Numbers

Factors - Divisibility test for 4

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

- State the divisibility rule for 4
- Test divisibility of numbers by 4
- Value accuracy in applying divisibility rules

- Underline digits in ones and tens place value
- Check if number formed by last two digits is divisible by 4
- Practice with various numbers

How do we test if a number is divisible by 4?

- Smart Minds Mathematics Learner's Book pg. 29
- Number cards
- Charts

- Written exercises - Oral questions - Observation

Numbers

Factors - Divisibility tests for 5 and 6

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

- Written assignments - Class activities - Oral questions

Numbers

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 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

- Written exercises - Oral questions - Class activities

Numbers

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 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

- Written exercises - Oral questions - Class activities

Numbers

Factors - Prime factors of composite numbers

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

- Written assignments - Oral questions - Observation

Numbers

Factors - GCD and LCM of numbers

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

- Define GCD and LCM
- Work out GCD and LCM of numbers by factor method
- Appreciate the application of GCD and LCM in real life

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

How do we find the GCD and LCM of numbers?

- Smart Minds Mathematics Learner's Book pg. 37
- Factor charts
- Number cards

- Written exercises - Class activities - Oral questions

Numbers

Fractions - Comparing fractions

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

- Oral questions - Written exercises - Observation

Numbers

Fractions - Arranging fractions in order

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

- Written assignments - Class activities - Oral questions

Numbers

Fractions - Arranging fractions in order

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

- Written assignments - Class activities - Oral questions

Numbers

Fractions - Adding 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

- Written exercises - Oral questions - Observation

Numbers

Fractions - Subtracting fractions

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

- Explain the process of subtracting fractions
- Subtract fractions with different denominators
- Value accuracy in subtracting fractions

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

How do we subtract fractions with different denominators?

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

- Written assignments - Class activities - Oral questions

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

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 - 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

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

- Written exercises - Oral questions - Observation

Numbers

Fractions - Dividing whole numbers by fractions and mixed fractions

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

- Written assignments - Class activities - Oral questions

Numbers

Fractions - Creating fraction sequences

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

- Class activities - Written exercises - Observation

Numbers

Decimals - Place value of digits in decimals

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

- Oral questions - Written exercises - Observation

Numbers

Decimals - Place value of digits in decimals

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

- Oral questions - Written exercises - Observation

Numbers

Decimals - Total value of digits in 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

- Written assignments - Class activities - Oral questions

Numbers

Decimals - Multiplying decimals by whole numbers

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

- Explain the effect of multiplying decimals by 10 and 100
- Multiply decimals by whole numbers
- Show confidence in multiplying decimals

- Observe that multiplying by 10 moves decimal point 1 place right
- Observe that multiplying by 100 moves decimal point 2 places right
- Solve problems like mass of logs and metallic rods

How do we multiply decimals by whole numbers?

- Smart Minds Mathematics Learner's Book pg. 60
- Number cards
- Calculators

- Written exercises - Oral questions - Observation

Numbers

Decimals - Multiplying 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

- Written assignments - Class activities - Oral questions

Numbers

Decimals - Dividing decimals by 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

- Written exercises - Oral questions - Observation

Numbers

Decimals - Dividing decimals by 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

- Written exercises - Oral questions - Observation

Numbers

Decimals - Dividing decimals by decimals

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

- Written assignments - Class activities - Oral questions

Numbers

Squares and Square Roots - Squares of whole numbers

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

- Oral questions - Written exercises - Observation

Numbers

Squares and Square Roots - Squares of 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

- Written assignments - Class activities - Oral questions

Numbers

Squares and Square Roots - Squares 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

- Written exercises - Oral questions - Observation

Numbers

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

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

- Written assignments - Class activities - Oral questions

Numbers

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

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

- Written assignments - Class activities - Oral questions

Numbers

Squares and Square Roots - Square roots of decimals

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

- Written exercises - Oral questions - Class activities

Algebra

Algebraic Expressions - Forming 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

- Oral questions - Written exercises - Observation

Algebra

Algebraic Expressions - Forming expressions involving multiplication and division

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

- Written assignments - Class activities - Oral questions

Algebra

Algebraic Expressions - Simplifying expressions involving addition and subtraction

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

- Written exercises - Oral questions - Observation

Algebra

Algebraic Expressions - Simplifying expressions involving addition and subtraction

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

- Written exercises - Oral questions - Observation

Algebra

Algebraic Expressions - Simplifying expressions involving multiplication and division

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

- Written assignments - Class activities - Oral questions

Algebra

Algebraic Expressions - Application of simplifying expressions

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

- Identify algebraic expressions in geometric figures
- Simplify expressions to find perimeter and volume
- Appreciate the application of algebraic expressions in geometry

- Find perimeter of triangles with sides as algebraic expressions
- Find volume of figures with dimensions as expressions
- Solve problems involving rectangles with algebraic dimensions

Where do we apply algebraic expressions in real life?

- 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

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)

- Oral questions - Written exercises - Observation

Algebra

Linear Equations - Forming equations from word problems

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

- Written assignments - Class activities - Oral questions

Algebra

Linear Equations - Forming equations from word problems

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

- Written assignments - Class activities - Oral questions

Algebra

Linear Equations - Forming equations involving multiplication and division

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

- Written exercises - Oral questions - Observation

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

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 - 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 - 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 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