Maths Teachers Guide
Maths Teachers Guide
Maths Teachers Guide
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MATHEMATICS
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MATHEMATICS
TEACHER’S GUIDE
SENIOR ONE
LOWER SECONDARY
CURRICULUM
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MATHEMATICS
TEACHER’S GUIDE
SENIOR ONE
LOWER SECONDARY
CURRICULUM
DISCLAIMER!!
This material has been developed strictly for training purposes. Content and images
have been adapted from several sources which we might not fully acknowledge. This
document is therefore restricted from being reproduced for any commercial purposes
Contents
Preface ................................................................................................................ vi
Acknowledgements............................................................................................ vii
Topic 1 .................................................................................................................. 1
NUMBER BASES.................................................................................................... 1
Sub-topic 1: Representing Numbers in Different Bases on the Abacus.......... 1
Sub-topic 1.2: Identifying Place Values Using the Abaci ................................. 3
Sub-topic 1.3: Converting Numbers from base ten to any other base ........... 4
Sub-topic 1.4: Operation on Numbers in Various Bases .................................. 5
Topic 2: ................................................................................................................. 9
WORKING WITH INTEGERS .................................................................................. 9
Sub-topic 2.1: Natural Numbers ...................................................................... 9
Sub-topic 2.2: Differentiate between Natural Numbers and Whole
Numbers/Integers .......................................................................................... 10
Sub-topic 2.3: Use Directed Numbers (limited to integers) in Real-life
Situations ....................................................................................................... 11
Sub-topic 2.4: Use the Hierarchy of Operations to Carry Out the Four
Mathematical Operations on Integers ........................................................... 12
Sub-topic 2.5: Identify Even, Odd, Prime and Composite Numbers .............. 12
Sub-topic 2.6: Finding the Prime Factors of any Number .............................. 12
Sub-topic 2.7: Relate Common Factors with HCF and Multiples with LCM ... 13
Sub-topic 2.8: Work out and Use Divisibility Tests of some Numbers .......... 13
Sub-topic 2.9: Least Common Multiple (LCM) ............................................... 13
Topic 3: ............................................................................................................... 14
FRACTIONS, PERCENTAGES AND DECIMALS ...................................................... 14
Sub-topic 3.1: Describe Different Types of Fractions .................................... 15
Sub-topic 3.2: Convert Improper Fractions to Mixed Numbers and Vice
Versa .............................................................................................................. 15
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SENIOR ONE
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MATHEMATICS
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BEARINGS ........................................................................................................... 39
Sub-topic 7.2: Bearings .................................................................................. 41
Topic 8: ............................................................................................................... 45
GENERAL AND ANGLE PROPERTIES OF GEOMETRIC FIGURES ........................... 45
8.1: Identify Different Angles ........................................................................ 45
Sub- topic 8.2: Angles on a Line and Angles at a Point .................................. 45
Topic 9: ............................................................................................................... 46
DATA COLLECTION AND PRESENTATION ........................................................... 46
Sub-topic 9.1: Types of Data .......................................................................... 46
Sub-topic 9.2: Collecting Data ........................................................................ 47
Topic 10: ............................................................................................................. 51
REFLECTION........................................................................................................ 51
Sub-topic 10.1: Identify Lines of Symmetry for Different Figures ................. 51
Sub-topic 10.2: Reflection in the Cartesian Plane.......................................... 52
Topic 11: ............................................................................................................. 53
EQUATION OF LINES AND CURVES .................................................................... 53
Sub-topic 11.1 Function Machines ................................................................ 55
Sub-topic 11.2: Linear Equations ................................................................... 56
Topic 12: ............................................................................................................. 59
TIME AND TIME TABLES ..................................................................................... 59
Subtopic 12.1: Telling the Time ..................................................................... 59
Sub-topic 12.2: 12-hour and 24-hour Clocks ................................................. 61
Sub-topic 12.3: Units of time ......................................................................... 62
Sub-topic 12.4: Timetables ............................................................................ 63
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SENIOR ONE
Preface
This Teacher’s Guide has been designed to enable the teacher to interpret
the revised curriculum and use the accompanying learner textbook
effectively. The Teacher’s Guide provides guidance on what is required
before, during and after the teaching and learning experiences.
To ease the work of the teacher, all the activities and instructions in the
Learner’s Book have been incorporated in this Guide but with additional
information and possible responses to the activities. The guide has been
designed bearing in mind the major aim of the revised curriculum which is to
build in the learners the key competences that are required in the 21st
century while promoting values and attitudes and effective learning and
acquisition of skills, to prepare the learner for higher education and
eventually the world of work.
This book has been written in line with the Revised Lower Secondary School
Curriculum. The book has incorporated knowledge, skills partly required to
produce a learner who has the competences that are required in the 21st
century; promoting values and attitudes; effective learning and acquisition of
skills in order to reduce unemployment among school graduates.
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MATHEMATICS
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Acknowledgements
National Curriculum Development Centre (NCDC) would like to express its
appreciation to all those who worked tirelessly towards the production of the
Teacher’s Guide.
Our gratitude goes to the various institutions which provided staff who
worked as a panel, the Subject Specialist who initiated the work and the
Production Unit at NCDC which ensured that the work produced meets the
required standards. Our thanks go to Enabel which provided technical
support in textbook development.
The Centre is indebted to the learners and teachers who worked with the
NCDC Specialist and consultants from Cambridge Education and Curriculum
Foundation.
Last but not least, NCDC would like to acknowledge all those behind
the scenes who formed part of the team that worked hard to finalise
the work on this Learner’s Book.
Grace K. Baguma
Director, National Curriculum Development Centre
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SENIOR ONE
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MATHEMATICS
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Topic 1
NUMBER BASES
By the end of this topic, the learner should be able to:
Activity 1.1: In your groups, identify situations in which you have ever used
number bases in your life.
Observe the learners as they do the activity. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group.
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SENIOR ONE
Note down what you have observed and assist the learner where necessary.
a) 234five b) 351six
c) 897ten d) 645nine
e) 120three
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MATHEMATICS
PROTOTYPE
Observe the learners as they do the activity. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group.
Note down what you have observed and assist the learner accordingly.
Note: In (ix) there are spaces after numeral e, because each individual learner
can use different symbols to represent different numerals in base sixteen
after numeral e.
Let the individual learner tell you what he/she knows about the place values
in various number bases.
Prepare the materials to be used in making the abaci by the learners prior to
the beginning of the Mathematics lesson in which the learners will make the
Abaci.
The learners can make their own abaci if the School does not have enough
abaci.
Observe the learners as they do the activity. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Guide the groups if necessary.
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SENIOR ONE
Guide the learners to correctly read and state what each digit in the numbers
represents.
= 2x 25 + 4x5 + 4x1
= 50 + 20 +4 = 74
(You should teach the learners the second approach of converting numbers
to base ten. (This is the repeated multiplication)
Observe the learners as they do the activity. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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MATHEMATICS
PROTOTYPE
Let the learners write the responses in their exercise books. They can also
explain how they have worked out the answers. The explanation can be done
to you or the class.
The arrangement of the responses is that they start from the first box on the
right hand side then write the responses towards the left side. So, the
arrangement is 1110. We are using only two numerals which is the binary
system.
Therefore, 1110two = 1x23 + 1x22 + 1x21 + 0x20 = 8+4+2+0 = 14. Hence, the
number the learners selected is 14.
Inform the learners that number bases can be used in coding, storage of
secret information, communication etc.
Number Game:
Presentation of responses
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SENIOR ONE
Example: If the responses are that the number is not in box 1 (this is
represented by 0), then the number is in box 2; it is represented by 1. The
number is in box 3, the response is 1 and the response is that number is in
box 4, this is represented by1.
Let the learners do the exercise in this sub-topic in their exercise books.
Situation of Integration
A community is hit by famine and the government decides to give each
member in the household a potato to solve their problem of hunger.
This should be done through group discussions. You should guide the
learners’ discussions.
You can give another scenario apart from that one in the Learner’s Textbook.
Output /3 /3 /3 /1
(planning)
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MATHEMATICS
PROTOTYPE
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SENIOR ONE
C1 C2 C3 C4 (Excellent)
Output /3 /3 /3 /1
(planning)
Total Mark = 10
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MATHEMATICS
PROTOTYPE
Topic 2:
WORKING WITH INTEGERS
By the end of this topic, the learner should be able to carry out calculations
with positive and negative integers by:
In groups, let the learners discuss what the natural numbers are. Record
individual learner’s and groups’ achievements
Let the learners do the exercise in this sub-topic in their exercise books.
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SENIOR ONE
Prepare the numbers, the board and the box prior to this activity. You may
use the learners to make the cards and write the numbers both in words and
in figure on the cards.
Observe the learners as they go through this sub-topic. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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MATHEMATICS
PROTOTYPE
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
Observe the learners as they go through this activity in groups or pairs. Look
out for the individual learner’s active participation, cooperation with
members, and how he/she communicates with members of the group. Try to
find out what mathematical skills the learners are using.
Discuss the use of integers in real life situations with Individual learners.
Observe the learners as they go through this activity. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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SENIOR ONE
Use the learners to make the number cards and let them write the numbers
on the cards. The numbers written are natural numbers.
Observe the learners as they go through this activity. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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MATHEMATICS
PROTOTYPE
Let the learners be in groups as work out the answers Harmonize their
answers. Let them exchange their books and mark each other’s work.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
Guide the learners in carrying out the activities and answering questions in
Learner’s Book (p. 34).
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SENIOR ONE
Topic 3:
FRACTIONS, PERCENTAGES AND
DECIMALS
By the end of this topic, the learner should be able to understand and use
fractions, decimals and percentages by: describing different types of
fractions (k).
i) converting improper fractions to mixed numbers and vice versa (k, s).
ii) working out problems from real-life situations (u, s).
iii) adding, subtracting, dividing and multiplying decimals (u, s).
iv) converting fractions to decimals and vice versa (u, s).
v) identifying and classifying decimals as terminating, non-terminating
and recurring decimals (u).
vi) converting recurring decimals into fractions (u, s).
vii) converting fractions and decimals into percentages and vice versa (u,
s).
viii) calculating a percentage of a given quantity (s).
ix) working out real-life problems involving percentages (u, s, v/a).
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss what the natural numbers are.
Let the learners do the exercise in this sub-topic in their exercise books.
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MATHEMATICS
PROTOTYPE
Let the learners create a park of different cards and label them with different
types of fractions, decimals and percentages.
Create different study play areas in class based on the numbers put on the
cards.
From the park of the cards, let the learners pick a card and place it in the
most appropriate play area.
Observe the learners as they go through this sub-topic. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
Observe the learners as they go through this sub-topic. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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SENIOR ONE
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
1 3
In their groups, let the learners use a sheet of paper to work out + . Let
5 5
them fold the paper into five equal parts. Let them shade off one part of the
five equal parts.
They should shade the three parts of the five equal parts.
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MATHEMATICS
PROTOTYPE
Observe the learners as they carry out the activity. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
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SENIOR ONE
Observe the learners as they play the game. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
Observe the learners as they carry out the above activity. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using. Let the learners discuss their
answers.
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MATHEMATICS
PROTOTYPE
Situation of Integration
A primary school has two sections, that is, lower primary (P1-P4) and upper
primary (P5-P7). The head teacher needs to draw a timetable for both
sections. The two sections should start and end their morning lessons at the
same time before break, start and end their break time at the same time.
Then after break, lessons start at the same time. The lunch break for both
sections starts at the same time.
Support: The time for the two sections to start is 8.00am. The duration of the
lesson for the lower section is 30 minutes and that of the upper
section is 40 minutes.
Task: Help the Head teacher by drawing the timetable up to lunch break for
the two sections. How many lessons does each section have up to
lunch break?
Express the total number of lessons for the lower primary as a fraction of the
total number of lessons for the whole School. (Consider lessons up to lunch
break.)
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SENIOR ONE
This should be done in group discussions. You should guide the learners
during the discussions.
You can give a scenario apart from that one in the Learner’s Textbook.
C1 C2 C3 C4 (Excellent)
Output /3 /3 /3 /1
(planning)
Total Mark = 10
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MATHEMATICS
PROTOTYPE
Topic 4:
RECTANGULAR CARTESIAN
COORDINATES IN 2 DIMENSIONS
By the end of this topic, the learner should be able to plot and interpret
points in a range of contexts by:
i)identifying the y-axis and x-axis (k, s).
ii)drawing and labelling the Cartesian plane (k).
iii)reading and plotting points on the Cartesian plane (k, s).
iv) choosing and using appropriate scale for a given data set (k, u, s).
v) identifying places on a map using coordinates [apply coordinates in
real-life situations] (u s).
In this topic, you should make sure the learners have grid papers and
mathematical sets for better delivery.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss what the natural numbers are.
Let the learners do the exercise in this topic in their exercise books.
The learners should display their work graphs so that other class members
can give their comments.
In groups, let the learners work out the answers to the exercises. Harmonize
their answers. Let them exchange their books and mark each other’s
exercises.
Allow the learners to comment on each other’s work.
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SENIOR ONE
Observe the learners as they go through drawing and making of the shapes.
Look out for the individual learner’s active participation, cooperation with
members, and how they communicate with members of the group. Try to
find out what mathematical skills the learners are using.
In groups, let the learners discuss what the natural numbers are.
Let the learners do the exercise in this sub-topic in their exercise books.
You can give an assignment to the learners to name more other polygons.
In groups, let the learners work out the answers to the exercises. Harmonize
their answers. Let them exchange their books and mark each other’s
exercises.
Allow the learners to comment on each other’s work. For number 2, the
learners should do it practically.
Activity 4.3
This exercise requires the learners to have the working materials such as grid
papers, mathematical sets, pencils etc. in order to do it practically.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s
exercise.
Allow the learners to comment on each other’s work.
Situation of Integration: A Senior One learner has reported in her class and
has settled at her desk.
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MATHEMATICS
PROTOTYPE
Support: The classroom is arranged in rows and columns. It is a big class and
each learner has his/ her own desk.
Resources: Knowledge of horizontal and vertical lines i.e. rows and columns,
coordinates.
Knowledge: Counting numbers
Task: The mathematics teacher has asked her to explain in writing how she
can access her seat, starting from the entrance of the class. Discuss
whether there are other ways of reaching her seat.
This should be in a group discussion. You should guide the learners during
the discussions.
You can give a scenario apart from the one in the Learner’s Textbook.
Output /3 /3 /3 /1
(planning)
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SENIOR ONE
Total Mark = 10
C1 C2 C3 C4 (Excellent)
Output /3 /3 /3 /1
(planning)
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MATHEMATICS
PROTOTYPE
Total Mark = 10
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SENIOR ONE
Topic 5:
GEOMETRIC CONSTRUCTION SKILLS
By the end of this topic, the learners should be able to use the angle
properties of lines and shapes to solve problems by:
i) drawing perpendicular and parallel lines.
ii) constructing perpendiculars, angle bisectors, mediators and parallel
lines.
iii) using compass and a ruler to construct special angles (600, 450).
iv) describing a locus.
v) relating parallel lines, perpendicular bisector, angle bisector, straight
line and a circle as loci.
vi) drawing parallel lines and polygons.
vii) measuring lines and angles.
viii) constructing geometrical figures such as triangle, square, rectangle,
rhombus, parallelogram.
Observe the learners as they carry out the activity. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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MATHEMATICS
PROTOTYPE
Let the learners work in pairs and let them compare their answers. Observe
the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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SENIOR ONE
Look out for the individual learner’s active participation, cooperation with
members, and how he/she communicates with members of the group. Try to
find out what mathematical skills the learners are using.
Situation of Integration
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MATHEMATICS
PROTOTYPE
Task: The community asks you to accurately construct the foundation plan
for this old man’s house.
Explain to the class how you have accurately constructed the foundation
plan. Discuss whether there are other ways of constructing an accurate
foundation plan.
The learners need to have materials and resources such as strings, sticks,
machete, tape measure, knowledge of horizontal and vertical lines, and
knowledge of construction of geometric figures.
In this topic, group the learners and let them have discussions. You should
guide them during their discussion.
You can give a scenario apart from that one in the Learner’s Textbook.
Output /3 /3 /3 /1
(planning)
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SENIOR ONE
Total Mark = 10
Output /3 /3 /3 /1
(planning)
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MATHEMATICS
PROTOTYPE
Total Mark = 10
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SENIOR ONE
Topic 6:
SEQUENCE AND PATTERNS
By the end of this topic, the learners should be able to explore number
patterns and sequences by:
i) drawing and identify the patterns.
ii) describing a general rule of a given pattern.
iii) describing a sequence.
iv) determining a term in a sequence.
v) finding the missing numbers in a given sequence.
In this topic, you should make sure the learners discuss and explain how they
have formed and determined the patterns, and the sequences.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss what the patterns and sequences are.
Let the learners do the exercise in this topic in their exercise books.
Multiples were well covered in primary school level, so allow them to revise
what they studied in primary. Let them be in groups and share their
experiences with their neighbours.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
The multiples of 3 from the table are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,
39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.
The number is 4
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MATHEMATICS
PROTOTYPE
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
Note: The learners require some materials such as grid paper, colour pencils
etc.
The learners need to practise finding the missing and next terms in a
sequence.
Observe the learners as they go through finding and determining the missing
terms.
Look out for the individual learner’s active participation, cooperation with
members, and how he/she communicates with members of the group. Try to
find out what mathematical skills the learners are using.
In groups, let the learners discuss what the missing and next terms are.
Let the learners do the exercise in this sub-topic in their exercise books.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
a) 78, 90, 102. b) 7.1, 7.7, 8.3. c) 26, 38. d) 19, 43. E) 4.12, 4.26, 4.40.
f) 7, 6.5, 6.
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SENIOR ONE
In groups, let the learners discuss how they are generating terms.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
Let the learners relate what they have done in this exercise with generating
number sequence.
Guide the learners in their groups to work out the exercises to harmonise
their answers.
Find:
Answer
a) You can see that 4 is added each time to get the next term.
So you obtain 19, 23, 27.
b) To find the 100th term, starting at 3, you add 3 to4 times ninety-nine
times giving 3 + 4 x 99 = 3 + 396 = 399
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MATHEMATICS
PROTOTYPE
I can go one step further and write down the formula for a general term i.e.
the nth term.
This is 3 + 4 x (n – 1) = 3 + 4n - 4
= 4n – 1.
Let the learners use the knowledge they acquired in primary school level to
carry out the activity.
Learners should display their work graphs so that other class members can
give their comments.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers Let them exchange their books and mark each other’s work.
Situation of Integration
Task: The family requests you to plant the hedge around their rectangular
compound so that it looks beautiful.
Explain how you will plant the hedge, making sure that the plants at the
corners of the compound are the same in terms of colour.
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SENIOR ONE
The learners need to have materials and resources such as strings, sticks,
machete, tape measure, and knowledge of horizontal and vertical lines,
seedlings of different colours.
In this topic, group the learners and let them discuss. You should guide the
learners during the discussion.
You can give a scenario apart from the one in the Learner’s Textbook.
Output /3 /3 /3 /1
(planning)
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MATHEMATICS
PROTOTYPE
Total Mark = 10
Output /3 /3 /3 /1
(planning)
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SENIOR ONE
Total Mark = 10
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MATHEMATICS
PROTOTYPE
Topic 7:
BEARINGS
By the end of this topic, the learners should be able to understand and use
compass points, bearings and scale drawings by:
i) reviewing the compass.
ii) describing the direction of a place from a given point using cardinal
points.
iii) describing the bearing of a place from a given point.
iv) drawing suitable sketches from the given information.
v) choosing and use appropriate scale to draw an accurate diagram.
vii) differentiating
vi) drawing between a sketch and a scale.
viii) applying bearings in real-life situations.
In this topic, you should make sure the learners discuss and explain the
difference between direction and bearings.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss what bearing, sketch and scale drawing
are.
Make the following turnings and in each case state the size of the angle you
have turned through.
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SENIOR ONE
Let the learners use the knowledge they acquired in their primary school
level to carry out the activity.
Exercise
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PROTOTYPE
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. The learners should discuss how they obtained the answers.
Let them exchange their books and mark each other’s work.
In groups, let the learners work out the answers to the exercise. Harmonize
their answers. Let them exchange their books and mark each other’s work.
From your school flag post, estimate the bearings of each building found in
the school.
Note: Three figures are used to give bearings. All bearings are measured in a
horizontal plane.
Exercise
1. Find the bearing of each of the following directions:
3. Draw a scale diagram to show the position of a ship which is 270 km away
from a port on a bearing of 110o.
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SENIOR ONE
Answers
Situation of Integration
Ajok is in Kampala City and has been told to use a car to move to Lira town.
She has never gone to Lira. She has been given the map of Uganda showing
routes through which she can access Lira town.
Explain how Ajok can determine the shortest distance. Using the Map given to
her, is it possible for Ajok to use the shortest distance she has determined?
Explain your answer.
The learners need to have materials and resources such as strings, sticks,
machete, tape measure, and knowledge of horizontal and vertical lines,
seedlings of different colours.
In this topic, group the learners and let them discuss. You should guide the
learners during the discussion.
You can give a scenario apart from the one in Learner’s Textbook.
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Output /3 /3 /3 /1
(planning)
C1 - Correct C2 - Correct C3 - C4 -
Interpretation of the Use of Subject Coherence Excellence
Problem Matter Flow Ideas
Resources
Total Mark = 10
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Output /3 /3 /3 /1
(planning)
Total Mark = 10
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PROTOTYPE
Topic 8:
GENERAL AND ANGLE PROPERTIES OF
GEOMETRIC FIGURES
By the end of this topic, learners should be able to use the angle properties of
lines and shapes to solve problems by:
i) identifying different angles.
ii) solving problems involving angles on a straight line, angles on
transversal and parallel lines.
iii) stating and using angle properties of polygons in solving problems.
In this topic, you should make sure the learners discuss and explain the angle
properties and use them to solve problems.
Learners should be encouraged to own their own mathematical set and all
activities in this topic should be practical.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
Guide the learners as they identify different polygons. Let them work in pairs.
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Topic 9:
DATA COLLECTION AND PRESENTATION
By the end of this topic, the learners should be able to collect and present
different sorts of data by:
Which of the following terms best describe each of the information listed (i)
to (vii)?
• Qualitative data
• Continuous quantitative data
• Discrete quantitative data
(i) Age
(ii) Birth place
(iii) Height
(iv) World ranking
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(v) Aces
(vi) First serve the school
(vii) School life
Solution
In groups, let the learners work out the answers to the exercise.
The groups should defend their answers. Harmonize their answers. Let them
exchange their books and mark each other’s work.
i) Pictograms
ii) Bar charts
iii) Pie charts
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by bus. You could investigate this using a survey. A tally chart can be used to
record your data.
In groups, let the learners work out the answers to the exercise.
The groups should defend their answers. Harmonize their answers. Let them
exchange their books and mark each other’s work.
Situation of Integration
The Games Master at your school wants to buy football boots for the three
teams in the school. The three teams are the under 18 years, under 16 years
and the under 1.
Task: The total number of players for the three teams is 54. The Games
Master wants to know the size of the boots for each player and the
number of pairs for each size.
Explain how the Games Master will get the required data and how to
determine the total cost for buying the football boots for the 54 players.
Is there another way of getting the required data other than what you have
explained above?
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PROTOTYPE
Output /3 /3 /3 /1
(planning)
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SENIOR ONE
C1 C2 C3 C4 (Excellent)
Output /3 /3 /3 /1
(planning)
Total Mark = 10
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PROTOTYPE
Topic 10:
REFLECTION
By the end of this topic, the learners should be able to reflect shapes in a
range of contexts and identify lines of symmetry by:
In this topic, you should make sure the learners discuss and do reflection
practically.
Learners should have the following materials for the practicals for example
mirror, grid papers etc.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
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Let them exchange their books and mark each other’s work.
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Topic 11:
EQUATION OF LINES AND CURVES
By the end of this topic, the learners should be able to understand and use
linear equations and their graphs by:
i) forming linear equations with given points (k, s).
ii) drawing the graph of a line given its equation (u, s).
iii) differentiating between a line and a curve (u, s).
In this topic, you should make sure the learners discuss and explain the
difference between lines and curves.
The learners need to understand that when equations are being solved, it’s
like balancing a weighing machine when measuring masses.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss what a line and a curve are.
In this section, you should let the learners review some fundamental
algebraic skills they studied in their primary school level by examining codes
and how to use formulae.
Example
If a = 4, b = 7 and c = 3, calculate:
Solution
(a) 6 + b = 6 + 7 = 13
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(b) 2a + b = 2x4 + 7 = 8 + 7 = 15
(c) ab = 4x7 = 28
(d) a(b – c) = 4 x (7 – 3) = 4 x 4 = 16
Example
(a) 2x + 4x (b) 5p + 7q – 3p + 2q
(c) y + 8y – 5y (d) 3t + 4s
Solution
(a) 2x + 4x = 6x
(c) y + 8y – 5y = 9y – 5y = 4y
(d) 3t + 4s = 3t + 4s.
In groups, let the learners work out the answers to the exercise.
The groups should defend their answers. Harmonize their answers. Let them
exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
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In groups, let the learners discuss how they are generating terms.
Example
(a) 4 →x5 →?
(c) -3 →+8→x7→?
Solution
4 → x5 → 20
(b) The input is multiplied by 2 to give 10, and then 1 is subtracted from this
to give 9:
5→ x2 →-1 →→9
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(c) First, 8 is added to the input to give 5, and this is then multiplied by 7 to
give 35:
-3 →+8 →x7 → 3
In groups, let the learners work out the answers to the exercise.
The groups should present and defend their answers. Harmonize their
answers. Let them exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
To solve the equation, you need to reorganize it so that the unknown value is
by itself on one side of the equation. This is done by performing operations
on the equation. When you do this, in order to keep the equality of the sides,
you must remember that “Whatever you do to one side of an equation, you
must also do the same to the other side”.
In groups, let the learners discuss how they are generating terms.
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Example
Solve these equations:
a) (a) x + 2 = 8 (b) x- 4 = 3 (c ) 3x = 12
b) (d) 2x + 5 = 11 (e) 3 – 2x = 7
Solution
(a) To solve this equation, subtract 2 from each side of the equation:
X+2=8
X + 2 -2 = 8 – 2
X=6
X–4=3
X–4+4=3+4
X=7
(c) To solve this equation, divide both sides of the equation by3:
3x = 12
3x ÷ 3 = 12 ÷ 3
X=4
2x + 5 = 11
2x + 5 -5 = 11 – 5
2x = 6
2x ÷ 2 = 6 ÷ 2
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X = 3.
3 – 2x = 7
3 – 3 – 2x = 7 – 3
-2x = 4
-2x ÷ -2 = 4 ÷ -2
X = -2.
In groups, let the learners work out the answers to the exercise.
The groups should present and defend their answers. Harmonize their
answers. Let them exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
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Topic 12:
TIME AND TIME TABLES
By the end of this topic, the learner should be able to understand and use
time by:
In this topic, you should make sure the learners discuss and explain the
difference between time and timetables and how time is measured.
Observe the learners as they go through this topic. Look out for the individual
learner’s active participation, cooperation with members, and how he/she
communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss what a line and a curve are.
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Observe the learners as they go through this subtopic. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
In groups, let the learners discuss how they are generating terms.
Example
Write each time using digits and show the position of the hands on a clock
face:
(a) twenty-five past eight.
(b) quarter to ten.
Solution
(a) Twenty-five past eight using digits is 8:25
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Or
45 minutes past 9 o’clock
So, using digits, quarter to ten is 9:45
In groups, let the learners work out the answers to the exercise.
The groups should present and defend their answers. Harmonize their
answers. Let them exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
Example
Write these times in 24-hour clock:
(a) 3:06 am (b) 8:14 pm
Solution
(a) As this is am the time remains the same except you add a zero in front of
3, so the time becomes 0306 in a 24-hour clock.
(b) As this is pm, you add 12 to the hours to give you 2014 in a 24-hour clock.
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In groups, let the learners work out the answers to the exercise.
The groups should present and defend their answers. Harmonize their
answers. Let them exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
Activity 14.2
Let the learners work in pairs as you observe them
Observe the learners as they go through this sub-topic. Look out for the
individual learner’s active participation, cooperation with members, and how
he/she communicates with members of the group. Try to find out what
mathematical skills the learners are using.
1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 week = 7 days
1 year = 365 0r 366 days
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Solution
(a) You could write out the 7 days like this:
Friday 25
Saturday 26
Sunday 27
Monday 28
Tuesday 1
Wednesday 2
Thursday 3
Friday 4
Or
25 + 7 = 32
32 – 28 = 4
So the next Friday will be 4th March.
The groups should present and defend their answers. Harmonize their
answers. Let them exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
Explain to learners what the following words mean: Duration, Arrival and
Departure in relation to time and timetables.
In groups, let the learners work out the answers to the exercise.
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The groups should present and defend their answers. Harmonize their
answers.
Let them exchange their books and mark each other’s work.
Later on collect their exercise books to confirm whether the books have been
marked correctly.
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National Curriculum
Development Centre,
P.O. Box 7002, Kampala.
www.ncdc.go.ug