Numbers

Fractions - Multiplying mixed numbers

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

- Written assignments - Class activities - Oral questions

Numbers

Fractions - Reciprocals and dividing fractions
Fractions - Dividing whole numbers by fractions and mixed fractions

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

- Written exercises - Oral questions - Observation

Numbers

Fractions - Creating fraction sequences
Decimals - Place value of digits in decimals

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

- Identify patterns in fraction sequences
- Create fraction sequences using different rules
- Enjoy creating fraction puzzles

- Identify patterns in fraction sequences
- Create fraction sequences using different rules
- Play games creating number puzzles with fractions using IT devices

How do we identify and create fraction sequences?

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

- Class activities - Written exercises - 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

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

- Written exercises - Oral questions - Observation

Numbers

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

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

- Define the square of a number
- Determine squares of whole numbers by multiplication
- Show interest in finding squares of numbers

- Draw square grids to find squares of numbers
- Calculate area of square flowerbeds
- Use long multiplication to find squares

How do we find the square of a whole number?

- Smart Minds Mathematics Learner's Book pg. 64
- Square grids
- Calculators
- Smart Minds Mathematics Learner's Book pg. 65
- Fraction charts
- Number cards

- Oral questions - Written exercises - Observation

Numbers

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:

- State the rule for decimal places when squaring decimals
- Determine squares of decimals
- Value accuracy in calculating squares of decimals

- Cut out ribbons and make square figures during Visual Arts
- Find area of squares with decimal sides
- Observe that square has double the decimal places

How do we find the square of a decimal?

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

- Written exercises - Oral questions - Observation

Algebra

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

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

- Oral questions - Written exercises - Observation

Algebra

Algebraic Expressions - Simplifying expressions involving addition and subtraction
Algebraic Expressions - Simplifying expressions involving multiplication and division
Algebraic Expressions - Application of simplifying expressions

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

- Define like terms in algebraic expressions
- Simplify algebraic expressions by grouping like terms
- Show confidence in simplifying expressions

- Read story of Otieno buying pens and pencils at different prices
- Write expression for total amount spent
- Group like terms together and simplify

What are like terms in algebraic expressions?

- Smart Minds Mathematics Learner's Book pg. 74
- Shopping items
- Price lists
- Smart Minds Mathematics Learner's Book pg. 75
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 76
- Geometric shapes
- Digital devices

- Written exercises - Oral questions - Observation

Algebra

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:

- Define a linear equation
- Form linear equations involving addition and subtraction
- Show interest in forming equations

- Use beam balance with 5 kg mass on one side
- Place 2 kg mass and add sand of unknown mass x until balanced
- Write equation to show relationship: x + 2 = 5

What is a linear equation?

- 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

- Oral questions - Written exercises - Observation

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

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

- Written exercises - Oral questions - Observation

Algebra

Linear Equations - Application of linear equations

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

- Identify real life problems involving linear equations
- Solve problems using linear equations
- Show interest in applying equations to real life

- Solve problems about Mwandawiro's salary and school fees
- Find interior angles of triangles using equations
- Solve problems about Kahuho's bags of maize

Where do we apply linear equations in daily life?

- Smart Minds Mathematics Learner's Book pg. 81
- Triangle diagrams
- Digital devices

- Written assignments - Class activities - Oral questions

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
Linear Inequalities - Forming inequalities involving addition and subtraction

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

- Written assignments - Class activities - Oral questions

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

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

- Written exercises - Oral questions - Observation

Algebra
Measurements
Measurements

Linear Inequalities - Application of compound inequalities
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 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
- Smart Minds Mathematics Learner's Book pg. 91
- Square grids
- Rulers and pencils

- Written assignments - Class activities - Oral questions

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

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

- Oral questions - Written exercises - Observation

Measurements

Length - Subtraction involving length
Length - Multiplication involving length
Length - Division involving length

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

- Describe the process of subtracting lengths
- Subtract lengths involving Hm, Dm, m, dm and cm
- Show confidence in subtracting lengths

- Make cards with subtraction problems
- Regroup where necessary (borrow from higher unit)
- Solve problems comparing distances covered by Joan and John

How do we subtract lengths with different units?

- Smart Minds Mathematics Learner's Book pg. 98
- Number cards
- Charts
- Smart Minds Mathematics Learner's Book pg. 99
- Word problems
- Calculators
- Smart Minds Mathematics Learner's Book pg. 100

- Written exercises - Oral questions - Observation

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

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

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of a rhombus
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 rhombus
- Calculate area of rhombuses
- Value accuracy in calculating area

- Cut out square WXYZ and mark point K on line WX
- Cut triangle WKZ and paste on line XY to form rhombus
- Discover: Area = Base length × Perpendicular height

How do we find the area of a rhombus?

- Smart Minds Mathematics Learner's Book pg. 112
- Square cut-outs
- Scissors
- 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 assignments - Class activities - Oral questions

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

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

- Oral questions - Practical activities - Observation

Measurements

Volume and Capacity - Converting cm³ to m³
Volume and Capacity - Volume of cubes
Volume and Capacity - Volume of cuboids

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

- Explain conversion of cm³ to m³
- Convert cubic centimetres to cubic metres
- Show confidence in converting units of volume

- Make number cards with volumes in cm³ (2,000,000 cm³, 7,000,000 cm³)
- Convert to m³ by dividing by 1,000,000
- Solve problems about oil tankers and water tanks

How do we convert cubic centimetres to cubic metres?

- Smart Minds Mathematics Learner's Book pg. 124
- Number cards
- Calculators
- Smart Minds Mathematics Learner's Book pg. 125
- Clay, plasticine
- Manila paper
- Smart Minds Mathematics Learner's Book pg. 126
- Clay, cartons
- Rulers

- Written exercises - Oral questions - Observation

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
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:

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

- Written exercises - Oral questions - Observation