GES-JHS-MATHEMATICS-CCP-CURRICULUM-B7-B10

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

E.g.4: Construct a regular hexagon within a circle given the length of a side

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

E.g.5 Use intersecting circles to construct a regular hexagon and measure it sides

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

E.g.6: Construct a perpendicular bisector (mediator) as a locus and explain why the
perpendicular bisector is a locus

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

E.g. 7 Construct an angle bisector as a locus of points equidistant from two lines that
meet and explain why the angle bisector is a locus

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

E.g.8: Construct parallel lines as a locus (i.e. tracing the path of a point say P which moves
in such a way that its distance from line BC is always the same).

E.g.9: perform Perform geometric constructions to proveof that two given lines are
parallel

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S/N CONTENT STANDARDS Strand 3 Geometry and Measurement COMPETENCIES
Sub-strand 2: Measurement

INDICATORS AND EXEMPLARS

B.8.3.2.1 B8.3.2.1.2 1 Use the relationship between the diameter and circumference of Create simple logic trees
Apply the Pythagoras a circle to deduce the formula finding the area and use this to solve to think through problems
theorem, the primary problems Demonstrate a thorough
trigonometric ratios and the understanding of a
formulas for determining the Eg 1: Divide the circle into sectors (minimum of 16) then cut the sectors and arrange to generalised concept and
area of circle to solve real form a rectangle deduce the Area of the circle. facts specific to task or
problemsB.8.3.2.1 Thus length of situation
Apply the Pythagoras rectangle = w id th
theorem and the formulas for =
determining the area of a = × = 2
triangle and circle to solve
real problems

E.g. 2 Solve problems on area of a circle Provide new insight into
(i) Find the area of a circle whose radius is 14cm (Take π = 22/7) controversial situation or
task
(ii) Find the area of a semi-circle whose radius is 7cm (Take π = 22/7)
(iii) Two circles with common centre, the small circle has radius 7cm, the big circle also
has radius 14cm .with big circle shaded. .Find the shaded area. (Take π = 22/7).

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

B8.3.2.1.2 Establish the relationship between the hypotenuse ‘c’ and the two Ability to combine
other sides ‘a’ and ‘b’ of a right-angled triangle (i.e. a2 + b2 = c2) and use Information and ideas
it to solve problems from several sources to
reach a conclusion
E.g.1Construct squares on the three sides of a
right-angled triangle in a square grid and
compare the area of the square on the
hypotenuse to the squares on the other
two sides to state the relationship
between the hypotenuse ‘c’ and the two
other sides ‘a’ and ‘b’ of a right-angled
triangle i.e. a2 + b2 = c2

E.g. 2 Using a pair of compasses and ruler, construct squares on the three sides of a Analyse and make distinct
right-angled triangle and measure the area of the judgment about
square on the hypotenuse and compare to the viewpoints expressed in
squares on the other two sides to state the an argument
relationship between the hypotenuse ‘c’ and the
two other sides ‘a’ and ‘b’ of a right-angled
triangle i.e. a2 + b2 = c2.

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E.g. 3 Solve problems involving Pythagoras theorem.

i. Determine the missing side marked h in the figure.
ii. Find the height AB.

iii. If the legs of a right triangle are of the same length,
what is the length of the hypotenuse?

B8.3.2.1.3 Use the Pythagorean theorem to solve problems on right-angled Develop and defend a
triangle logical plausible resolution
to a confusion,
E.g.1 An isosceles triangle has equal sides,6cm long and a base of 4cm long. Find the uncertainty or
altitude of the triangle. contradiction surrounding
an event

E.g.2 Find the length of each of the diagrams indicated below, 157
(i) the length x
(ii) the length CB
(iii) the longer length

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

B8.3.2.1.3 5 Use Pythagoras theorem to calculate area of a triangle in real life Ability to select
problems alternative(s) that
E.g.1 . adequately meet selected
A boat travels 2m South and then 9m east. (i) How far is the boat from its starting point. criteria
E.g.2 Ability to mentor peers
Yeboah hangs a picture frame of width 15cm on the wall. The distance from the nail to the
edge of the picture frame is 10cm
(i) Find the length of the wire used to hang the picture frame. (ii) Find the area of the triangle.

E.g.3 A ladder leans against a vertical wall of height 13m. If the foot of the ladder is 6m away
from the wall, calculate the length of the ladder.
E.g4 The length of a side of an equilateral triangle is 12cm .Find
(1) the height of the triangle
(11) the area of the triangle
(111) the perimeter of the triangle

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Preparedness to recognise
B8.3.2.1.6 Establish the relationship between the basic trigonometric ratios and and explain results after
solve problems involving right-angled triangles implementation of plans
E.g.1 Identify and recognize the three primary trigonometric ratios
Implement strategies with
i. Establish the sine, cosine and tangent of an angle in a right-angled triangle accuracy

ii. Find , a n d i n t h e diagram Ability to keep group
iii. Write two trig ratios of the angle marked i n the diagram working on relevant
activities

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E.g. 2 Explain the angles of elevation and
depression in real life

E.g.3 Use trig ratios and the Pythagoras theorem to solve problems involving angles of elevation
and depression

i. A hunter sees a fire at an angle of depression 30˚. The height of the hunter is 1.8m.
What is the distance between the fire and the hunter? Round off your answer to 2
significant figures

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Strand 3 Geometry and Measurement
Sub-strand 2: Measurement

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Generate hypothesis to help
B8.3.3.2 Demonstrate B8.3.3.2. Add, subtract and find the scalar multiplication of vectors in the answer complex problems
understanding of addition component form
and subtraction of vectors E.g1 Add vectors using the graphical method 161
and their application in E.g.2 Add and Ssubtracte vectors in their corresponding components.
solving basic problems

If AB =  a  and BC =  c 
b d

then AC = AB + BC

=  a  +  c  =  ba + c 
b d + d

If AB =  a  and BC =  c 
b d

then AC = AB - BC

=  a  -  c  = � −− �
b d

E.g3 Multiply a vector by a scalar k�� = k� �

E.g.4 If p=�−21� , q=�43� , and r=�−32�, find (i) 3q-2p (ii) r-3p (ii) q-p+2r

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Generate hypothesis to help
B8.3.3.2.2 Demonstrate understanding of vector equality answer complex problems
E.g.1 Investigate the properties of equal vectors

E.g.2 If a=�53� ,b=�27� and c=�−−43�, Caculate | | , if p=a+ ½(b-c)
E.g.3 If M = N ,find x and y given that M=�− − 2 � and N=�2 −1 1 �

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S/N CONTENT STANDARDS Strand 3 Geometry and Measurement COMPETENCIES
Sub-strand 2: Measurement

INDICATORS AND EXEMPLARS

1. B8.3.3.15 B8.3.3.15.1 Understand rotation and can identify real-life situations involving rotation. Demonstrate a
thorough
2. Perform a single E.g. 1. Know Identify examples of rotation situations in everyday life and the nature of movements – understanding of a
transformation (i.e. clockwise and anti-clockwise. generalised concept
rotation) on a 2D shape and facts specific to
using graph paper including i. State the object points and its corresponding image task or situation
technology and describe the points under a given rotation
properties of the image
under the transformation
(i.e. congruence, similarity,
etc.) ii. Draw points of shapes under a clockwise or anti-

clockwise rotation through a given angle about the

origin (90º, 180º, 270º)

3. B8.3.3.15.2 Draw rotation image in coordinate plane and determine angle of rotation. Identification of

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

4. E.g. 1. Rotate a shape through a given center centre of rotation and angle of rotation using rotation requirements of a
rules. given situation and
justification of more
iii. State the object points and its corresponding image points under a given rotation than one creative
tool that will be
iv. Draw points of shapes under a clockwise or anti-clockwise rotation through a given suitable.
angle about the origin (90º, 180º, 270º) Ability to visualise
alternatives, seeing
E.g. 2. Determine the angle of rotation using the points of an object, its their images and center possibilities,
centre of rotation (NB: use protractor to measure). problems and
challenges.
Ability to try
alternatives and
fresh approaches

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Ability to ascertain
5. B8.3.3.15.3 Investigate the concept of congruent and similar shapes when information is
E.g. 1. Using multiple and varied examples of rotation on coordinate plane to verify congruent and needed and be able
similar shapes using their properties. to identify, locate,
evaluate and
effectively use them
to solve a problem

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S/N CONTENT STANDARDS Strand 4: Data COMPETENCIES
Sub-strand 1: Data Handling

INDICATORS AND EXEMPLARS

1. B8.4.1.1 B8.4.1.1.1 – Identify types of given data. including numerical, categorical, Ability to ascertain when
ungrouped and grouped data information is needed and
Select, justify, and use E.g. 1 Learners discuss, in small groups, an information collected in the process of be able to identify, locate,
appropriate methods to investigation which may be numeric. evaluate and effectively use
collect data (quantitative and them to solve a problem
qualitative), use the data
(grouped/ungrouped) to
construct and interpret i. Numeric (and discrete): the number of Nissan cars sold by Japan Motors, Ghana in
a year; the number of children in a family; the number of learners in B8 class
frequency tables, bar charts,
pie charts, and pictograms to ii. Numeric (and continuous): weight of babies in a creche (e.g. 4.5kg) which contains
solve and/or pose problems. fractional value

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2. E.g. 2 Learners, in small groups, discuss an information collected in the process of
investigation which may be non-numeric
i. Non-nNnumeric (cannot be quantified): sex (male or female); income group, movie
type, age group, marital status, boxers’ weight class, etc.
ii. Lead leaners to sort out the examples of the non-numeric in (i) that have values
that can be put on ordinal scale (boxers’ weight class; age group)
iii. Lead leaners to sort out the examples of the non-numeric in (i) that can be put
into categories (Categorical data): sex (male or female); marital status; income
group, etc.

3. E.g. 3 Can effectively evaluate the
success of solutions they
i. The scores for 11 learners in a class test are 25, 30, 35, 40, 45, 26, 29, 50, 45, 37 have used to attempt to
and 47. (these individual scores are not grouped in any way) solve a complex problem

ii. Learners find out those in the group 25 to 35 (i.e. 5) and those in the group 36
to 50 (i.e. 6).data now grouped

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Preparedness to recognise
4. B8.4.1.1.2 - Select and justify a method to collect data (quantitative and and explain results after
qualitative) to answer a given question. implementation of plans

5. E.g. 1- To study how eating cream crackers influence/affect one’s output of work Create simple logic trees to
(productivity), let learners identify which method they will use to gather the facts think through problems
for each of the following situations. (i.e. refer to methods stated in E.g. 2 of
B7.4.1.1.1) Demonstrate behaviour
and skills of working
i. Will eating twice a person's normal number of cream crackers increase their towards group goals

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his/her productivity? Understand and use
ii. Are people who eat more cream crackers more productive? interpersonal skills
iii. Does a group of students study better when cream crackers are present or

absent?

6. E.g. 2 -Learners should select the study they wish to undertake and design an appropriate Understand roles during
form to be used in collecting the data. group activities

7. B8.4.1.1.3 - Organize data (grouped/ungrouped), present it in frequency tables, Ability to ascertain when
line graphs, pie graphs, bar graphs and/or pictographs (representations information is needed and
include info graphics, waffle diagrams, box and whisker plots and stem be able to identify, locate,
and leaf plots) and analyse it to solve and/or pose problems. evaluate and effectively use
them to solve a problem

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

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8. E.g. 1 -The following set of raw data shows the lengths, in millimetres, measured to the Can effectively evaluate the
nearest mm, of 340 leaves taken from plants of a certain species. success of solutions they
have used to attempt to
solve a complex problem

Make Copy and complete the table of frequency distribution, using the table distribution Preparedness to recognise
table below, using the data set above.. and explain results after
implementation of plans
Lengths (mm) Tally Frequency
Create simple logic trees to
25 – 29 think through problems
Demonstrate behaviour
30 – 34 and skills of working
towards group goals
35 - 39 Understand and use
interpersonal skills
40 – 44

45 – 49

50 – 54

55 - 59

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9. E.g. -2 A cleaner of a small office spent GH₵120 the salary on food; GH₵80 on rent; Understand roles during
GH₵40 on clothing; GH₵110 on transport and saved GH₵50. Organize the data group activities
and draw (i) a bar chart and (b) a pie chart to represent the data.

10. E.g. -3 – The waffle chart (i.e. a 10 X 10 cell grid in which each cell represents percentage
point summing up to total 100%.) shows that the average score obtained by B7
learners in a mathematics test conducted, is 10%.

i. Read and record the average scores obtained by B8, B9 and B10.

ii. In a mathematics quiz Cordei scored 75%, Kofi scored 80%, Maama scored 35%,
Kpakpo scored 70% and Adjoa scored 50%.
Draw a waffle chart to represent the data.

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11. E.g. 4 – Learners make a stem and leaf plot (a stem-and-leaf display or stem-and-leaf plot is
a method for presenting quantitative data in a graphical format to assist in
visualizing the shape of a distribution and giving a great idea about the distribution
of the data.)
i. The data below are scores for 14 B8 learners in
a test marked out of a maximum of 100.
Learners should make a stem and leaf plot to
represent the data

(
Learners should note that though there are no
scores 30s and 40s, 0s should not be put against
stem 3 and stem 4.those spaces must left blank.
However, 0 should be put against 8 for 80)
ii. From the plot, what can we say about the

performance of the 14 B8 learners?
Where:

2 3 means 23
7 112 means 71, 71,72

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
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12. E.g. 5 – The stem and leaf plot shows the scores obtained by
learners in a test. Use it to answer the following
questions:
i. What are the scores? Write themn in ascending
order.

ii. What is the mode of the scores?
iii. What is the median of the scores?

13. B8.4.1.2 Demonstrate an B8.4.1.2.1 -Calculate the mean, median and mode for a given set of ungrouped Interpret correctly and
understanding of measures of data, and explain why these values may be the same or different. respond to non- verbal
central tendency (mean, communication such as
median, mode) and range for E.g. 1 The bar graph on the right shows the sales of a small business from Monday to facial expressions, cues and
grouped data and explain Friday. Calculate the mean, median and mode for amounts collected during the gestures
when it’s most appropriate to
use the mean, median, or period and explain your findings (i.e. why the values are the same) Provide feedback in areas
of ideas, organisation, voice,
mode. Chart Title word choice and sentence
fluency in communication
Sales Collected (GH₵) 400 Mon
300 Tue Ability to identify important
200 Wed and appropriate criteria to
100 Thu evaluate each alternative.
Fri
0
1

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14. E. g. 2 The table below shows the area of the sitting room floors of each of 7 Real Estates
houses (A, B C, …) in Kwashi Kumaman

Houses A B C D E F G
Area (m2) 22 24 26 30 48 30 30

i. In small groups, let learners work out the mean, median, mode.
ii. Draw a bar chart to represent the data collected, and
iii. Explain why the values are the same.

15. E.g. 3. The table below shows the occurrence of the data values from 1 to 7 and
represented by the corresponding bar graph.

Data Value Frequency FREQUENCY 15
1 1 10
2 11
5
3 5 0
4 4
5 2 1234567
6 1 DATA VALUE
7 1

i. Calculate the mean, median, mode
ii. Locate them on the corresponding graph, and
iii. Explain why the values are different.

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
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16. B8.4.1.2.2-Justify a context in which the mean, median or mode is the most Interpret correctly and
appropriate measure of central tendency to use when reporting findings. respond to non- verbal
communication such as

17. E.g. Kojo’s says his taxi makes a number of journeys trips each day as shown in the table facial expressions, cues and
below. gestures

Monday Tuesday Wednesday Thursday Friday Saturday Sunday Provide feedback in areas
8 6 10 10 9 10 3
of ideas, organisation, voice,
word choice and sentence
fluency in communication

i. Ability to identify important
ii. and appropriate criteria to
evaluate each alternative.
iii. In small groups, let learners calculate the mean, median and mode
for Kojo’s week

ii. Which measure of central tendency best represents or describes the number of
journeys trips that Kojo makes each day

iii. Learners must justify their decisions.

Strand 4: Data

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Sub-strand 1: Probability

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

18. B8.4.2.1 B8.4.2.1.1.-Perform a probability experiment involving two independent events Preparedness to
such as drawing coloured bottle tops from a bag with replacement and list the recognise and explain
Identify the sample space for a elements of the sample space results after
probability experiment implementation of plans.
involving two independent Implement strategies with
19. events and express the E.g. 1 -In an experiment, Emmanuel was asked to pick one bottle top from a bag, three accuracy.
probabilities of given events as times, which contains 3 red, 2 green and 1 pink bottle tops.

fractions, decimals, i. List the elements of the sample space of the events.
percentages and/or ratios to
solve problems. ii. The sample space of the event of picking a red bottle top, R, with replacement is
………….

iii. The probability of picking a red bottle top is …………. Can see the importance

20. E.g. 2 -Consider the following two events: (a) throwing of a fair six-sided die and (b) tossing of including all team
a fair coin members in discussions
and actively encourage
i. What is the sample space for (a) and for (b)? contributions from their

ii. Does the occurrence of event (a) affect the occurrence of event (b)? peers in their team.

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?

21. 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 event involving Ampofo affect that of Serwa?
ii. Can the two events occur together?

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Develop and defend a
22. B8.4.2.1.2. Express the probabilities of the events as fractions, decimals, logical plausible
percentages and/or ratios. e.g.by using a tree diagram, table or other graphic resolution to a confusion,
organizer uncertainty or
contradiction
23. E.g. 1- The arrow on the spinner if spun twice and the number of surrounding an event
wins recorded.
i. Identify the sample space Actively assist group
ii. Calculate the probability of a win P(W) and the identify changes or
probability of a lose, P(L) modifications necessary
iii. Copy and complete the probability tree diagram that in the group activities and
seeks to represent below of the events, i.e. the 1st work towards carrying
and 2nd spins out those changes
iv. Express the probabilities stated on the branches in
decimals, percentages and ratios

24. E.g. 2-A box contains 3 blue pens and 4 pink pens. A pen is taken from the box, its colour
noted, and then replaced. Another pen is taken and its colour noted.
i. What is the sample space of the 1st and 2nd trials?
ii. Draw probability tree diagram.

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Develop and exhibit a
25. E.g. 2 -A die is thrown at most three times. If 6 is scored the game stops. sense of cultural identity.

i. Copy and complete the probability tree diagram Identify and explain a
ii. Explain why some of the branches of the tree diagram have disappeared. confusion, uncertainty, or
a contradiction
surrounding an event

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BASIC 9

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S/N CONTENT STANDARDS Strand 1: Number COMPETENCIES
1. 9.1.1.1.1 Apply the Sub-strand 1: Number and Numeration System
understanding of place value in
solving real life problems INDICATORS AND EXEMPLARS
involving integers of any size,
rounding this to given decimal 9.1.1.1.1 Express integers to given number of significant and decimal places Provide feedback in
places and significant figures areas of ideas,
E.g.1. Express integers to a number of significant figures organisation, voice,
(i) 857,386,321 word choice and
-five significant figures sentence fluency in
-four significant figures communication
-three significant figures Think beyond their
etc task and actively
support other team
E.g.2. Express decimal numbers to a given number of decimal places members to complete
(i) 98745.9674 correct to their task.
-three decimal places Division of task into
-two decimal places solvable units and
-one decimal place assign group members
to task units
9.1.1.1.2. Use knowledge and understanding of place value to solve real life problems

E.g.1. Create and solve a real-life problem or a story problem and write the answer in Ability to select the
standard form most effective creative
(I) I am a 6-digit number. My first digit is 5 more than the last digit, but 2 less than my tools for working and
second digit. My second digit is the third multiple of 3, while my fourth digit is the preparedness to give
second multiple of 3. My third digit is the quotient when the fourth digit is divided by my explanations
last digit. However, my fourth and fifth digits are consecutive numbers. What number
am I?

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
2.
Think second digit: 3x3=9

fourth digit: 2x3=6

first digit: 9-2=7

last digit: 7-5=2

fifth digit: 6-1=5

third digit: 6 

So the number is 793652 = 7.93652 x 105

E.g.2 Create similar real story problems and solve

3. B9.1.1.2 B9.1.1.2.1 Solve problems on relationship between members of the rational number Knowledge and
system using knowledge and understanding of the concept of union and intersection of recognition of ethical
Demonstrate an understanding two sets use of information
of the relationship between
members of the rational number
system and solve real life E.g. 1 Use sets diagrams to show the relationship among the Real numbers namely Recognise and
problems involving union and -(R) Irrational numbers generalise information
intersection of three sets and experience ;
-Irrational numbers (QI ) search for trends and

-Rational numbers (Q) patterns

- Integers (Z)

-Whole numbers (W)

-Natural or Counting numbers (N)

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Interpret correctly and
4. E.g. 2 Write the factors of 12 and 15 and represent them on a Venn diagram. respond to non- verbal
12={1, 2, 3, 4, 6, 12} communication such as
facial expressions, cues
15={1, 3, 5, 15} and gestures

5. B9.1.1.2.2 Apply the concept of sets of sets to solve problems on relationship between
members of rational number system and solve real life problems involving union and
intersection of two sets

6. E.g.1 Create and solve real life problems to show union and intersection of two sets.
i.There are 80 farmers in a certain village who grow either maize or beans. Fifty of them
grow beans while sixty grow maize. If each farmer grows at least one of the two crops,
represent the information on a Venn diagram and hence find the number of farmers who
grow;

a. both crops.
b. only one crop.

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Strand 1: Number
Sub-strand 12: Number and Numeration System Operations

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
7.
B.9.1.2.1 Apply mental B9.1.2.1.1 Multiply and divide given numbers by multiples of 10 including Identify words or
8. mathematics and properties to decimals and benchmark fractions sentences in context
determine answers for addition E.g.1. Recall multiplication facts up to 144 and related division facts. or appropriately
9. and subtraction of basic facts.

E.g.2. Recall decimal names of given benchmark fractions converted to decimals or Analyse and make
percentages (and vice versa) distinct judgment
about viewpoints
E.g. 3. Find the product of a given decimal number when it is multiplied by 10, 100, expressed in an
argument
1000, 1 , 1010, 10100, etc.
10

B9.1.1.2 B.9.1.2.1.2 Demonstrate the ability to determine commutative properties of Identify underlying
Demonstrate an understanding addition and multiplication. themes, implications
of the relationship between E.g1. Recognize that for any two numbers a and b; and issues when
members of the rational number listening
system and solve real life i. a + b = b + a Identify and prove
problems involving union and i.e. 25 + 32 = 32 + 25 = 57 misconceptions about
intersection of three sets a generalised concept
ii. a × b = b × a or fact specific to a
i.e. 17 × 8 = 8 × 17 = 136 task or situation

B9.1.2.1.3 Use the associative property of addition and multiplication.

E.g1. Recognize that for any three numbers a, b and c;
i. a + (b + c) = (a + b) + c
or a + (b + c) = (a + c) + b

i.e. 15 + (6 + 9) = (15 + 6) + 9 = 30
ii. (a × b) × c = a × (b × c)
i.e. (12 × 5) × 4 = 12 × (5 × 4) = 240

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10.
B9.1.1.4 Use the distributive property in solving problems.
11. E.g1. Recognize that for any three numbers a, b and c;

i. a × (b + c) = (a × b) + (a × c)
i.e. 5 × (10 + 7) = (5 × 10) + (5 × 7) = 85

B9.1.2.2 ii. a × (b - c) = (a × b) - (a × c) Evaluate the quality
Apply the understanding of the i.e. 5 × (10 - 7) = (5 × 10) - (5 × 7) = 15 and validity of
addition, subtraction, information
multiplication and division of B9.1.2.2.1 Solve operations involving addition, subtraction, multiplication
decimal numbers to solve and division using word problems.9.1.1.1.1 Express integers to given Look and think about
problems and round answers to number of significant and decimal places things differently and
given decimal places and from different
significant figures9.1.1.1.1 Apply E.g. Create and solve story problems involving a combination of two or more of the perspective
the understanding of place value basic operations
in solving real life problems (×, ÷, ─,+). Demonstrate sense of
involving integers of any size, i) A trader sells oranges from two baskets, A and B. Basket A contained 85 oranges feeling or
rounding this to given decimal and she sold 48. She sold 59 oranges from basket B and was left with the same number belongingness to a
places and significant figures of oranges as in basket A. How many oranges were originally in basket B.E.g.1. Express
integers to a number of significant figures
(i) 857,386,321 group
-five significant figures
-four significant figures
-three significant figures
etc

E.g.2. Express decimal numbers to a given number of decimal places

(i) 98745.9674 correct to

-three decimal places

-two decimal places

-one decimal place

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12.

9.1.1.1.2. Use knowledge and understanding of place value to solve real life
problemE.g.1. Create and solve a real-life problem or a story problem and write the
answer in standard form

(I) I am a 6-digit number. My first digit is 5 more than the last digit, but 2 less than my
second digit. My second digit is the third multiple of 3, while my fourth digit is the
second multiple of 3. My third digit is the quotient when the fourth digit is divided by
my last digit. However, my fourth and fifth digits are consecutive numbers. What
number am I?

Think second digit: 3x3=9

fourth digit: 2x3=6

first digit: 9-2=7

last digit: 7-5=2

fifth digit: 6-1=5

third digit: 6 

So the number is 793652 = 7.93E.g.2 Create similar real story problems and solve

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13. B9.1.1.2 B9.1.2.2.2 Solve word problems involving the four basic operations and Use digital tools to
Demonstrate an understanding round the answers to the nearest two decimal figures or to some significant create novel things
of the relationship between figures.B9.1.1.2.1 Solve problems on relationship between members of the Identification of
members of the rational number rational number system using knowledge and understanding of the concept requirements of a
system and solve real life of union and intersection of two sets given situation and
problems involving union and justification of more
intersection of three sets ii) The price of a jacket is three times that of a shirt. The price of a jacket is than one creative tool
that will be suitable
GH₵560.65. Mr Mensa bought two of the jackets and four shirts for his twin sons.
Calculate the total amount Mr Mensa paid for the items, correct your answer to:

) t wo decimal places

)three significant figures

E.g. 1 Use sets diagrams to show the relationship among the Real numbers namely

-Irrational numbers

-Rational numbers (Q)

- Integers

-Whole numbers (W)

-Natural or Counting numbers (N)

14. B9.1.1.2.2 Apply the concept of sets to solve problems on relationship between
members of rational number system and solve real life problems involving union and
intersection of two sets

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Strand 1,
Sub-Strand 2: Number Operations

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
B9.1.2.3 Recognise and
Demonstrate understanding of surds B9.1.2.3.1identify simple and compound surds generalise information
as real numbers, the process of and experience ;
adding and subtracting of surds as E.g.1 Simple surds E.g.2 Compound surds search for trends and
well as determining (using a patterns
calculator) the approximate square √2, 7√3, 2√5 (√3 + √7 − √5) Identification of
root of a number that is not a perfect requirements of a
square. B9.1.2.3.2 Explain the identities/rules of surds given situation and
justification of more
Rule 1 Rule 4 than one creative tool
√ × = √ × √ that will be suitable
√ ± √ = ( ± )√
Interpret correctly
Rule 2 Rule 5 and respond to non-
verbal communication
√ = √ = × − √ such as facial
√ + √ + √ − √ expressions, cues and
gestures
Rule 3 Rule 6 Generate hypothesis
to help answer
= × √ = √ = × + √ complex problems
√ √ √ − √ − √ + √
185
B9.1.2.3.3 Simplify given surds
E.g. Simplify:

i. √27

i. √72

ii. √8

16

iii. √12

121

iv. (√2)2

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Demonstrate sense
B9.1.2.3.4 Approximate the square roots of non-perfect squares with of feeling or
calculators/tables. belongingness to a
E.g. Square roots of non-perfect squares group

i. √2 Develop and exhibit
ii. √5 ability to defend one's
iii. √12 cultural beliefs,
iv. √30 practices and norms

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S/N CONTENT STANDARDS Strand 1, COMPETENCIES
Sub-Strand 2: Number Operations Understand and use
interpersonal skills
INDICATORS AND EXEMPLARS
Generate hypothesis
1. B9.1.3.1 Apply the B9.1.3.1.1 Review fractions and solve problems involving basic operations on to help answer
understanding of operations fractions complex problems
on fractions to solve
2. problems involving fractions E.g. 1. Review concept of fraction
of given quantities and round
3. the results to given decimal
and significant places

i. Shade given the fraction of squares in the rectangle that is equal to the shaded portion of Build a concept and
the circle. understanding of one's
ii. Write down 3 fractions equivalent to 2 self (strength and
iii. weaknesses, goals and
iv. 5 aspiration, reaction and
adjustment to novel
Cancel Express the fraction 15down to in its simplest form: 15 situation)

10 10

Convert Express 12to as a mixed numbers: 12

55
v. Convert Express 25to as an improper fractions: 25
99

4. E.g. 2. Review the basic operations on fractions

5. i. Adding &and Subtracting Fractions. Work out answers to the following:

a) 3 + 7 b) 1 1 + 54−65
2
48

ii. Multiplying &and Dividing Fractions. Work out answers to the following:

a) 2 × 34−83 b) 5 ÷ 21+2
3
8 23

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1. B9.1.3.1.2 Add and/or subtract, multiply and/or divide given fractions, using the
principle of order of operations including the use of the (through BODMAS or
2. PEMDAS) rule, and apply the understanding of these to solve problems Ability to set and
maintain personal
E.g. 1. Use the order of operations (BODMAS or PEDMAS) to simplify whole number standards and values
expressions with more than two operations. PEDMAS is Parenthesis, Exponents,
Multiply/Divide (going from left to right), and Add/Subtract (going from left to right).

i. 34 ÷ 32 + 40 – 23 × 32 ÷ 9

ii. 18 ÷ 6 × (4 - 3) + 6

iii. 18 ÷ 32 × (4 - 3) × 10

3. E.g. 2. Use the order of operations (BODMAS or PEDMAS) to simplify whole number
expressions with more than two operations.

a) 2 × 43−85÷ 2 1
3 2

b) 3 ÷ 3 + (54−21)
4 8

c) (3 + 5) × 141−12

4 8

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4. B9.1.3.1.3. Review word problems involving basic operations on fractions

5. E.g. 1. Solve word problems based on fractions word problems. Adjustment to the

i. A test is made up of 20 questions, how many questions must you answer correctly to demands of customs,
get a score of 80%? traditions, values and
attitudes of society
ii. What percent was a television set reduced if it was marked GH¢2250 and sold for
GH¢19502,025?

iii. In an election involving two contestants, one candidate claimed 52% of the votes, Identification of
while the other candidate claimed 2681 votes. If 5000 people voted, how do you requirements of a
know the election results are invalid? given situation and
justification of more
iv. A rectangle is 2 1 cm by 33cm. Calculate its (i) perimeter and (ii) area. than one creative tool
v. that will be suitable
34

YaaEsi and Alamisi Fusena made orange drink by mixing orange squash and water. Esi

drink was made of 23 orange squash and Fusena’s was made up of 12 orange squash.
Whose drink tastes78stronger of orange? 45

] 189
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B9 Strand 1,
Sub-Strand 4: Number: Ratios and Proportion

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
Anticipate and
B9.1.4.1 B9.1.4.1.1 Represent proportional relationships by equations. overcome
Apply the understanding of difficulties relating
ratio, rate and proportions to E.g.1 If total cost (t) is proportional to the number of items (n) purchased at a constant price (p), initiatives
solve problems that involve the relationship between the total cost and the number of items can be expressed as t = pn.
rates, ratios, and B9.1.4.1.2 Use proportional relationships to solve multistep ratio and percent Demonstrate a
proportional reasoning and problems, examples: simple interest, tax, discount and commissions, NHIL, thorough
use it to solve real-world depreciation, insurance, etc. understanding of a
mathematical problems E.g.1 solve problems on simple interest generalised concept
and facts specific to
• A girl deposited Gh¢ 4500 at the bank at a rate of 3% per annum for three years. Find the task or situation
simple interest. What is the amount at the end of the fifth year?

E.g.2 solve problems on tax (VAT)

• The rate of VAT rate of a country Ghana is 1512.5%. A man bought an item at Gh¢
4500.00, VAT inclusive. Calculate:

a) The basic cost of the item.
b) The VAT paid by the man.

E.g.3 solve problems on discount
• If a car cost Gh¢ 80,500.00. What is its new value if there is a discount of 10%?

E.g.4 solve problems on commission

• A car agent’s commission on the sale of a car is 3 1%. Calculate her commission on a house
2
car sold for Gh¢68,000.00.

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E.g.5 solve problems on depreciation
The value of a mobile phone depreciates according to the following:

Year of manufacture Depreciation on the
original value
In the first year 5%Nil
In the second year
In the third year 10%
In the fourth year 15%
22%

The original value of the mobile phone is Gh¢ 1800.00. Find the value of the mobile phone at the end
of each of the first four years.
E.g.6 Solve problems involving NHIL

• The NHIL inclusive price of a television set is Gh¢ 1200.00. if the NHIL is charged at a rate
of 2.5%, find

a) The cost of the television set (NHIL exclusive)
b) The NHIL charged.

E.g.7 Solve problems based on insurance
• Kofi Mereku insured his house and paid a premium of Gh¢ 30,000.00. If the insurance
company fixed the rate at 5% of the value of the house computer, calculate the insured value
of the house.

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B9.1.4.1.3 Recognize and Graph proportional relationships, interpreting the unit rate as Ability to find and
the slope of the graph and use these to solve problems. consume digital
E.g.1 In the figure above, the graph shows the cost of avocados. content
Putting forward
constructive
comments, ideas,
explanations and
new ways of doing
things

The unit rate from the data is ¢1.50 per avocado, which is the same as the slope of the line
connecting the data points is 3.
From the graph, how much do2 es eight avocados cost?
Also, using the graph how much does 15 avocados cost?

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S/N CONTENT STANDARDS B9 Strand 2 COMPETENCIES
Sub-strand 1 Patterns and Relations
Understanding of
INDICATORS AND EXEMPLARS influences of
globalisation on
B9.2.1.1 Demonstrate the B9.2.1.1.1 Draw Construct a table of values for two linear relations and graph the relation traditions, languages
ability to draw construct and cultures
tables of values for pairs of E.g.1Draw Construct a table of values for two linear E.g.2 Draw graph for two linear
linear relations, graph the relations and to draw the graphs of the relations relations
relations in a number
plane and determine the Copy and complete the table of values for the relations
intersection of the lines to
solve simultaneous linear 1 = − + 5 and 2 = 1 − 3 for from -4 to 3.
equation. 2

-3 -2 -1 0 1 2 3

1 = − + 5 8 4

2 = 1 − 3 -4 -1.5
2

E.g.3Draw Construct a table of values for two linear E.g.4 Draw graph for two linear
relations relations

Copy and complete the table of values for the relations Implement strategies
− 2 = −2 and − 2 = 2 for from -4 2 to 32. with accuracy

x -2 -1 0 1 2 193

− 2 = −2 y= ( + 0 2
2)/2

− 2 = 2 = ( - 0
− 2)/2 11

2

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S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES

B9.2.1.1.3 Use graphs of two linear relations to determine subsequent missing elements in
ordered pairs of the relation.
E.g.1 Find the missing elements of ordered pairs on

graphs of two linear relations.

The graph is drawn from a two linear relations;

= − + 4

= − 2

i. Determine the coordinates for the intersection of the
two lines.

ii. Determine the corresponding values for y for both
straight lines if x = -1.

iii. Use the graph to find the values for y for the two
relations.
6-3 7-2 8-1 90 1 2

= − + 4

= − 2

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195
B9.2.1.1.3 Use graphs to solve equations involving two linear relations.

E.g.1 Solve two linear equations simultaneous using the
graph.

i. Solve the following equations simultaneously using a
graph.

= − + 7

= 2 + 1

Hint. Draw the graphand find the coordinates for the
intersection of the two lines.

In the graph shown the values of (x, y) = (2, 5)

E.g.2 Solve two linear equations simultaneous using the
graph.

From the graph, determine the values of x and y that makes
the linear equations true.

= + 4

= 6 −

© NaCCA, Ministry of Education 2020

B9 Strand 2
Sub-strand 2 Algebraic Expressions

S/N CONTENT STANDARDS INDICATORS AND EXEMPLARS COMPETENCIES
B9.2.2.1 B9.2.1.1.1 Perform change of subject of a given formula and use it to solve problems. Identify and explain
Demonstrate an understanding a confusion,
of (i) change of subject (ii) E.g.1 Perform change of subject for given formulae uncertainty, or a
substituting values to evaluate Make the subject of the following formulae contradiction
expressions, and (iii) factorize surrounding an
expressions that have simple event
binomial as a factor.

E.g.2 Use the concept of change of subject to solve problems involving formulae Ability to visualise
i. The area of a rectangle is 24 2. If the length is 8cm, find the value of the width. alternatives, seeing
ii. The formula for calculating the area of a circle is given as 2. If a circle has an area of possibilities,
154 2, what is its radius [ = 22] problems and
iii. The triangle below has an area of 54 7 2. Find the value of the height of the triangle. challenges
iv. The cylinder below has an area volume of 330 3. Find the value of the height of the

cylinder. [ = 22]

7

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B9.2.1.1.2 Substitute values into given formulae to evaluate it and use it to solve
problems.

E.g. Find the value of ( − ) – ( − ) = = −
i.
Make the subject of the formula:
ii. √( + )

=


If = 8 , = 3, ℎ = 2, = 32, ℎ .
3 5 −2
iii. = 2 +3 and = 2 − −21; express d in terms of a. hence find the value of a, if =

3 = 2

iv. The formula for finding the volume of the shape below is given as 1 2ℎ . Find the

3

volume = 7, ℎ = 21, = 22

7

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B9.2.1.1.3 Factorize expressions that have simple binomial.
E.g.

i. 3x + 4xy = x (3 +4y)

ii. 12ab ± 16b = 4b (3a ± 4)

iii. -13xy + 39x= -13x(y-3)

iv. 5y-2y2+3y=-3y+3y

v. 8y-2y2= 2y(4-y)

vi. -6x+12=-3(2x-4)
B9.2.1.1.4 Use the knowledge of simplifying and factorizing expressions to solve real

world problems.

E.g.1 You purchased 10 items from a shopping plaza, and now you need plastic bags to carry them Ability to look at
home. If each bag can hold only 3 items, how many plastic bags you will need to accommodate 10 alternatives in
items? creating new things
Preparedness to
Solution: We use simple algebraic formula to calculate the number of bags. make better
decision with
x = Number of items purchased = 10 information at hand
y = Capacity of 1 bag = 3

Hence,
10 = 3.333
b3ags = 4 bags
So, we need 4
shopping bags
to put 10 items.

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