosceles triangles, equilateral triangles, obtuse-angled triangle, — Curriculum p. 132
23. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 133
24. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 134
25. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 135
26. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 136
27. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 137
28. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 138
29. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 139
30. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 140
31. B8 • Construct loci under given conditions including: (i) the locus of sets of points from a fixed — Curriculum p. 141
32. B9 • Derive the formula for calculating the sum of angles in any polygon and use this to calculate the — Curriculum p. 196
33. B9 • Derive the formula for calculating the sum of angles in any polygon and use this to calculate the — Curriculum p. 197
34. B9 • Identify similar and congruent triangles and use the knowledge to solve related problems — Curriculum p. 198
35. B9 • Draw inscribed and circumscribed circles for triangles under given conditions — Curriculum p. 199
36. B9 • Draw inscribed and circumscribed circles for triangles under given conditions — Curriculum p. 200
37. B9 • Construct parallelograms (i.e. square, rectangle, rhombus) under given conditions — Curriculum p. 201
38. B9 • Construct parallelograms (i.e. square, rectangle, rhombus) under given conditions — Curriculum p. 202
39. B9 • Construct parallelograms (i.e. square, rectangle, rhombus) under given conditions — Curriculum p. 203
40. B9 • Construct parallelograms (i.e. square, rectangle, rhombus) under given conditions — Curriculum p. 204

1. B7 • Calculate the perimeter of given shapes whose dimensions are in two units (i.e. cm and mm, m and — Curriculum p. 59
2. B7 • Use the relationships between the diameter and the circumference to deduce the formula for finding — Curriculum p. 60
3. B7 • Use the relationships between the diameter and the circumference to deduce the formula for finding — Curriculum p. 61
4. B7 • Use the relationships between the diameter and the circumference to deduce the formula for finding — Curriculum p. 62
5. B7 • Draw in a square grid rectangles and triangles with given dimensions — Curriculum p. 63
6. B7 • Use the relationships between a triangle and a rectangle (or parallelogram) to deduce the formula — Curriculum p. 64
7. B7 • Use the relationships between a triangle and a rectangle (or parallelogram) to deduce the formula — Curriculum p. 65
8. B7 • Determine the area of a triangle — Curriculum p. 66
9. B7 • Describe the bearing of a point from another point — Curriculum p. 67
10. B7 • Describe the bearing of a point from another point — Curriculum p. 68
11. B7 • Explain how to find the back bearing when the direction of travel has a bearing which is less than — Curriculum p. 69
12. B7 • Distinguish between scalar and vector quantities — Curriculum p. 70
13. B7 • Convert vectors in the column (component) form ቀ𝒙𝒚𝒚ቁ to the Magnitude–Bearing form (𝒌𝒌, 𝜽𝜽) and — Curriculum p. 71
14. B8 • Use the relationship between the diameter and circumference of a circle to deduce the formula for — Curriculum p. 142
15. B8 • Establish the relationship between the hypotenuse c and the two other sides ‘a’ and ‘b’ of a — Curriculum p. 143
16. B8 • Use the Pythagorean theorem to solve problems on right- angled triangle — Curriculum p. 144
17. B8 • Use the Pythagoras theorem to calculate the area of a triangle in real life problems — Curriculum p. 145
18. B8 • Use the Pythagoras theorem to calculate the area of a triangle in real life problems — Curriculum p. 146
19. B8 • Use the Pythagoras theorem to calculate the area of a triangle in real life problems — Curriculum p. 147
20. B8 • Use the Pythagoras theorem to calculate the area of a triangle in real life problems — Curriculum p. 148
21. B8 • Add, subtract and find the scalar multiplication of vectors in the component form — Curriculum p. 149
22. B8 • Demonstrate understanding of vector equality — Curriculum p. 150
23. B9 • Measurement — Curriculum p. 205
24. B9 • Measurement — Curriculum p. 206
25. B9 • Measurement — Curriculum p. 207
26. B9 • Measurement — Curriculum p. 208

1. B7 • Determine shapes in real life that have reflectional (or fold) symmetries — Curriculum p. 72
2. B7 • Plot points and shapes (i.e. plane figures) on a coordinate plane and draw their images under — Curriculum p. 73
3. B7 • Plot points and shapes (i.e. plane figures) on a coordinate plane and draw their images under — Curriculum p. 74
4. B7 • Plot points and shapes (i.e. plane figures) on a coordinate plane and draw their images under — Curriculum p. 75
5. B7 • Verify the concept of congruent and similar shapes in coordinate plane using properties of both the — Curriculum p. 76
6. B8 • Understand rotation and identify real-life situations involving rotation — Curriculum p. 151
7. B8 • Draw rotation image in a coordinate plane and determine the angle of rotation — Curriculum p. 152
8. B9 • Position and Transformation — Curriculum p. 209
9. B9 • Position and Transformation — Curriculum p. 210

1. B7 • - Select and justify a method to collect data (quantitative and qualitative) to answer a given — Curriculum p. 77
2. B7 • - Design and administer a questionnaire for collecting data to answer questions and record the — Curriculum p. 78
3. B7 • - Organise and present data from a survey into a table and/or chart, and analyse it to solve and/or — Curriculum p. 79
4. B7 • - Organise and present data from a survey into a table and/or chart, and analyse it to solve and/or — Curriculum p. 80
5. B7 • - Organise and present data from a survey into a table and/or chart, and analyse it to solve and/or — Curriculum p. 81
6. B7 • - Organise and present data from a survey into a table and/or chart, and analyse it to solve and/or — Curriculum p. 82
7. B7 • Calculate the mean for a given ungrouped data and use it to solve problems — Curriculum p. 83
8. B7 • Calculate the median for a given ungrouped data and use it to solve problems — Curriculum p. 84
9. B7 • Calculate the median for a given ungrouped data and use it to solve problems — Curriculum p. 85
10. B8 • Identify types of given data including numerical, categorical, ungrouped and grouped data — Curriculum p. 153
11. B8 • - Select and justify a method to collect data (quantitative and qualitative) to answer a given — Curriculum p. 154
12. B8 • - Organise data (grouped/ungrouped), present it in frequency tables, line graphs, pie graphs, bar — Curriculum p. 155
13. B8 • - Organise data (grouped/ungrouped), present it in frequency tables, line graphs, pie graphs, bar — Curriculum p. 156
14. B8 • - Organise data (grouped/ungrouped), present it in frequency tables, line graphs, pie graphs, bar — Curriculum p. 157
15. B8 • Calculate the mean, median and mode for a given set of ungrouped data, and explain why these values — Curriculum p. 158
16. B8 • Calculate the mean, median and mode for a given set of ungrouped data, and explain why these values — Curriculum p. 159
17. B8 • Justify a context in which the mean, median or mode is the most appropriate measure of central — Curriculum p. 160
18. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 211
19. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 212
20. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 213
21. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 214
22. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 215
23. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 216
24. B9 • Data Collection, Organisation, Presentation and Interpretation — Curriculum p. 217
25. B9 • of the data, if one of the bulbs is replaced with a new bulb 300 hours, find the new mean of the — Curriculum p. 218

1. B7 • Demonstrate understanding of likelihood of a single outcome occurring by providing examples of — Curriculum p. 86
2. B7 • Classify the likelihood of a single outcome occurring in a probability experiment as impossible, — Curriculum p. 87
3. B7 • Classify the likelihood of a single outcome occurring in a probability experiment as impossible, — Curriculum p. 88
4. B8 • Perform a probability experiment involving two independent events such as drawing coloured bottle — Curriculum p. 161
5. B8 • Express the probabilities of the events as fractions, decimals, percentages and/or ratios. e.g.by — Curriculum p. 162
6. B8 • Express the probabilities of the events as fractions, decimals, percentages and/or ratios. e.g.by — Curriculum p. 163
7. B9 • Perform a probability experiment involving two dependent events e.g. drawing coloured bottle tops — Curriculum p. 219
8. B9 • Perform a probability experiment involving two dependent events e.g. drawing coloured bottle tops — Curriculum p. 220