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

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

- Written assignments - Oral questions - Class activities

Numbers

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:

- Identify numbers written in symbols up to hundreds of millions
- Read numbers up to hundreds of millions
- Show confidence in reading large numbers

- Read aloud numbers on number cards
- Write numbers in symbols from word statements
- Practice with numbers like 124,755,212

Why do we write numbers in symbols?

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

- Oral questions - Written exercises - Observation

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
Whole Numbers - Identifying prime 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
- Smart Minds Mathematics Learner's Book pg. 19

- Written assignments - Oral questions - Class activities

Numbers

Whole Numbers - Adding whole numbers up to hundreds of millions

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

- Describe the process of adding large numbers
- Add whole numbers up to hundreds of millions using place value charts
- Show confidence in adding large numbers

- Make number cards and form 9-digit numbers
- Add two 9-digit numbers using place value charts
- Solve addition problems like company sales

How do we add large numbers?

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

- Written exercises - Class activities - Oral questions

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)

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

- Written exercises - Oral questions - Class activities

Numbers

Whole Numbers - Applying combined operations in real life

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

- Identify real life situations involving combined operations
- Solve real life problems using combined operations
- Appreciate the use of combined operations

- Solve problems like tomato sales and tree planting
- Work out stadium seating arrangements
- Apply combined operations in bread trading scenarios

Where do we use combined operations in daily life?

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

- Written assignments - Class activities - Oral questions

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

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

- Written assignments - Class activities - Oral questions

Numbers

Factors - Prime factors of composite numbers
Factors - GCD and LCM of numbers
Fractions - Comparing fractions

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

- Define prime factors and composite numbers
- Express composite numbers as product of prime factors
- Value the relationship between factors and prime factors

- List factors using factor rainbow
- Use factor tree method to find prime factors
- Express numbers like 56 and 98 as products of prime factors

How do we express numbers as products of prime factors?

- 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
- Fraction cards
- Fraction charts

- Written assignments - Oral questions - Observation

Numbers

Fractions - Arranging fractions in order
Fractions - Adding fractions
Fractions - Subtracting fractions

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

- Describe the process of ordering fractions
- Arrange fractions in ascending and descending order
- Appreciate the use of fractions in sharing

- Find LCM of denominators
- Convert fractions to equivalent fractions
- Arrange fractions from largest to smallest

How do we arrange fractions in ascending and descending order?

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

- Written assignments - Class activities - Oral questions

Numbers

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

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
- Fraction cut outs
- Models

- Written exercises - Oral questions - Observation

Numbers

Fractions - Reciprocals and dividing fractions
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:

- 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

- Written exercises - Oral questions - Observation

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
Decimals - Dividing decimals by decimals

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
- Smart Minds Mathematics Learner's Book pg. 63
- Conversion tables

- Written assignments - Class activities - Oral questions

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
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

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

- Written assignments - Class activities - Oral questions

Algebra

Linear Equations - Forming equations involving addition and subtraction
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:

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

- Oral questions - Written exercises - Observation

Algebra

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

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
- Word problem cards
- Calculators

- Written assignments - Class activities - Oral questions

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
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:

- 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
- Word problem cards
- Digital devices

- Written assignments - Class activities - Oral questions