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

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

- Written assignments - Oral questions - Class activities

Numbers

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

By the end of the lesson, the learner should be able to:
- Explain the relationship between place value and total value
- Work out total value of underlined digits in numbers
- Value the importance of total value in daily activities

- Work out total value of digits in various numbers
- Solve word problems involving total value
- Discuss real life applications such as counting coffee trees or vaccinations

Where do we apply total value in daily life?

- Smart Minds Mathematics Learner's Book pg. 7
- Number cards
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 8
- Number charts
- Smart Minds Mathematics Learner's Book pg. 9
- Charts

- Written assignments - Class activities - Oral questions

Numbers

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

By the end of the lesson, the learner should be able to:
- State the rules for writing numbers in words
- Form different 7-digit numbers and read them in words
- Enjoy reading large numbers in words

- Make number cards 1-9
- Form four different 7-digit numbers
- Fill in place value charts and read numbers formed

How do we read large numbers in words?

- Smart Minds Mathematics Learner's Book pg. 10
- Number cards
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 11
- Dummy cheques
- Number cards
- Smart Minds Mathematics Learner's Book pg. 12
- Charts

- Oral questions - Observation - Class activities

Numbers

Whole Numbers - Practice reading and writing numbers

By the end of the lesson, the learner should be able to:
- Identify situations where numbers are written in words
- Read and write various numbers in words correctly
- Appreciate the use of numbers in daily activities

- Read numbers like 268,197 and write in words
- Write numbers from health campaigns and milk companies in words
- Find areas where numbers are written in both symbols and words

Where are numbers written in words in real life?

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

- Written assignments - Oral questions - Observation

Numbers

Whole Numbers - Rounding off to the nearest ten 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

- Written exercises - Oral questions - Class activities

Numbers

Whole Numbers - Rounding off to the nearest hundreds of millions
Whole Numbers - Practice rounding off numbers

By the end of the lesson, the learner should be able to:
- Identify the digit to consider when rounding off to hundreds of millions
- Round off numbers to the nearest hundreds of millions
- Value accuracy in rounding off numbers

- Read stories involving large numbers like supermarket sales
- Consider digit in tens of millions place value
- Apply rules: retain if 0-4, increase by 1 if 5-9

How do we round off to the nearest hundred million?

- Smart Minds Mathematics Learner's Book pg. 14
- Number cards
- Place value charts
- Smart Minds Mathematics Learner's Book pg. 16
- Calculators

- Written assignments - Class activities - Oral questions

Numbers

Whole Numbers - Identifying even 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

- Oral questions - Written exercises - Observation

Numbers

Whole Numbers - Identifying odd numbers

By the end of the lesson, the learner should be able to:
- Define odd numbers
- Identify odd numbers from a set of numbers
- Appreciate the difference between even and odd numbers

- Make number cards and sort those not divisible by two
- Identify digits in ones place (1, 3, 5, 7, 9)
- Classify numbers from production data as odd or even

What are odd numbers?

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

- Written assignments - Oral questions - Class activities

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

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

- Written exercises - Class activities - Observation

Numbers

Whole Numbers - Dividing whole numbers

By the end of the lesson, the learner should be able to:
- Explain the long division method
- Divide whole numbers systematically
- Value accuracy in division

- Read stories involving division (cement transportation)
- Work out division step by step
- Solve problems with and without remainders

How do we divide large numbers?

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

- Written assignments - Oral questions - Class activities

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

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

- Oral questions - Written exercises - Observation

Numbers

Whole Numbers - Creating number sequences
Factors - Divisibility test for 2

By the end of the lesson, the learner should be able to:
- Explain different rules for creating sequences
- Create addition, subtraction, multiplication and division sequences
- Enjoy creating number puzzles

- Create subtraction sequence starting from 1000
- Create addition sequence starting from 1012
- Play games creating number puzzles using IT devices

How do we create number sequences?

- Smart Minds Mathematics Learner's Book pg. 26
- Number cards
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 27
- Divisibility worksheets

- Class activities - Written exercises - Observation

Numbers

Factors - Divisibility test for 3
Factors - Divisibility test for 4
Factors - Divisibility tests for 5 and 6

By the end of the lesson, the learner should be able to:
- State the divisibility rule for 3
- Test divisibility of numbers by 3
- Appreciate patterns in divisibility tests

- Make number cards and add digits in each number
- Check if sum of digits is divisible by 3
- Work out exercises on divisibility by 3

How do we test if a number is divisible by 3?

- Smart Minds Mathematics Learner's Book pg. 28
- Number cards
- Worksheets
- Smart Minds Mathematics Learner's Book pg. 29
- Charts
- Smart Minds Mathematics Learner's Book pg. 30
- Divisibility charts

- Written assignments - Oral questions - Class activities

Numbers

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

By the end of the lesson, the learner should be able to:
- State divisibility rules for 8, 9, 10 and 11
- Test divisibility of numbers by 8, 9, 10 and 11
- Appreciate the use of divisibility tests

- Check if last 3 digits divisible by 8
- Add digits and check divisibility by 9
- Check if number ends in 0 for 10
- Find difference of alternate digit sums for 11

How do we test divisibility by 8, 9, 10 and 11?

- Smart Minds Mathematics Learner's Book pg. 32
- Number cards
- Divisibility charts
- Smart Minds Mathematics Learner's Book pg. 36
- Factor rainbow diagrams
- Factor trees
- Smart Minds Mathematics Learner's Book pg. 37
- Factor charts
- Number cards

- Written exercises - Oral questions - Class activities

Numbers

Fractions - Comparing fractions
Fractions - Arranging fractions in order

By the end of the lesson, the learner should be able to:
- Explain strategies for comparing fractions
- Compare fractions using different methods
- Show interest in comparing fractions

- Discuss strategies for comparing fractions
- Use fraction cards to arrange fractions
- Practice arranging fractions in increasing order

How do we compare fractions?

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

- Oral questions - Written exercises - Observation

Numbers

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

By the end of the lesson, the learner should be able to:
- State the steps for adding fractions
- Add fractions with different denominators
- Show confidence in adding fractions

- Use cut outs and fraction cards to add fractions
- Find LCM of denominators
- Add numerators and simplify results

How do we add fractions with different denominators?

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

- Written exercises - Oral questions - Observation

Numbers

Fractions - Multiplying mixed 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:
- 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
- Fraction cards
- IT devices

- Written assignments - Class activities - Oral questions

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
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

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

- Written assignments - Class activities - Oral questions

Numbers
Algebra

Squares and Square Roots - Square roots of whole numbers and fractions
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:
- Explain methods of finding square roots
- Determine square roots of whole numbers and fractions
- Show confidence in finding square roots

- Express numbers as products of prime factors
- Pair up similar factors and select one from each pair
- Use division method for larger numbers
- Find square root of numerator and denominator separately

How do we find the square root of a number?

- Smart Minds Mathematics Learner's Book pg. 68
- Factor trees
- Number cards
- Smart Minds Mathematics Learner's Book pg. 70
- Number cards
- Calculators
- Smart Minds Mathematics Learner's Book pg. 72
- Real objects (oranges, pencils)

- Written assignments - Class activities - Oral questions

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
Linear Equations - Solving equations involving addition and subtraction

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

- Written assignments - Class activities - Oral questions

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
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

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
Linear Inequalities - Forming compound inequalities

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

- Written exercises - Oral questions - Observation

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

Linear Inequalities - Application of compound inequalities

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

- Written assignments - Class activities - Oral questions