Numbers and Algebra

Real Numbers - Odd and even numbers
Real Numbers - Prime and composite numbers

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

- Identify odd and even numbers
- Classify numbers as odd or even based on the ones place value
- Relate odd and even numbers to real life situations like sharing items equally

- Measure the height of classmates in centimetres and record in a table
- Classify each recorded number as odd or even
- Discuss with peers reasons for classification based on the digit in the ones place value

Why are numbers important?

- Mentor Essential Mathematics pg. 1
- Number cards
- Charts on odd and even numbers
- Mentor Essential Mathematics pg. 3
- Factor charts
- Number cards

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Rational and irrational numbers

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

- Define rational and irrational numbers
- Classify real numbers as rational or irrational
- Relate rational numbers to everyday measurements like prices and quantities

- Use digital devices to search for meaning of rational and irrational numbers
- Classify given numbers as rational or irrational
- Discuss examples of rational numbers in daily transactions

Why are numbers important?

- Mentor Essential Mathematics pg. 5
- Digital devices
- Number charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Rational and irrational numbers
Real Numbers - Combined operations on rational numbers

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

- Distinguish between terminating and non-terminating decimals
- Identify irrational numbers from square roots
- Connect irrational numbers to real measurements like diagonals of squares

- Express fractions as decimals and identify terminating decimals
- Determine which square roots are rational or irrational
- Discuss practical examples where irrational numbers appear

Why are numbers important?

- Mentor Essential Mathematics pg. 5
- Calculators
- Digital resources
- Mentor Essential Mathematics pg. 7
- Word problem cards

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Real Numbers - Combined operations on rational numbers
Real Numbers - Reciprocal of numbers

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

- Perform multiplication and division of rational numbers
- Solve problems involving all four operations
- Apply combined operations to solve problems on temperature changes and measurements

- Work out problems involving multiplication and division of fractions and decimals
- Solve word problems requiring multiple operations
- Discuss scenarios like temperature variations during the day

Why are numbers important?

- Mentor Essential Mathematics pg. 8
- Calculators
- Thermometer charts
- Mentor Essential Mathematics pg. 9
- Scientific calculators
- Digital devices

- Written tests - Class activities - Oral questions

Numbers and Algebra

Real Numbers - Application of rational numbers

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

- Apply rational numbers in solving real-life problems
- Solve problems involving fractions, decimals and mixed operations
- Connect rational numbers to daily activities like cooking, farming and finance

- Solve problems on sharing resources, measuring ingredients and calculating distances
- Discuss applications in budgeting, farming and construction
- Work with peers on real-life case scenarios

Why are numbers important?

- Mentor Essential Mathematics pg. 11
- Word problem cards
- Calculators

- Written tests - Portfolio - Class activities

Numbers and Algebra

Indices - Powers and bases

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

- Identify the base and power in index notation
- Express numbers as products of prime factors in index form
- Relate index form to expressing large numbers like population figures

- Write numbers as products of repeated factors
- Express products in index form identifying base and power
- Discuss how index notation simplifies large numbers

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 13
- Number cards
- Charts on indices

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices - Expressing numbers in index form

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

- Express whole numbers in simplest index form
- Express fractions in index form
- Apply index notation to scientific measurements and data

- Break down numbers into prime factors and express in index form
- Express fractions with numerator and denominator in index form
- Search for population data and express in index form

Why are indices important?

- Mentor Essential Mathematics pg. 14
- Calculators
- Digital resources

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Multiplication law

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

- State the multiplication law of indices
- Apply the multiplication law to simplify expressions
- Connect the multiplication law to calculating areas and volumes

- Write index numbers in expanded form
- Multiply numbers with the same base and add the powers
- Work out problems on area using index notation

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 15
- Index law charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Division law

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

- State the division law of indices
- Apply the division law to simplify expressions
- Relate division of indices to sharing and distribution problems

- Divide numbers with the same base by subtracting powers
- Simplify expressions using the division law
- Solve problems on distributing items among groups

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 16
- Index law charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Indices - Power of a power

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

- State the power of a power law
- Apply the law to simplify expressions with powers raised to powers
- Apply the law to compound growth calculations

- Expand expressions with powers of powers
- Multiply indices when a power is raised to another power
- Discuss applications in compound interest calculations

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 17
- Index law charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices - Zero index

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

- State the zero index law
- Apply the zero index to simplify expressions
- Understand why any non-zero number raised to power zero equals one

- Use division law to derive the zero index law
- Simplify expressions involving zero index
- Verify the zero index law using calculators

Why are indices important?

- Mentor Essential Mathematics pg. 18
- Calculators
- Index law charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices - Zero index

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

- State the zero index law
- Apply the zero index to simplify expressions
- Understand why any non-zero number raised to power zero equals one

- Use division law to derive the zero index law
- Simplify expressions involving zero index
- Verify the zero index law using calculators

Why are indices important?

- Mentor Essential Mathematics pg. 18
- Calculators
- Index law charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices - Applying laws of indices

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

- Apply multiple laws of indices in computations
- Simplify complex expressions using combined laws
- Apply indices to scientific notation and large number calculations

- Work out computations requiring multiple index laws
- Simplify expressions with mixed operations
- Use digital resources to explore applications of indices

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 19
- Calculators
- Digital devices

- Written tests - Class activities - Portfolio

Numbers and Algebra

Indices - Applying laws of indices in numerical computations

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

- Solve complex problems using laws of indices
- Evaluate numerical expressions involving indices
- Apply indices to solve real-world problems in science and technology

- Evaluate expressions combining all laws of indices
- Solve word problems involving indices
- Discuss applications in computing and scientific calculations

How are the laws of indices applied in real life?

- Mentor Essential Mathematics pg. 19
- Calculators
- Digital resources

- Written exercises - Class activities - Observation

Numbers and Algebra

Indices - Problem solving with indices

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

- Apply indices to solve practical problems
- Work collaboratively to solve index problems
- Connect indices to technological applications like data storage

- Work with peers on practical problems involving indices
- Present solutions and discuss different approaches
- Research applications of indices in computer memory and data

Why are indices important?

- Mentor Essential Mathematics pg. 20
- Digital devices
- Calculators

- Portfolio - Observation - Written tests

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions

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

- Form algebraic expressions from word statements
- Use letters to represent unknown quantities
- Relate algebraic expressions to real situations like shopping and measurements

- Read case scenarios and form algebraic expressions
- Use letters to represent unknown quantities
- Discuss how expressions represent real-life situations

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 21
- Word problem cards
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions

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

- Form algebraic expressions from word statements
- Use letters to represent unknown quantities
- Relate algebraic expressions to real situations like shopping and measurements

- Read case scenarios and form algebraic expressions
- Use letters to represent unknown quantities
- Discuss how expressions represent real-life situations

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 21
- Word problem cards
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Formation of algebraic expressions from real life

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

- Form complex algebraic expressions from multiple quantities
- Simplify algebraic expressions
- Apply algebraic expressions to calculate costs, distances and areas

- Form expressions involving multiple unknown quantities
- Simplify expressions by collecting like terms
- Solve problems on cost, profit and measurements

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 22
- Word problem cards
- Calculators

- Written exercises - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Formation of quadratic expressions

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

- Identify quadratic expressions
- Form quadratic expressions by multiplying binomials
- Relate quadratic expressions to calculating areas of rectangles

- Expand products of two binomials
- Identify the structure of quadratic expressions
- Discuss how quadratic expressions represent area problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 23
- Rectangular cut-outs
- Charts

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Quadratic expressions from real life situations

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

- Form quadratic expressions from real-life contexts
- Interpret word problems to generate quadratic expressions
- Apply quadratic expressions to floor plans, gardens and picture frames

- Read scenarios on area and form quadratic expressions
- Draw diagrams to visualize the problems
- Work out expressions for paths around gardens and margins

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 24
- Diagram charts
- Graph paper

- Written exercises - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Formation of quadratic equations

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

- Distinguish between quadratic expressions and equations
- Form quadratic equations from given conditions
- Apply quadratic equations to problems on area and dimensions

- Form quadratic equations from area problems
- Set up equations where expression equals a given value
- Discuss volleyball pitch and room dimension problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 25
- Diagram charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Formation of quadratic equations

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

- Distinguish between quadratic expressions and equations
- Form quadratic equations from given conditions
- Apply quadratic equations to problems on area and dimensions

- Form quadratic equations from area problems
- Set up equations where expression equals a given value
- Discuss volleyball pitch and room dimension problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 25
- Diagram charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Quadratic equations from word problems

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

- Form quadratic equations from various word problems
- Interpret real-life situations as quadratic equations
- Model age, product and sharing problems using quadratic equations

- Read and interpret word problems
- Form quadratic equations from age and product problems
- Discuss seedbed and carpet area problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 26
- Word problem cards
- Calculators

- Written tests - Class activities - Portfolio

Numbers and Algebra

Quadratic Equations - Factorisation of quadratic expressions

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

- Identify the coefficients a, b and c in quadratic expressions
- Find factor pairs of ac that sum to b
- Apply factorisation to expressions of the form x² + bx + c

- Identify values of a, b and c in quadratic expressions
- List factor pairs and identify the pair with required sum
- Factorise expressions by splitting the middle term

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 27
- Factor pair charts
- Calculators

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Factorisation by grouping

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

- Factorise quadratic expressions by grouping
- Apply the grouping method to various expressions
- Verify factorisation by expanding the factors

- Split the middle term into two terms
- Group terms and factorise each group
- Extract the common factor and complete factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 27
- Worked examples charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c

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

- Factorise quadratic expressions where a ≠ 1
- Apply systematic methods to factorise complex expressions
- Connect factorisation to finding dimensions from area expressions

- Find factors of ac and identify the pair summing to b
- Factorise expressions with leading coefficient greater than 1
- Discuss practical applications of factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Factor charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Factorisation of expressions ax² + bx + c

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

- Factorise quadratic expressions where a ≠ 1
- Apply systematic methods to factorise complex expressions
- Connect factorisation to finding dimensions from area expressions

- Find factors of ac and identify the pair summing to b
- Factorise expressions with leading coefficient greater than 1
- Discuss practical applications of factorisation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Factor charts
- Calculators

- Written tests - Class activities - Observation

Numbers and Algebra

Quadratic Equations - Solving by factorisation

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

- Apply factorisation to solve quadratic equations
- Find solutions by equating each factor to zero
- Verify solutions by substitution into the original equation

- Factorise the quadratic expression
- Set each factor equal to zero and solve for x
- Check solutions by substituting back into the equation

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 28
- Worked examples charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Equations - Solving equations with repeated roots

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

- Solve quadratic equations with repeated roots
- Identify perfect square trinomials
- Interpret the meaning of repeated roots in context

- Factorise perfect square trinomials
- Solve equations yielding single solutions
- Discuss what repeated roots mean in area problems

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 29
- Calculators
- Worked examples

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Equations - Applications to real life problems

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

- Apply quadratic equations to solve area problems
- Form and solve equations from word problems
- Interpret solutions in real-life contexts like room dimensions and garden sizes

- Form quadratic equations from dimension problems
- Solve and interpret solutions
- Determine dimensions of rooms, carpets and gardens

How are quadratic equations applied in real life?

- Mentor Essential Mathematics pg. 29
- Diagram charts
- Calculators

- Written tests - Portfolio - Class activities

Measurements and Geometry

Similarity and Enlargement - Properties of similar figures

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

- Identify properties of similar figures
- Compare corresponding sides and angles of similar figures
- Relate similarity to real life objects like photographs and maps

- Collect objects from the environment and sort similar objects together
- Measure corresponding sides of similar triangles and determine ratios
- Measure corresponding angles of similar figures
- Discuss reasons why objects are considered similar

How do we identify similar figures in our environment?

- Mentor Essential Mathematics pg. 31
- Similar objects (containers, shapes)
- Rulers and protractors
- Digital resources

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Properties of similar figures

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

- Determine whether given figures are similar
- Calculate ratios of corresponding sides
- Connect similar figures to everyday items like photo frames and tiles

- Work out ratios of corresponding sides of triangles
- Use protractor to measure corresponding angles
- Determine if rectangles are similar by comparing ratios
- Share findings with classmates

What conditions must be met for two figures to be similar?

- Mentor Essential Mathematics pg. 33
- Protractors
- Rulers
- Cut-outs of similar shapes

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Centre of enlargement and linear scale factor
Similarity and Enlargement - Linear scale factor

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

- Determine the centre of enlargement of similar figures
- Locate the centre by joining corresponding vertices
- Recognize how enlargement is used in projectors and magnifying glasses

- Trace objects and images on plain paper
- Join corresponding vertices and extend lines to find centre of enlargement
- Measure distances from centre to object and image
- Discuss findings with peers

How do we locate the centre of enlargement?

- Mentor Essential Mathematics pg. 37
- Plain paper
- Rulers
- Pencils
- Mentor Essential Mathematics pg. 38
- Graph paper
- Calculators

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Drawing images under enlargement
Similarity and Enlargement - Drawing images on Cartesian plane

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

- Draw the image of an object given centre and scale factor
- Construct enlarged images accurately
- Connect enlargement to photocopying and image resizing

- Draw objects on Cartesian plane
- Use given centre and scale factor to locate image points
- Construct images under different scale factors
- Compare object and image dimensions

How do we draw an image under enlargement?

- Mentor Essential Mathematics pg. 40
- Graph paper
- Rulers
- Geometrical instruments
- Mentor Essential Mathematics pg. 41
- Pencils

- Observation - Practical work - Written assignments

Measurements and Geometry

Similarity and Enlargement - Area scale factor

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

- Determine the area scale factor of similar figures
- Calculate areas of objects and their images
- Relate area scale factor to land surveying and floor planning

- Draw right-angled triangle and enlarge with scale factor 3
- Calculate areas of object and image
- Determine ratio of areas
- Discuss relationship between linear and area scale factors

What is the relationship between linear scale factor and area scale factor?

- Mentor Essential Mathematics pg. 42
- Graph paper
- Calculators
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Area scale factor calculations
Similarity and Enlargement - Volume scale factor

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

- Calculate area scale factor from given measurements
- Apply area scale factor formula
- Use area scale factor in calculating painting and carpeting costs

- Work out area scale factors for various similar figures
- Solve problems involving area scale factor
- Apply area scale factor to real-life scenarios
- Share solutions with peers

How is area scale factor applied in real life?

- Mentor Essential Mathematics pg. 44
- Calculators
- Rulers
- Digital resources
- Mentor Essential Mathematics pg. 43
- Similar containers
- Calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Relating linear, area and volume scale factors

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

- Relate linear scale factor to area and volume scale factors
- Convert between different scale factors
- Apply scale factor relationships to model making and engineering

- Make similar cylinders of different sizes
- Calculate ratios of heights, areas, and volumes
- Compare the three ratios and establish relationships
- Solve problems involving all three scale factors

How are the three scale factors related?

- Mentor Essential Mathematics pg. 45
- Manila paper
- Calculators
- Scissors

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Relating linear, area and volume scale factors

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

- Relate linear scale factor to area and volume scale factors
- Convert between different scale factors
- Apply scale factor relationships to model making and engineering

- Make similar cylinders of different sizes
- Calculate ratios of heights, areas, and volumes
- Compare the three ratios and establish relationships
- Solve problems involving all three scale factors

How are the three scale factors related?

- Mentor Essential Mathematics pg. 45
- Manila paper
- Calculators
- Scissors

- Observation - Oral questions - Written tests

Measurements and Geometry

Similarity and Enlargement - Application to area

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

- Apply linear scale factor to find areas of similar figures
- Solve problems on area using scale factors
- Connect similarity concepts to architectural blueprints and scale models

- Calculate areas of similar figures using scale factors
- Solve word problems involving area scale factor
- Use digital devices to explore applications
- Present solutions to peers

How do we apply area scale factor to solve problems?

- Mentor Essential Mathematics pg. 46
- Calculators
- Digital resources
- Reference books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Application to volume

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

- Apply linear scale factor to find volumes of similar objects
- Solve problems on volume using scale factors
- Use similarity in estimating storage capacities and tank volumes

- Calculate volumes of similar solids using scale factors
- Solve word problems involving volume scale factor
- Complete project on making similar containers
- Document processes and take pictures

How do we apply volume scale factor to solve problems?

- Mentor Essential Mathematics pg. 47
- Calculators
- Manila paper
- Locally available materials

- Observation - Project assessment - Written tests