Numbers

Whole Numbers - Place value of digits up to hundreds of millions

By the end of the lesson, the learner should be able to:
- Define place value of digits up to hundreds of millions
- Use place value charts to determine place value of digits
- Show interest in learning place value concepts

- Discuss and identify place value of digits using place value apparatus
- Fill in numbers in place value charts
- Work in groups to determine place value of digits in different numbers

Why do we need to understand place value of digits?

- Smart Minds Mathematics Learner's Book pg. 4
- Place value charts
- Number cards

- Oral questions - Observation - Written exercises

Numbers

Whole Numbers - Place value of digits in hundreds of millions
Whole Numbers - Total value of digits up to hundreds of millions
Whole Numbers - Working out total value of digits
Whole Numbers - Reading and writing numbers in symbols up to hundreds of millions

By the end of the lesson, the learner should be able to:
- State the place value of any digit in numbers up to hundreds of millions
- Draw an abacus to show place value of digits
- Appreciate the use of place value in real life

- Use abacus to work out place value of digits
- Practice identifying place value in numbers involving hundreds of millions
- Share work with other learners in class

What is the place value of a digit in a given number?

- Smart Minds Mathematics Learner's Book pg. 5
- Abacus
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 6
- Number cards
- Smart Minds Mathematics Learner's Book pg. 7
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 8
- Number charts

- Written assignments - Oral questions - Class activities

Numbers

Whole Numbers - Converting words to symbols up to millions
Whole Numbers - Reading and writing numbers in words up to millions
Whole Numbers - Writing numbers in words on cheques

By the end of the lesson, the learner should be able to:
- Describe the process of converting numbers from words to symbols
- Write numbers involving millions correctly in symbols
- Appreciate the importance of writing numbers in symbols

- Read and interpret number statements
- Write numbers such as tree seedlings planted in symbols
- Practice converting word problems to numerical symbols

Where do we write numbers in symbols?

- Smart Minds Mathematics Learner's Book pg. 9
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 10
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 11
- Dummy cheques
- Number cards

- Written assignments - Class activities - Oral questions

Numbers

Whole Numbers - Writing numbers in words up to millions
Whole Numbers - Practice reading and writing numbers

By the end of the lesson, the learner should be able to:
- Describe how to write numbers in words using place value
- Write numbers in words using place value and total value
- Show interest in writing numbers correctly

- Break down numbers by place value and total value
- Write each component in words
- Practice with numbers like car prices and milk production

How do we write large numbers in words accurately?

- Smart Minds Mathematics Learner's Book pg. 12
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 13
- Digital devices

- Written exercises - Class activities - Oral questions

Numbers

Whole Numbers - Rounding off to the nearest ten millions
Whole Numbers - Rounding off to the nearest hundreds of millions

By the end of the lesson, the learner should be able to:
- State the rules for rounding off numbers
- Round off numbers to the nearest ten millions
- Show interest in rounding off numbers

- Make number cards with 9-digit numbers
- Round off numbers like 87,148,729 to nearest ten million
- Fill amounts in place value charts

Why do we round off numbers?

- Smart Minds Mathematics Learner's Book pg. 15
- Number cards
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 14

- Written exercises - Oral questions - Class activities

Numbers

Whole Numbers - Practice rounding off numbers

By the end of the lesson, the learner should be able to:
- Explain the application of rounding off in estimation
- Solve real life problems involving rounding off
- Appreciate the use of rounding off in estimations

- Round off tax amounts and farm areas
- Work out rounding off exercises like 219,486,272 to nearest hundred million
- Apply rounding off in real contexts

Where do we apply rounding off in daily life?

- Smart Minds Mathematics Learner's Book pg. 16
- Number cards
- Calculators

- Written exercises - Oral questions - Class activities

Numbers

Whole Numbers - Identifying even numbers
Whole Numbers - Identifying odd numbers

By the end of the lesson, the learner should be able to:
- Define even numbers
- Identify even numbers from a set of numbers
- Show interest in classifying numbers

- Make number cards with various numbers
- Sort numbers divisible by two
- Identify digits in ones place (0, 2, 4, 6, 8)

What are even numbers?

- Smart Minds Mathematics Learner's Book pg. 17
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 18

- Oral questions - Written exercises - Observation

Numbers

Whole Numbers - Identifying prime numbers
Whole Numbers - Adding whole numbers up to hundreds of millions

By the end of the lesson, the learner should be able to:
- Define prime numbers
- Identify prime numbers from a set of numbers
- Value the uniqueness of prime numbers

- Copy tables and work out divisors of numbers
- Identify numbers with only two divisors (1 and itself)
- Note that 2 is the only even prime number

What makes a number prime?

- Smart Minds Mathematics Learner's Book pg. 19
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 20
- Place value charts
- Number cards

- Oral questions - Written exercises - Observation

Numbers

Whole Numbers - Subtracting whole numbers up to hundreds of millions

By the end of the lesson, the learner should be able to:
- Explain the process of subtracting large numbers
- Subtract whole numbers up to hundreds of millions
- Appreciate the use of subtraction in daily life

- Read stories involving subtraction (coffee export)
- Use place value charts to work out subtraction
- Solve problems like milk production and sales

Where do we use subtraction in real life?

- Smart Minds Mathematics Learner's Book pg. 21
- Place value charts
- Number cards

- Written assignments - Oral questions - Class activities

Numbers

Whole Numbers - Multiplying whole numbers
Whole Numbers - Dividing whole numbers

By the end of the lesson, the learner should be able to:
- Describe the long multiplication method
- Multiply whole numbers systematically
- Enjoy solving multiplication problems

- Make number wheel and spin to multiply
- Arrange numbers vertically and multiply by ones, tens, hundreds
- Solve problems like worker salaries

How do we multiply large numbers?

- Smart Minds Mathematics Learner's Book pg. 22
- Number wheel
- Calculators
- Smart Minds Mathematics Learner's Book pg. 23
- Number cards

- Written exercises - Class activities - Observation

Numbers

Whole Numbers - Working out combined operations (DMAS)
Whole Numbers - Applying combined operations in real life

By the end of the lesson, the learner should be able to:
- State the DMAS rule for combined operations
- Work out expressions with multiple operations
- Show interest in solving combined operations

- Make cards with combined operations expressions
- Discuss order: Division, Multiplication, Addition, Subtraction
- Work out expressions like 260-255+340-105

What is the order of operations in DMAS?

- Smart Minds Mathematics Learner's Book pg. 24
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 25
- Calculators

- Written exercises - Oral questions - Class activities

Numbers

Whole Numbers - Identifying number sequences
Whole Numbers - Creating number sequences

By the end of the lesson, the learner should be able to:
- Define a number sequence
- Identify patterns in number sequences
- Show curiosity in number patterns

- Make number cards (2, 4, 8, 16, 32)
- Identify the rule creating the sequence
- Find next numbers in sequences like prime numbers

What is a number sequence?

- Smart Minds Mathematics Learner's Book pg. 25
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 26
- Digital devices

- Oral questions - Written exercises - Observation

Numbers

Factors - Divisibility test for 2
Factors - Divisibility test for 3
Factors - Divisibility test for 4

By the end of the lesson, the learner should be able to:
- State the divisibility rule for 2
- Test divisibility of numbers by 2
- Show interest in divisibility tests

- Make number cards with various numbers
- Identify numbers ending with even numbers or zero
- Determine which numbers are divisible by 2

How do we test if a number is divisible by 2?

- Smart Minds Mathematics Learner's Book pg. 27
- Number cards
- Divisibility worksheets
- Smart Minds Mathematics Learner's Book pg. 28
- Worksheets
- Smart Minds Mathematics Learner's Book pg. 29
- Charts

- Oral questions - Written exercises - Observation

Numbers

Factors - Divisibility tests for 5 and 6
Factors - Divisibility tests for 8, 9, 10 and 11
Factors - Prime factors of composite numbers

By the end of the lesson, the learner should be able to:
- State divisibility rules for 5 and 6
- Test divisibility of numbers by 5 and 6
- Show interest in divisibility patterns

- Identify numbers ending in 5 or 0 for divisibility by 5
- Test divisibility by both 2 and 3 for divisibility by 6
- Practice with various numbers

How do we test divisibility by 5 and 6?

- Smart Minds Mathematics Learner's Book pg. 30
- Number cards
- Divisibility charts
- Smart Minds Mathematics Learner's Book pg. 32
- Smart Minds Mathematics Learner's Book pg. 36
- Factor rainbow diagrams
- Factor trees

- Written assignments - Class activities - Oral questions

Numbers

Factors - GCD and LCM of numbers
Fractions - Comparing fractions
Fractions - Arranging fractions in order
Fractions - Adding fractions

By the end of the lesson, the learner should be able to:
- Define GCD and LCM
- Work out GCD and LCM of numbers by factor method
- Appreciate the application of GCD and LCM in real life

- List factors of numbers like 12 and 36 to find GCD
- List multiples of numbers like 8 and 12 to find LCM
- Solve problems like cutting sticks and ribbon lengths

How do we find the GCD and LCM of numbers?

- Smart Minds Mathematics Learner's Book pg. 37
- Factor charts
- Number cards
- Smart Minds Mathematics Learner's Book pg. 36
- Fraction cards
- Fraction charts
- Cut outs
- Fraction cut outs

- Written exercises - Class activities - Oral questions

Numbers

Fractions - Subtracting fractions
Fractions - Multiplying fractions by whole numbers and fractions
Fractions - Multiplying mixed numbers

By the end of the lesson, the learner should be able to:
- Explain the process of subtracting fractions
- Subtract fractions with different denominators
- Value accuracy in subtracting fractions

- Use cut outs and models to subtract fractions
- Find common denominators
- Subtract numerators and simplify results

How do we subtract fractions with different denominators?

- Smart Minds Mathematics Learner's Book pg. 36
- Fraction cut outs
- Concrete objects
- Fraction cards
- Charts
- Models

- Written assignments - Class activities - Oral questions

Numbers

Fractions - Reciprocals and dividing fractions
Fractions - Dividing whole numbers by fractions and mixed fractions
Fractions - Creating fraction sequences
Decimals - Place value of digits in decimals

By the end of the lesson, the learner should be able to:
- Define a reciprocal of a fraction
- Identify reciprocals and divide fractions using reciprocals
- Show confidence in dividing fractions

- Use flip cards to discuss reciprocals
- Multiply by reciprocal to divide fractions
- Practice division of fractions by whole numbers

What is the reciprocal of a fraction?

- Smart Minds Mathematics Learner's Book pg. 36
- Flip cards
- Fraction cards
- Fraction cards
- IT devices
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 56
- Place value charts
- Measuring instruments

- Written exercises - Oral questions - Observation

Numbers

Decimals - Total value of digits in decimals
Decimals - Multiplying decimals by whole numbers
Decimals - Multiplying decimals by decimals

By the end of the lesson, the learner should be able to:
- Define total value of digits in decimals
- Calculate total value of digits in decimal numbers
- Appreciate the use of total value in decimals

- Draw abacus showing decimal numbers
- Write down numbers represented on abacus
- Calculate total value by multiplying digit by its place value

How do we find the total value of a digit in a decimal?

- Smart Minds Mathematics Learner's Book pg. 59
- Abacus
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 60
- Number cards
- Calculators
- Smart Minds Mathematics Learner's Book pg. 61
- Square diagrams

- Written assignments - Class activities - Oral questions

Numbers

Decimals - Dividing decimals by whole numbers
Decimals - Dividing decimals by decimals
Squares and Square Roots - Squares of whole numbers

By the end of the lesson, the learner should be able to:
- Explain the process of dividing decimals by whole numbers
- Divide decimals by whole numbers
- Show interest in division of decimals

- Calculate width of compound given area and length
- Use long division method with decimals
- Solve problems involving cutting strings and packing flour

How do we divide decimals by whole numbers?

- Smart Minds Mathematics Learner's Book pg. 62
- Number cards
- Calculators
- Smart Minds Mathematics Learner's Book pg. 63
- Conversion tables
- Smart Minds Mathematics Learner's Book pg. 64
- Square grids

- Written exercises - Oral questions - Observation

Numbers

Squares and Square Roots - Squares of fractions
Squares and Square Roots - Squares of decimals
Squares and Square Roots - Square roots of whole numbers and fractions
Squares and Square Roots - Square roots of decimals

By the end of the lesson, the learner should be able to:
- Explain how to find squares of fractions
- Determine squares of proper and mixed fractions
- Appreciate the use of squares in real life

- Complete charts showing fractions and their squares
- Square numerator and denominator separately
- Convert mixed fractions to improper fractions before squaring

How do we find the square of a fraction?

- Smart Minds Mathematics Learner's Book pg. 65
- Fraction charts
- Number cards
- Smart Minds Mathematics Learner's Book pg. 66
- Square cut-outs
- Calculators
- Smart Minds Mathematics Learner's Book pg. 68
- Factor trees
- Smart Minds Mathematics Learner's Book pg. 70
- Number cards

- Written assignments - Class activities - Oral questions

Algebra

Algebraic Expressions - Forming expressions involving addition and subtraction
Algebraic Expressions - Forming expressions involving multiplication and division
Algebraic Expressions - Simplifying expressions involving addition and subtraction

By the end of the lesson, the learner should be able to:
- Define an algebraic expression
- Form algebraic expressions involving addition and subtraction from real life situations
- Show interest in forming algebraic expressions

- Discuss objects like oranges owned by different learners using letters x and y
- Write expressions for total number of items
- Form expressions from stories involving cows, eggs and ages

How do we form algebraic expressions from real life situations?

- Smart Minds Mathematics Learner's Book pg. 72
- Real objects (oranges, pencils)
- Number cards
- Smart Minds Mathematics Learner's Book pg. 73
- Pencils, sharpeners
- Price tags
- Smart Minds Mathematics Learner's Book pg. 74
- Shopping items
- Price lists

- Oral questions - Written exercises - Observation

Algebra

Algebraic Expressions - Simplifying expressions involving multiplication and division
Algebraic Expressions - Application of simplifying expressions
Linear Equations - Forming equations involving addition and subtraction
Linear Equations - Forming equations from word problems

By the end of the lesson, the learner should be able to:
- Explain how to remove brackets in algebraic expressions
- Simplify algebraic expressions involving brackets
- Value accuracy in simplifying expressions

- Make number cards with expressions like 5(x+4)+8(x+5)
- Remove brackets by multiplying number outside with terms inside
- Group like terms and simplify

How do we simplify expressions with brackets?

- Smart Minds Mathematics Learner's Book pg. 75
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 76
- Geometric shapes
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 77
- Beam balance
- Masses (weights)
- Smart Minds Mathematics Learner's Book pg. 78
- Word problem cards
- Number cards

- Written assignments - Class activities - Oral questions

Algebra

Linear Equations - Forming equations involving multiplication and division
Linear Equations - Solving equations involving addition and subtraction

By the end of the lesson, the learner should be able to:
- Explain how to form equations involving multiplication and division
- Form linear equations involving multiplication and division
- Show confidence in forming equations

- Read number card: "I think of a number. If I multiply by 3, I get 27"
- Form equation 3n = 27
- Write equations for area of rectangles: y × 5 = 40

How do we form equations involving multiplication and division?

- Smart Minds Mathematics Learner's Book pg. 79
- Number cards
- Rectangle diagrams
- Smart Minds Mathematics Learner's Book pg. 80
- Charts

- Written exercises - Oral questions - Observation

Algebra

Linear Equations - Solving equations involving multiplication and division
Linear Equations - Application of linear equations

By the end of the lesson, the learner should be able to:
- Explain how to solve equations with brackets
- Solve linear equations involving multiplication and division
- Appreciate the application of equations in real life

- Read story of Grace giving a third of her pencils to friends
- Open brackets and collect like terms
- Divide both sides by coefficient of unknown

How do we solve equations with brackets?

- Smart Minds Mathematics Learner's Book pg. 80
- Word problem cards
- Calculators
- Smart Minds Mathematics Learner's Book pg. 81
- Triangle diagrams
- Digital devices

- Written exercises - Oral questions - Observation

Algebra

Linear Inequalities - Inequality symbols
Linear Inequalities - Applying inequality symbols to statements

By the end of the lesson, the learner should be able to:
- Identify inequality symbols (<, >, ≤, ≥)
- Use inequality symbols to compare quantities
- Show interest in using inequality symbols

- Use see-saw to compare masses of learners
- Write Mary's mass > John's mass or John's mass < Mary's mass
- Fill spaces with correct inequality symbols

What are inequality symbols?

- Smart Minds Mathematics Learner's Book pg. 81
- See-saw
- Inequality cards
- Smart Minds Mathematics Learner's Book pg. 82
- Inequality cards
- Charts

- Oral questions - Written exercises - Observation

Algebra

Linear Inequalities - Forming inequalities involving addition and subtraction

By the end of the lesson, the learner should be able to:
- Define a linear inequality
- Form simple linear inequalities involving addition and subtraction
- Show confidence in forming inequalities

- Use beam balance with 5 kg on one side and 3 kg + sand on other side
- Let mass of sand be b kg and form inequality
- Form inequalities from stories about buses, oranges and goats

How do we form linear inequalities?

- Smart Minds Mathematics Learner's Book pg. 84
- Beam balance
- Masses

- Written exercises - Oral questions - Observation

Algebra

Linear Inequalities - Forming inequalities involving multiplication and division
Linear Inequalities - Illustrating simple inequalities on a number line

By the end of the lesson, the learner should be able to:
- Explain how to form inequalities from multiplication and division situations
- Form simple linear inequalities involving multiplication and division
- Value the use of inequalities in problem solving

- Read story of Eric and Maureen buying pencils at sh 10 each
- Form inequality: 10x + 10(x+3) < 100
- Form inequalities about plates, shirts and bananas

How do we form inequalities involving multiplication and division?

- Smart Minds Mathematics Learner's Book pg. 85
- Word problem cards
- Number cards
- Smart Minds Mathematics Learner's Book pg. 86
- Number lines
- Inequality cards

- Written assignments - Class activities - Oral questions

Algebra

Linear Inequalities - Forming compound inequalities
Linear Inequalities - Illustrating compound inequalities on a number line

By the end of the lesson, the learner should be able to:
- Define a compound inequality
- Form compound inequalities from two simple inequalities
- Appreciate the use of compound inequalities

- Look at inequality cards: y ≥ 2 and y < 7 combined as 2 ≤ y < 7
- Read story about Grade 7 Red with learners less than 45 but more than 40
- Form compound inequalities like 5 < y < 12

What is a compound inequality?

- Smart Minds Mathematics Learner's Book pg. 87
- Inequality cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 88
- Number lines
- Inequality cards

- Written assignments - Class activities - Oral questions

Algebra
Measurements

Linear Inequalities - Application of compound inequalities
Pythagorean Relationship - Sides of a right-angled triangle

By the end of the lesson, the learner should be able to:
- Identify real life situations involving compound inequalities
- Form and illustrate compound inequalities from word problems
- Value the application of inequalities in daily life

- Solve problems about farmers with goats (less than 8 but more than 6)
- Form compound inequality and illustrate on number line
- Solve problems about Katana buying oranges

Where do we use compound inequalities in real life?

- Smart Minds Mathematics Learner's Book pg. 88
- Word problem cards
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 89
- Ladders
- Right-angled triangle models

- Written assignments - Class activities - Oral questions

Measurements

Pythagorean Relationship - Establishing the relationship
Pythagorean Relationship - Finding unknown sides
Pythagorean Relationship - Real life applications
Length - Converting units of length

By the end of the lesson, the learner should be able to:
- State the Pythagorean relationship
- Verify Pythagorean relationship by counting squares
- Appreciate the relationship between sides of a right-angled triangle

- Trace and draw right-angled triangle with sides 3 cm, 4 cm and 5 cm
- Draw squares on each side and divide into 1 cm squares
- Count squares and compare: squares on height + squares on base = squares on hypotenuse

What is the Pythagorean relationship?

- Smart Minds Mathematics Learner's Book pg. 91
- Square grids
- Rulers and pencils
- Smart Minds Mathematics Learner's Book pg. 92
- Calculators
- Triangle diagrams
- Smart Minds Mathematics Learner's Book pg. 93
- Puzzles
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 94
- Conversion charts
- Metre rulers

- Written assignments - Class activities - Oral questions

Measurements

Length - Addition involving length
Length - Subtraction involving length
Length - Multiplication involving length

By the end of the lesson, the learner should be able to:
- Explain the process of adding lengths with different units
- Add lengths involving Hm, Dm, m, dm and cm
- Appreciate the use of addition of length in real life

- Study map showing distances between home, school and shopping centre
- Add lengths and regroup where necessary
- Solve problems like Munyao walking from home to market to school

How do we add lengths with different units?

- Smart Minds Mathematics Learner's Book pg. 96
- Maps
- Number cards
- Smart Minds Mathematics Learner's Book pg. 98
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 99
- Word problems
- Calculators

- Written assignments - Class activities - Oral questions

Measurements

Length - Division involving length
Length - Perimeter and circumference of circles
Area - Square metres, acres and hectares
Area - Area of a rectangle

By the end of the lesson, the learner should be able to:
- Describe the process of dividing lengths
- Divide lengths involving Hm, Dm, m, dm and cm
- Show interest in division of lengths

- Read story of relay race team of 4 members covering 6 Hm 5 Dm 6 m
- Divide each unit starting from highest, convert remainders
- Solve problems about road sections tarmacked by workers

How do we divide lengths by whole numbers?

- Smart Minds Mathematics Learner's Book pg. 100
- Word problems
- Charts
- Smart Minds Mathematics Learner's Book pg. 101
- Circular objects
- Tape measures
- Smart Minds Mathematics Learner's Book pg. 106
- Metre rulers
- Smart Minds Mathematics Learner's Book pg. 108
- Rectangular cut-outs
- Grid papers

- Written exercises - Oral questions - Observation

Measurements

Area - Area of a parallelogram
Area - Area of a rhombus
Area - Area of a trapezium

By the end of the lesson, the learner should be able to:
- Derive the formula for area of a parallelogram
- Calculate area of parallelograms
- Show confidence in finding area of parallelograms

- Cut out rectangle ABCD and mark point E on line AD
- Cut triangle ABE and paste on line DC to form parallelogram
- Discover: Area = Base length × Perpendicular height

How do we find the area of a parallelogram?

- Smart Minds Mathematics Learner's Book pg. 110
- Paper cut-outs
- Scissors
- Smart Minds Mathematics Learner's Book pg. 112
- Square cut-outs
- Smart Minds Mathematics Learner's Book pg. 114
- Rulers

- Written exercises - Oral questions - Observation

Measurements

Area - Area of circles
Area - Area of borders
Area - Area of combined shapes

By the end of the lesson, the learner should be able to:
- Derive the formula for area of a circle
- Calculate area of circles using πr²
- Show interest in finding area of circles

- Draw circle with radius 7 cm and divide into 16 sectors
- Cut and rearrange sectors to form rectangle
- Discover: Length = πr, Width = r, Area = πr²

How do we find the area of a circle?

- Smart Minds Mathematics Learner's Book pg. 116
- Pair of compasses
- Manila paper
- Smart Minds Mathematics Learner's Book pg. 119
- Picture frames
- Diagrams
- Smart Minds Mathematics Learner's Book pg. 121
- Combined shape diagrams
- Calculators

- Written assignments - Class activities - Oral questions

Measurements

Volume and Capacity - The cubic metre (m³)
Volume and Capacity - Converting m³ to cm³
Volume and Capacity - Converting cm³ to m³
Volume and Capacity - Volume of cubes

By the end of the lesson, the learner should be able to:
- Identify the cubic metre as a unit of measuring volume
- Make a model of a 1 metre cube
- Show interest in measuring volume

- Use metre rule, long sticks and strings to measure and cut 12 sticks of 1 m each
- Join sticks using strings to form a 1 metre cube
- Observe safety when using panga to cut sticks

What is a cubic metre?

- Smart Minds Mathematics Learner's Book pg. 122
- Metre rule
- Long sticks, strings
- Smart Minds Mathematics Learner's Book pg. 123
- 1 metre cube model
- Calculators
- Smart Minds Mathematics Learner's Book pg. 124
- Number cards
- Smart Minds Mathematics Learner's Book pg. 125
- Clay, plasticine
- Manila paper

- Oral questions - Practical activities - Observation

Measurements

Volume and Capacity - Volume of cuboids
Volume and Capacity - Volume of cylinders
Volume and Capacity - Relating volume to capacity

By the end of the lesson, the learner should be able to:
- State the formula for volume of a cuboid
- Calculate volume of cuboids
- Appreciate the use of volume in real life

- Draw cuboid and shade one face (cross-sectional area)
- Establish: Volume = Length × Width × Height
- Model cuboids using locally available materials

How do we find the volume of a cuboid?

- Smart Minds Mathematics Learner's Book pg. 126
- Clay, cartons
- Rulers
- Smart Minds Mathematics Learner's Book pg. 128
- Coins, cylindrical objects
- Smart Minds Mathematics Learner's Book pg. 130
- Containers, basin
- Measuring cylinder

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Application of volume and capacity
Time, Distance and Speed - Units of measuring time
Time, Distance and Speed - Converting hours and minutes
Time, Distance and Speed - Converting minutes and seconds

By the end of the lesson, the learner should be able to:
- Calculate capacity of containers in litres
- Solve problems involving volume and capacity
- Appreciate the application of volume and capacity in daily life

- Collect containers of different shapes
- Find volume and convert to capacity in litres
- Solve problems about tanks, tins and pipes

Where do we use volume and capacity in daily life?

- Smart Minds Mathematics Learner's Book pg. 132
- Various containers
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 134
- Clock faces
- Stopwatches
- Smart Minds Mathematics Learner's Book pg. 136
- Paper clock faces
- Smart Minds Mathematics Learner's Book pg. 138
- Stopwatches
- Number cards

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Converting hours and seconds
Time, Distance and Speed - Converting units of distance
Time, Distance and Speed - Speed in km/h

By the end of the lesson, the learner should be able to:
- State the relationship between hours and seconds
- Convert hours to seconds and seconds to hours
- Value accuracy in converting time units

- Fill tables showing hours, minutes and seconds
- Establish: 1 hour = 3,600 seconds
- Solve problems about assignments, journeys and power saws

How do we convert hours to seconds?

- Smart Minds Mathematics Learner's Book pg. 140
- Calculators
- Conversion charts
- Smart Minds Mathematics Learner's Book pg. 142
- Maps
- Measuring tapes
- Smart Minds Mathematics Learner's Book pg. 144
- Athletics field
- Stopwatches

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Speed in m/s
Time, Distance and Speed - Converting km/h to m/s and vice versa
Temperature - Temperature in our environment

By the end of the lesson, the learner should be able to:
- Calculate speed in metres per second
- Solve problems involving speed in m/s
- Value the application of speed in real life

- Mark 100 m distance in the field
- Run 100 m race and record time using stopwatch
- Calculate speed in m/s

What is speed in metres per second?

- Smart Minds Mathematics Learner's Book pg. 145
- Measuring tape
- Stopwatches
- Smart Minds Mathematics Learner's Book pg. 146
- Conversion charts
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 149
- Thermometers
- Charts

- Written exercises - Oral questions - Observation

Measurements

Temperature - Comparing temperature
Temperature - Units of measuring temperature
Temperature - Converting °C to Kelvin
Temperature - Converting Kelvin to °C

By the end of the lesson, the learner should be able to:
- Compare temperature of different objects
- Use warmer, colder, hotter to compare temperature
- Appreciate the importance of temperature in daily life

- Shake hands with partner and compare warmth
- Compare coldness of tap water and ice cubes
- Compare temperature of metallic and wooden objects

How do we compare temperature?

- Smart Minds Mathematics Learner's Book pg. 150
- Ice cubes
- Metallic and wooden objects
- Smart Minds Mathematics Learner's Book pg. 151
- Thermometers
- Sufuria, water
- Smart Minds Mathematics Learner's Book pg. 153
- Calculators
- Smart Minds Mathematics Learner's Book pg. 154
- Temperature tables

- Written assignments - Class activities - Oral questions

Measurements

Temperature - Temperature changes
Money - Profit
Money - Loss

By the end of the lesson, the learner should be able to:
- Calculate rise or drop in temperature
- Solve problems involving temperature changes
- Show interest in temperature changes in daily life

- Record temperature at different times (8:00 a.m., 2:00 p.m.)
- Calculate temperature rise: Final temp - Initial temp
- Calculate temperature drop: Initial temp - Final temp

How do we calculate temperature changes?

- Smart Minds Mathematics Learner's Book pg. 155
- Thermometers
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 157
- Classroom shop
- Paper money
- Smart Minds Mathematics Learner's Book pg. 159
- Price tables
- Charts

- Written assignments - Class activities - Oral questions

Measurements

Money - Percentage profit
Money - Percentage loss
Money - Discount
Money - Percentage discount

By the end of the lesson, the learner should be able to:
- Define percentage profit
- Calculate percentage profit
- Show confidence in calculating percentage profit

- Draw tables with buying price, selling price and profit
- Work out percentage profit = (Profit ÷ Buying price) × 100%
- Solve problems about shirts, books and goods

How do we calculate percentage profit?

- Smart Minds Mathematics Learner's Book pg. 160
- Tables
- Calculators
- Smart Minds Mathematics Learner's Book pg. 162
- Smart Minds Mathematics Learner's Book pg. 164
- Price tags
- Charts
- Smart Minds Mathematics Learner's Book pg. 166

- Written exercises - Oral questions - Observation

Measurements

Money - Commission and percentage commission
Money - Interpreting bills
Money - Preparing bills

By the end of the lesson, the learner should be able to:
- Define commission as payment for selling goods
- Calculate commission and percentage commission
- Value the role of commission in business

- Read story of Mzee Mambo Leo's motor vehicle firm
- Study table showing Dansam's weekly commission
- Calculate: % Commission = (Commission ÷ Value of goods sold) × 100%

What is commission in business?

- Smart Minds Mathematics Learner's Book pg. 167
- Commission tables
- Calculators
- Smart Minds Mathematics Learner's Book pg. 171
- Sample bills
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 172
- Bill formats
- Paper money

- Written exercises - Oral questions - Observation

Measurements

Money - Postal charges

By the end of the lesson, the learner should be able to:
- Identify postal services and charges
- Calculate cost of sending letters, parcels and postcards
- Appreciate postal services in communication

- Visit nearby post office to gather information
- Prepare chart showing postal charges by mass limits
- Calculate costs for different letters and parcels

How do we calculate postal charges?

- Smart Minds Mathematics Learner's Book pg. 173
- Postal charge tables
- Charts

- Written assignments - Class activities - Oral questions

Measurements
Geometry

Money - Mobile money services
Money - Mobile money transactions
Angles - Angles on a straight line

By the end of the lesson, the learner should be able to:
- Identify mobile money services (deposit, withdraw, transfer, save, borrow)
- Explain the importance of mobile money services
- Value the convenience of mobile money

- Read story of Mr Mamboleo using mobile money in his shop
- Identify services: pay bill, transfer, save, withdraw, borrow
- Complete word puzzle circling mobile money services

What are mobile money services?

- Smart Minds Mathematics Learner's Book pg. 178
- Word puzzles
- Charts
- Smart Minds Mathematics Learner's Book pg. 179
- Transaction tables
- Calculators
- Smart Minds Mathematics Learner's Book pg. 184
- Protractors
- Rulers

- Written exercises - Oral questions - Observation

Geometry

Angles - Angles at a point
Angles - Vertically opposite angles
Angles - Alternate angles on a transversal

By the end of the lesson, the learner should be able to:
- Identify angles formed at a point
- State that angles at a point add up to 360°
- Appreciate the relationship between angles at a point

- Trace and cut out diagram with angles ACB, ACD and BCD
- Use protractor to measure each angle
- Find sum of angles and establish they add up to 360°

What is the sum of angles at a point?

- Smart Minds Mathematics Learner's Book pg. 186
- Protractors
- Paper cut-outs
- Smart Minds Mathematics Learner's Book pg. 187
- Scissors
- Smart Minds Mathematics Learner's Book pg. 188
- Rulers

- Written assignments - Class activities - Oral questions

Geometry

Angles - Corresponding angles on a transversal
Angles - Co-interior angles on a transversal
Angles - Angles in a parallelogram
Angles - Interior angles of triangles, rectangles, squares

By the end of the lesson, the learner should be able to:
- Identify corresponding angles on a transversal
- State that corresponding angles are equal
- Show interest in properties of corresponding angles

- Draw pair of parallel lines and a transversal
- Mark angles v and r, cut them out
- Compare by placing one on top of the other (corresponding angles are equal)

What are corresponding angles?

- Smart Minds Mathematics Learner's Book pg. 190
- Rulers
- Scissors, protractors
- Smart Minds Mathematics Learner's Book pg. 191
- Smart Minds Mathematics Learner's Book pg. 193
- Straws, string
- Protractors
- Smart Minds Mathematics Learner's Book pg. 195
- Protractors
- Polygon cut-outs

- Written exercises - Oral questions - Observation

Geometry

Angles - Interior angles of rhombus, parallelogram, trapezium, pentagon, hexagon
Angles - Exterior angles of polygons

By the end of the lesson, the learner should be able to:
- Identify interior angles of various polygons
- Calculate sum of interior angles using formula (n-2) × 180°
- Appreciate the relationship between sides and interior angles

- Trace and cut out rhombus, parallelogram, trapezium
- Measure interior angles and find sums
- Sub-divide pentagon into 3 triangles, hexagon into 4 triangles

How do we calculate sum of interior angles of any polygon?

- Smart Minds Mathematics Learner's Book pg. 197
- Polygon cut-outs
- Protractors
- Smart Minds Mathematics Learner's Book pg. 201

- Written exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Measuring angles
Geometrical Constructions - Bisecting angles
Geometrical Constructions - Constructing 90° angle

By the end of the lesson, the learner should be able to:
- Use a protractor to measure angles accurately
- Draw angles of given sizes
- Show interest in measuring angles

- Trace and draw figures with angles ABC, BAC, ACB, ACD
- Place protractor with centre at vertex, straight edge along one line
- Read angle measure from correct scale

How do we measure angles using a protractor?

- Smart Minds Mathematics Learner's Book pg. 207
- Protractors
- Rulers
- Smart Minds Mathematics Learner's Book pg. 208
- Pair of compasses
- Smart Minds Mathematics Learner's Book pg. 210
- Rulers, protractors

- Oral questions - Practical activities - Observation

Geometry

Geometrical Constructions - Constructing 45° angle
Geometrical Constructions - Constructing 60° angle
Geometrical Constructions - Constructing 30° angle
Geometrical Constructions - Constructing 120° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 45° by bisecting 90°
- Verify the constructed angle
- Value accuracy in geometrical constructions

- Draw horizontal line, mark point K
- Construct 90° angle (MKB = 90°)
- Bisect angle MKB: make arcs at S and R, draw arcs to intersect at O, join O to K

How do we construct an angle of 45°?

- Smart Minds Mathematics Learner's Book pg. 211
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 213
- Rulers, protractors
- Smart Minds Mathematics Learner's Book pg. 214
- Smart Minds Mathematics Learner's Book pg. 215

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 105° and 75° angles
Geometrical Constructions - Constructing equilateral triangles

By the end of the lesson, the learner should be able to:
- Construct angles of 105° and 75°
- Combine construction of 90° and 60° to get 105°
- Value the application of angle constructions

- Draw line MN, mark point T
- Construct 90° angle (NTO = 90°), then construct 60° on other side (angle KTO = 60°)
- Bisect angle KTO to get 30°, thus angle PTN = 90° + 15° = 105°

How do we construct an angle of 105°?

- Smart Minds Mathematics Learner's Book pg. 216
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 218

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing isosceles triangles
Geometrical Constructions - Constructing scalene triangles

By the end of the lesson, the learner should be able to:
- Construct isosceles triangles given side measurements
- Verify that two sides and two angles are equal
- Show confidence in constructing triangles

- Draw straight line, mark point M, mark point N 5 cm away
- With M as centre and radius 7 cm, draw arc above line
- With N as centre and radius 5 cm, draw arc to intersect at P, join points

How do we construct an isosceles triangle?

- Smart Minds Mathematics Learner's Book pg. 219
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 220

- Written assignments - Practical activities - Oral questions

Geometry
Data Handling and Probability
Data Handling and Probability

Geometrical Constructions - Constructing circles
Data Handling - Meaning of data and data collection
Data Handling - Frequency tables

By the end of the lesson, the learner should be able to:
- Construct circles given radius or diameter
- Measure and verify the dimensions of constructed circles
- Appreciate the application of geometrical constructions in real life

- Use pair of compasses to draw circles with different diameters
- Measure diameter of circles drawn
- Calculate radius from diameter (radius = diameter ÷ 2)

How do we construct circles with given measurements?

- Smart Minds Mathematics Learner's Book pg. 221
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 222
- Pieces of paper
- Basket
- Smart Minds Mathematics Learner's Book pg. 223
- Class registers
- Frequency table templates

- Written assignments - Practical activities - Oral questions

Data Handling and Probability

Data Handling - Determining suitable scale
Data Handling - Drawing pictographs
Data Handling - Drawing bar graphs

By the end of the lesson, the learner should be able to:
- Explain the importance of choosing appropriate scale
- Determine suitable scale for vertical and horizontal axes
- Show confidence in selecting scales for graphs

- Compare Anne's and Josephine's graph scales
- Observe that congested scales make graphs hard to interpret
- Use multiples of 2 or 5 to make divisions easy to plot

Why is it important to choose a suitable scale for graphs?

- Smart Minds Mathematics Learner's Book pg. 225
- Graph papers
- Rulers
- Smart Minds Mathematics Learner's Book pg. 226
- Bloating paper
- Scissors, glue
- Smart Minds Mathematics Learner's Book pg. 228
- Rulers, coloured pencils

- Written exercises - Oral questions - Observation

Data Handling and Probability

Data Handling - Interpreting information from bar graphs
Data Handling - Drawing pie charts
Data Handling - Interpreting pie charts
Data Handling - Drawing line graphs
Data Handling - Interpreting travel graphs

By the end of the lesson, the learner should be able to:
- Read and interpret information from bar graphs
- Answer questions based on bar graph data
- Show interest in analyzing data from bar graphs

- Study bar graph showing fruits sold by Bahati in five days
- Identify scale used on vertical and horizontal axes
- Answer questions about highest, lowest values and comparisons

How do we interpret information from bar graphs?

- Smart Minds Mathematics Learner's Book pg. 231
- Bar graph samples
- Worksheets
- Smart Minds Mathematics Learner's Book pg. 233
- Pair of compasses
- Protractors
- Smart Minds Mathematics Learner's Book pg. 236
- Pie chart samples
- Calculators
- Smart Minds Mathematics Learner's Book pg. 238
- Graph papers
- Rulers
- Smart Minds Mathematics Learner's Book pg. 240

- Written assignments - Class activities - Oral questions