Numbers

Fractions - Multiplying fractions by whole numbers and fractions

By the end of the lesson, the learner should be able to:

- Describe the process of multiplying fractions
- Multiply fractions by whole numbers and fractions
- Show interest in multiplying fractions

- Use fraction cards and models to multiply
- Convert whole numbers to fractions
- Multiply numerators and denominators

How do we multiply fractions?

- Smart Minds Mathematics Learner's Book pg. 36
- Fraction cards
- Charts

- Written exercises - Oral questions - Observation

Numbers

Fractions - Multiplying mixed numbers
Fractions - Reciprocals and dividing fractions

By the end of the lesson, the learner should be able to:

- Explain how to convert mixed numbers to improper fractions
- Multiply mixed numbers
- Appreciate the use of multiplication of fractions in real life

- Convert mixed numbers to improper fractions
- Multiply and convert answers to mixed numbers
- Solve real life problems involving multiplication

Where do we use multiplication of fractions in daily life?

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

- Written assignments - Class activities - Oral questions

Numbers

Fractions - Dividing whole numbers by fractions and mixed fractions
Fractions - Creating fraction sequences

By the end of the lesson, the learner should be able to:

- Explain the process of dividing whole numbers by fractions
- Divide whole numbers by fractions and mixed fractions
- Value the application of division of fractions

- Convert whole numbers to fractions
- Use reciprocals to divide
- Solve problems involving division of mixed fractions

How do we divide whole numbers by fractions?

- Smart Minds Mathematics Learner's Book pg. 36
- Fraction cards
- IT devices
- Digital devices

- Written assignments - Class activities - Oral questions

Numbers

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

By the end of the lesson, the learner should be able to:

- Identify place value of digits in decimals up to hundred thousandths
- Use place value charts to represent decimals
- Show interest in learning decimal place values

- Measure masses and record in decimals
- Fill masses in place value charts showing tenths, hundredths, thousandths, ten thousandths and hundred thousandths
- Discuss where decimals are used in real life

What is the place value of digits in decimals?

- Smart Minds Mathematics Learner's Book pg. 56
- Place value charts
- Measuring instruments
- Smart Minds Mathematics Learner's Book pg. 59
- Abacus
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 60
- Number cards
- Calculators

- Oral questions - Written exercises - Observation

Numbers

Decimals - Multiplying decimals by decimals
Decimals - Dividing decimals by whole numbers

By the end of the lesson, the learner should be able to:

- State the rule for decimal places in multiplication
- Multiply decimals by decimals
- Value accuracy in multiplying decimals

- Calculate area of innovative gardens in shape of squares
- Count total decimal places in both numbers
- Multiply and place decimal point correctly in answer

How do we multiply decimals by decimals?

- Smart Minds Mathematics Learner's Book pg. 61
- Square diagrams
- Calculators
- Smart Minds Mathematics Learner's Book pg. 62
- Number cards

- Written assignments - Class activities - Oral questions

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:

- Describe the method of dividing decimals by decimals
- Divide decimals by decimals using reciprocals
- Appreciate the application of division of decimals in real life

- Draw and complete tables converting decimals to fractions
- Multiply dividend by reciprocal of divisor
- Solve problems like cutting sugarcane and buying maize

How do we divide decimals by decimals?

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

- Written assignments - Class activities - Oral questions

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

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

- Written assignments - Class activities - Oral questions

Numbers
Algebra

Squares and Square Roots - Square roots of decimals
Algebraic Expressions - Forming expressions involving addition and subtraction

By the end of the lesson, the learner should be able to:

- Describe the process of finding square roots of decimals
- Determine square roots of decimals
- Appreciate the application of square roots in real life

- Convert decimals to fractions
- Find square root of the fraction
- Solve problems involving area of square gardens and tables

How do we find the square root of a decimal?

- Smart Minds Mathematics Learner's Book pg. 70
- Number cards
- Calculators
- Smart Minds Mathematics Learner's Book pg. 72
- Real objects (oranges, pencils)
- Number cards

- Written exercises - Oral questions - Class activities

Algebra

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:

- Explain the process of forming expressions involving multiplication and division
- Form algebraic expressions involving multiplication and division
- Appreciate the use of algebraic expressions in real life

- Collect objects like pencils and sharpeners and group similar objects
- Let selling price of pencil be sh p and sharpeners be sh b
- Write expressions for cost of buying multiple items

How do we form expressions involving multiplication and division?

- Smart Minds Mathematics Learner's Book pg. 73
- Pencils, sharpeners
- Price tags
- Smart Minds Mathematics Learner's Book pg. 74
- Shopping items
- Price lists

- Written assignments - Class activities - Oral questions

Algebra

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

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)

- Written assignments - Class activities - Oral questions

Algebra

Linear Equations - Forming equations from word problems
Linear Equations - Forming equations involving multiplication and division

By the end of the lesson, the learner should be able to:

- Interpret word problems to form equations
- Form linear equations from real life situations
- Appreciate the use of equations in solving problems

- Form equations from stories about money, oranges, bananas and eggs
- Write equations like y + 3 = 11 for Juma's oranges
- Practice forming equations from various contexts

How do we form equations from word problems?

- Smart Minds Mathematics Learner's Book pg. 78
- Word problem cards
- Number cards
- Smart Minds Mathematics Learner's Book pg. 79
- Number cards
- Rectangle diagrams

- Written assignments - Class activities - Oral questions

Algebra

Linear Equations - Solving equations involving addition and subtraction

By the end of the lesson, the learner should be able to:

- State the steps for solving linear equations
- Solve linear equations involving addition and subtraction
- Value accuracy in solving equations

- Make number cards with equations like 4x + 2 = 18
- Collect like terms on each side of the equation
- Solve to find the value of the unknown

How do we solve linear equations?

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

- Written assignments - Class activities - Oral questions

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

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

- Oral questions - Written exercises - Observation

Algebra

Linear Inequalities - Applying inequality symbols to statements

By the end of the lesson, the learner should be able to:

- Explain the meaning of "at least" and "at most"
- Apply inequality symbols to real life statements
- Appreciate the use of inequalities in daily life

- Read story of Harriet visiting nutritionist about eggs and fruits
- Write: Number of eggs ≤ 2, Number of fruits ≥ 3
- Form inequalities from statements about height and volume

How do we apply inequality symbols to real life situations?

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

- Written assignments - Class activities - Oral questions

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

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

- Written assignments - Class activities - Oral questions

Algebra

Linear Inequalities - Illustrating simple inequalities on a number line

By the end of the lesson, the learner should be able to:

- Describe how to represent inequalities on a number line
- Illustrate simple inequalities using open and closed points
- Show interest in representing inequalities graphically

- Study number lines and list numbers greater than, less than, or equal to 5
- Use open point (○) when number is not included
- Use closed point (●) when number is included

How do we represent inequalities on a number line?

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

- Written exercises - Oral questions - Observation

Algebra

Linear Inequalities - Forming compound inequalities

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

- Written assignments - Class activities - Oral questions

Algebra

Linear Inequalities - Illustrating compound inequalities on a number line
Linear Inequalities - Application of compound inequalities

By the end of the lesson, the learner should be able to:

- Explain how to illustrate compound inequalities
- Illustrate compound inequalities on a number line
- Show confidence in representing compound inequalities

- Make inequality cards with compound inequalities
- Illustrate 3 < x ≤ 7 showing x greater than 3 and less than or equal to 7
- Use open and closed points appropriately

How do we illustrate compound inequalities on a number line?

- Smart Minds Mathematics Learner's Book pg. 88
- Number lines
- Inequality cards
- Word problem cards
- Digital devices

- Written exercises - Oral questions - Observation

Measurements

Pythagorean Relationship - Sides of a right-angled triangle
Pythagorean Relationship - Establishing the relationship

By the end of the lesson, the learner should be able to:

- Identify the sides of a right-angled triangle
- Name the base, height and hypotenuse of a right-angled triangle
- Show interest in learning about right-angled triangles

- Read story of Linda and Methuselah using a ladder to climb a fruit tree
- Draw figure formed between tree, ladder and ground
- Identify the longest side (hypotenuse) and two shorter sides (base and height)

What are the sides of a right-angled triangle?

- Smart Minds Mathematics Learner's Book pg. 89
- Ladders
- Right-angled triangle models
- Smart Minds Mathematics Learner's Book pg. 91
- Square grids
- Rulers and pencils

- Oral questions - Written exercises - Observation

Measurements

Pythagorean Relationship - Finding unknown sides
Pythagorean Relationship - Real life applications

By the end of the lesson, the learner should be able to:

- Explain how to use Pythagorean relationship to find unknown sides
- Calculate unknown sides using a² + b² = c²
- Show confidence in applying the relationship

- Use formula c² = a² + b² to find hypotenuse
- Use formula a² = c² - b² to find shorter sides
- Solve problems like finding length of ramp and ladder

How do we find unknown sides using Pythagorean relationship?

- Smart Minds Mathematics Learner's Book pg. 92
- Calculators
- Triangle diagrams
- Smart Minds Mathematics Learner's Book pg. 93
- Puzzles
- Digital devices

- Written exercises - Oral questions - Observation

Measurements

Length - Converting units of length
Length - Addition involving length
Length - Subtraction involving length

By the end of the lesson, the learner should be able to:

- Identify units of length (cm, dm, m, Dm, Hm)
- Convert units of length from one form to another
- Show interest in converting units of length

- Study Washika going up stairs labelled cm, dm, m, Dm, Hm
- Note that each step is 10 times the previous
- Generate conversion tables: 1 Hm = 10 Dm = 100 m = 1000 dm = 10000 cm

Why do we convert units of length?

- Smart Minds Mathematics Learner's Book pg. 94
- Conversion charts
- Metre rulers
- Smart Minds Mathematics Learner's Book pg. 96
- Maps
- Number cards
- Smart Minds Mathematics Learner's Book pg. 98
- Number cards
- Charts

- Oral questions - Written exercises - Observation

Measurements

Length - Multiplication involving length
Length - Division involving length

By the end of the lesson, the learner should be able to:

- Explain how to multiply lengths by whole numbers
- Multiply lengths involving Hm, Dm, m, dm and cm
- Value accuracy in multiplication of lengths

- Read story of Natasha fetching water from river twice daily
- Multiply each unit and regroup where necessary
- Solve problems about Jared's daily distance to school

How do we multiply lengths by whole numbers?

- Smart Minds Mathematics Learner's Book pg. 99
- Word problems
- Calculators
- Smart Minds Mathematics Learner's Book pg. 100
- Charts

- Written assignments - Class activities - Oral questions

Measurements

Length - Perimeter and circumference of circles
Area - Square metres, acres and hectares

By the end of the lesson, the learner should be able to:

- Define perimeter and circumference
- Calculate perimeter of plane figures and circumference of circles
- Appreciate the use of perimeter and circumference in real life

- Measure distance around chalkboard, door and window
- Measure circumference and diameter of circular objects
- Establish relationship: Circumference ÷ Diameter = π (3.14 or 22/7)

How do we find the circumference of a circle?

- Smart Minds Mathematics Learner's Book pg. 101
- Circular objects
- Tape measures
- Smart Minds Mathematics Learner's Book pg. 106
- Metre rulers

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of a rectangle
Area - Area of a parallelogram
Area - Area of a rhombus

By the end of the lesson, the learner should be able to:

- State the formula for area of a rectangle
- Calculate area of rectangles
- Appreciate the use of area in real life

- Trace and cut out rectangles
- Find area by multiplying length and width
- Complete tables with length, width and area of rectangles

How do we find the area of a rectangle?

- Smart Minds Mathematics Learner's Book pg. 108
- Rectangular cut-outs
- Grid papers
- Smart Minds Mathematics Learner's Book pg. 110
- Paper cut-outs
- Scissors
- Smart Minds Mathematics Learner's Book pg. 112
- Square cut-outs

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of a trapezium
Area - Area of circles

By the end of the lesson, the learner should be able to:

- Derive the formula for area of a trapezium
- Calculate area of trapezia
- Appreciate the application of area in land measurement

- Trace and cut out figure ABCD, mark point M on line AB
- Cut triangle ADM to form trapezium
- Discover: Area = ½(a + b) × h where a and b are parallel sides

How do we find the area of a trapezium?

- Smart Minds Mathematics Learner's Book pg. 114
- Paper cut-outs
- Rulers
- Smart Minds Mathematics Learner's Book pg. 116
- Pair of compasses
- Manila paper

- Written exercises - Oral questions - Observation

Measurements

Area - Area of borders
Area - Area of combined shapes

By the end of the lesson, the learner should be able to:

- Define the area of a border
- Calculate area of borders (shaded regions)
- Value accuracy in calculating area of borders

- Read story of Mary putting picture in frame
- Calculate: Area of border = Area of larger shape - Area of smaller shape
- Solve problems about picture frames, carpets and swimming pools

How do we find the area of a border?

- Smart Minds Mathematics Learner's Book pg. 119
- Picture frames
- Diagrams
- Smart Minds Mathematics Learner's Book pg. 121
- Combined shape diagrams
- Calculators

- Written exercises - Oral questions - Observation

Measurements

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

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

- Oral questions - Practical activities - Observation

Measurements

Volume and Capacity - Volume of cubes
Volume and Capacity - Volume of cuboids

By the end of the lesson, the learner should be able to:

- State the formula for volume of a cube
- Calculate volume of cubes
- Value accuracy in calculating volume

- Draw cube and colour one face (cross-sectional area)
- Establish: Volume = Side × Side × Side
- Model cubes using clay, plasticine or manila paper

How do we find the volume of a cube?

- Smart Minds Mathematics Learner's Book pg. 125
- Clay, plasticine
- Manila paper
- Smart Minds Mathematics Learner's Book pg. 126
- Clay, cartons
- Rulers

- Written assignments - Class activities - Oral questions

Measurements

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 cylinder
- Calculate volume of cylinders using πr²h
- Show interest in finding volume of cylinders

- Arrange pile of similar coins to form cylinder
- Measure diameter and height
- Establish: Volume = πr² × height

How do we find the volume of a cylinder?

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

- Written assignments - Class activities - Oral questions

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

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

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Converting minutes and seconds
Time, Distance and Speed - Converting hours and seconds

By the end of the lesson, the learner should be able to:

- State the relationship between minutes and seconds
- Convert minutes to seconds and seconds to minutes
- Show confidence in converting time units

- Use stopwatch to observe seconds in different minutes
- Establish: 1 minute = 60 seconds
- Solve problems about water pumps, walking distances

How do we convert minutes to seconds?

- Smart Minds Mathematics Learner's Book pg. 138
- Stopwatches
- Number cards
- Smart Minds Mathematics Learner's Book pg. 140
- Calculators
- Conversion charts

- Written exercises - Oral questions - Observation

Measurements

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 kilometres and metres
- Convert kilometres to metres and metres to kilometres
- Appreciate the use of distance conversions

- Estimate distances to nearby places in kilometres
- Convert estimated distances to metres
- Establish: 1 km = 1,000 m

How do we convert kilometres to metres?

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

- Written exercises - Oral questions - Observation

Measurements

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

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

- Written exercises - Oral questions - Observation