Numbers and Algebra

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

By the end of the lesson, the learner should be able to:
- Define odd and even numbers
- Classify whole numbers as odd or even by examining the ones place value
- Use classification of odd and even numbers to solve everyday sharing and grouping problems

- Discuss with peers the meaning of odd and even numbers
- Classify given numbers by examining the digit in the ones place value
- Sort numbers from real-life contexts such as workshop inventories into odd and even categories

How do we determine whether a whole number is odd or even?

- Master Core Mathematics Grade 10 pg. 1
- Number cards
- Charts
- Master Core Mathematics Grade 10 pg. 3

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Composite numbers
Real Numbers - Rational and irrational numbers

By the end of the lesson, the learner should be able to:
- Define a composite number
- Distinguish composite numbers from prime numbers by listing factors
- Relate composite numbers to real-life situations such as grouping items equally in different ways

- Discuss the meaning of composite numbers
- List factors of given numbers and identify those with more than two factors
- Classify numbers as prime or composite from real-life scenarios

How do composite numbers differ from prime numbers?

- Master Core Mathematics Grade 10 pg. 5
- Number cards
- Charts
- Master Core Mathematics Grade 10 pg. 6
- Calculators
- Digital devices

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Reciprocal of real numbers by division
Real Numbers - Reciprocal of real numbers using tables

By the end of the lesson, the learner should be able to:
- Define the reciprocal of a number
- Determine the reciprocal of integers, fractions, and decimals by dividing 1 by the number
- Use reciprocals to solve everyday proportional problems such as recipes and sharing tasks

- Discuss how to get the reciprocal of whole numbers and fractions
- Work out reciprocals of given integers, decimals, and fractions by division
- Verify that the product of a number and its reciprocal equals 1

How do we find the reciprocal of a number using division?

- Master Core Mathematics Grade 10 pg. 8
- Calculators
- Master Core Mathematics Grade 10 pg. 9
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Reciprocal of real numbers using calculators

By the end of the lesson, the learner should be able to:
- Identify the reciprocal button on a scientific calculator
- Determine reciprocals of real numbers using a calculator
- Use calculators to solve real-life problems involving reciprocals such as subdividing land and cutting materials

- Identify the reciprocal button (x⁻¹ or 1/x) on the calculator
- Key in numbers and use the reciprocal function to determine their reciprocals
- Compare calculator results with those obtained from tables

Why is a calculator useful in finding reciprocals of numbers?

- Master Core Mathematics Grade 10 pg. 12
- Scientific calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Real Numbers - Application of reciprocals in computations
Indices and Logarithms - Numbers in index form

By the end of the lesson, the learner should be able to:
- Apply reciprocals of real numbers in mathematical computations
- Solve problems involving sums and differences of reciprocals using tables
- Use reciprocals to solve real-life problems involving mirror equations and liquid measurements

- Use reciprocal tables to work out expressions involving addition and subtraction of reciprocals
- Solve problems relating object distance, image distance, and focal length using reciprocals
- Work out real-life computations involving reciprocals

How are reciprocals used in everyday mathematical computations?

- Master Core Mathematics Grade 10 pg. 13
- Mathematical tables
- Calculators
- Master Core Mathematics Grade 10 pg. 15
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication law of indices
Indices and Logarithms - Division law of indices

By the end of the lesson, the learner should be able to:
- State the multiplication law of indices
- Simplify expressions by adding indices with the same base during multiplication
- Apply the multiplication law to calculate areas and volumes in real-life contexts such as rooms and swimming pools

- Discuss and derive the multiplication law of indices
- Simplify given expressions using the multiplication law
- Determine areas and volumes of shapes expressed in index form

What happens to the indices when we multiply numbers with the same base?

- Master Core Mathematics Grade 10 pg. 16
- Charts
- Master Core Mathematics Grade 10 pg. 17

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers, zero index and negative indices
Indices and Logarithms - Fractional indices and application of laws

By the end of the lesson, the learner should be able to:
- Apply the power of indices rule, zero index rule, and negative index rule
- Simplify expressions involving powers of indices, zero index, and negative indices
- Relate zero and negative indices to real-life contexts such as bacteria growth models and financial processing fees

- Discuss and derive the rules for powers of indices, zero index, and negative indices
- Simplify expressions such as (aᵐ)ⁿ, a⁰, and a⁻ⁿ
- Evaluate expressions involving zero and negative indices

How do we simplify expressions with zero or negative indices?

- Master Core Mathematics Grade 10 pg. 19
- Charts
- Calculators
- Master Core Mathematics Grade 10 pg. 22

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers of 10 and common logarithms

By the end of the lesson, the learner should be able to:
- Relate index notation to logarithm notation to base 10
- Convert between index form and logarithm form
- Use logarithm notation to express real-life quantities such as vaccination figures and bacteria counts

- Discuss the relationship between powers of 10 and logarithm notation
- Write numbers in logarithm form and convert from logarithm to index form
- Express given numbers in logarithm notation

How are powers of 10 related to common logarithms?

- Master Core Mathematics Grade 10 pg. 26
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers between 1 and 10
Indices and Logarithms - Logarithms of numbers greater than 10

By the end of the lesson, the learner should be able to:
- Read logarithms of numbers between 1 and 10 from mathematical tables
- Determine logarithms using the main columns and mean difference columns
- Express real-life measurements such as mass and density in the form 10ⁿ using tables

- Discuss the features of the logarithm table
- Read logarithms of numbers with 2, 3, and 4 significant figures from tables
- Express given quantities in the form 10ⁿ

How do we read logarithms of numbers from tables?

- Master Core Mathematics Grade 10 pg. 27
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 29

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms of numbers less than 1

By the end of the lesson, the learner should be able to:
- Determine logarithms of numbers less than 1 using standard form and tables
- Write the bar notation for negative characteristics
- Express real-life quantities such as pipe diameters and pollutant concentrations in the form 10ⁿ

- Express numbers less than 1 in standard form
- Read the logarithm of the number from tables and identify the negative characteristic
- Write logarithms using bar notation for the characteristic

Why do numbers less than 1 have negative characteristics?

- Master Core Mathematics Grade 10 pg. 30
- Mathematical tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Antilogarithms using tables

By the end of the lesson, the learner should be able to:
- Define antilogarithm as the reverse of a logarithm
- Determine antilogarithms of numbers using tables of antilogarithms
- Use antilogarithms to find actual values from logarithmic results in practical calculations

- Discuss antilogarithm as the reverse process of finding a logarithm
- Use tables of antilogarithms to determine numbers whose logarithms are given
- Determine antilogarithms of numbers with positive and negative (bar) characteristics

How do we use antilogarithm tables to find numbers?

- Master Core Mathematics Grade 10 pg. 31
- Mathematical tables
- Antilogarithm tables

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Logarithms and antilogarithms using calculators

By the end of the lesson, the learner should be able to:
- Determine logarithms and antilogarithms of numbers using a calculator
- Use the log and shift-log buttons to find logarithms and antilogarithms
- Compare calculator results with table values to build confidence in using digital tools for computation

- Identify the log button on a scientific calculator
- Determine logarithms and antilogarithms of numbers by keying values into the calculator
- Compare results obtained from calculators with those from tables

How do we use calculators to find logarithms and antilogarithms?

- Master Core Mathematics Grade 10 pg. 33
- Scientific calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Multiplication and division using logarithms

By the end of the lesson, the learner should be able to:
- Use logarithms to multiply and divide numbers
- Apply the steps of finding logarithms, adding or subtracting them, and finding the antilogarithm
- Solve real-life multiplication and division problems efficiently using logarithms

- Determine logarithms of numbers, add them to perform multiplication, and find the antilogarithm of the sum
- Determine logarithms, subtract them to perform division, and find the antilogarithm of the difference
- Arrange solutions in a table format

How do logarithms simplify multiplication and division?

- Master Core Mathematics Grade 10 pg. 35
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Powers and roots using logarithms

By the end of the lesson, the learner should be able to:
- Use logarithms to evaluate powers and roots of numbers
- Multiply or divide logarithms by the index to find powers or roots
- Use logarithms to solve real-life problems involving squares, cubes, and roots

- Determine the logarithm of a number and multiply by the power to evaluate squares and cubes
- Divide the logarithm by the root order to evaluate square and cube roots
- Make the bar characteristic exactly divisible when dividing logarithms with bar notation

How do logarithms help in finding powers and roots of numbers?

- Master Core Mathematics Grade 10 pg. 37
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Indices and Logarithms - Combined operations using logarithms

By the end of the lesson, the learner should be able to:
- Use logarithms to evaluate expressions involving combined operations of multiplication, division, powers, and roots
- Organise logarithmic computations systematically in a table format
- Apply logarithms to solve complex real-life calculations involving multiple operations

- Add logarithms of the numerator and denominator separately
- Subtract the sum of denominator logarithms from the sum of numerator logarithms
- Find the antilogarithm of the result to obtain the final answer

How do we use logarithms to evaluate complex expressions?

- Master Core Mathematics Grade 10 pg. 38
- Mathematical tables
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Formation of quadratic expressions

By the end of the lesson, the learner should be able to:
- Define a quadratic expression and identify its terms
- Expand and simplify products of two binomials to form quadratic expressions
- Relate quadratic expressions to real-life measurements such as areas of desks, tiles, and rooms

- Measure the sides of a desk and express the area in terms of a variable x
- Expand expressions such as (x+3)(x+5) and (2x−1)(x−3) by multiplying each term
- Identify the quadratic term, linear term, and constant term in the expansion

How do we form quadratic expressions from given factors?

- Master Core Mathematics Grade 10 pg. 40
- Rulers

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Formation of quadratic expressions

By the end of the lesson, the learner should be able to:
- Define a quadratic expression and identify its terms
- Expand and simplify products of two binomials to form quadratic expressions
- Relate quadratic expressions to real-life measurements such as areas of desks, tiles, and rooms

- Measure the sides of a desk and express the area in terms of a variable x
- Expand expressions such as (x+3)(x+5) and (2x−1)(x−3) by multiplying each term
- Identify the quadratic term, linear term, and constant term in the expansion

How do we form quadratic expressions from given factors?

- Master Core Mathematics Grade 10 pg. 40
- Rulers

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Quadratic identities (a+b)² and (a−b)²

By the end of the lesson, the learner should be able to:
- Derive the quadratic identities (a+b)² = a²+2ab+b² and (a−b)² = a²−2ab+b² using the concept of area
- Expand expressions using the identities
- Relate the identities to calculating areas of square floors, parking lots, and table mats

- Draw a square of side (a+b) and divide it into regions to derive (a+b)²
- Draw a square of side a and cut out regions to derive (a−b)²
- Use the identities to expand given expressions

How do we derive and use the identities (a+b)² and (a−b)²?

- Master Core Mathematics Grade 10 pg. 43
- Rulers
- Graph papers

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Difference of two squares identity and numerical applications

By the end of the lesson, the learner should be able to:
- Derive the identity (a+b)(a−b) = a²−b² using the concept of area of a rectangle
- Apply quadratic identities to evaluate numerical expressions mentally
- Use identities to quickly calculate areas of ranch lands, gardens, and metal plates

- Draw a rectangle with sides (a+b) and (a−b) and derive the difference of two squares
- Use identities to evaluate numerical squares such as 25², 82², and products like 1024 × 976
- Compare results with calculator answers

How do quadratic identities make numerical calculations easier?

- Master Core Mathematics Grade 10 pg. 44
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

By the end of the lesson, the learner should be able to:
- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

By the end of the lesson, the learner should be able to:
- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

By the end of the lesson, the learner should be able to:
- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

By the end of the lesson, the learner should be able to:
- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is one

By the end of the lesson, the learner should be able to:
- Identify pairs of integers whose sum and product match the linear and constant terms
- Factorise quadratic expressions of the form x²+bx+c by grouping
- Relate factorisation to finding dimensions of rectangular gardens and wooden boards

- Identify the coefficient of the linear term and the constant term
- Find a pair of integers whose sum equals b and product equals c
- Rewrite the middle term and factorise by grouping

How do we factorise quadratic expressions when the coefficient of x² is one?

- Master Core Mathematics Grade 10 pg. 48
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorisation when coefficient of x² is greater than one

By the end of the lesson, the learner should be able to:
- Identify pairs of integers whose sum equals the coefficient of the linear term and product equals (a × c)
- Factorise quadratic expressions of the form ax²+bx+c where a > 1
- Apply factorisation to determine dimensions of floors and grazing fields from area expressions

- Determine the product of the coefficient of x² and the constant term
- Find a pair of integers whose sum and product match the required values
- Rewrite the linear term using the pair and factorise by grouping

How do we factorise when the coefficient of x² is greater than one?

- Master Core Mathematics Grade 10 pg. 50
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorising perfect squares

By the end of the lesson, the learner should be able to:
- Identify a perfect square quadratic expression
- Factorise perfect square expressions into identical factors
- Use factorisation of perfect squares to find side lengths of square mats, tiles, and signboards

- Consider expressions and factorise them to observe identical factors
- Factorise expressions of the form a²+2ab+b² and a²−2ab+b²
- Determine the length of sides of square shapes from area expressions

How do we recognise and factorise perfect square expressions?

- Master Core Mathematics Grade 10 pg. 52
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Factorising difference of two squares
Quadratic Expressions and Equations - Formation of quadratic equations from roots

By the end of the lesson, the learner should be able to:
- Recognise expressions involving difference of two squares
- Factorise expressions of the form a²−b² into (a+b)(a−b)
- Apply difference of two squares to determine dimensions of rooms, gardens, and concrete slabs

- Rewrite expressions so that both terms are clearly perfect squares
- Factorise in the form (a+b)(a−b)
- Factorise expressions that require extracting a common factor first

How do we factorise expressions that are a difference of two squares?

- Master Core Mathematics Grade 10 pg. 54
- Charts
- Master Core Mathematics Grade 10 pg. 55

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Formation of quadratic equations from real-life situations

By the end of the lesson, the learner should be able to:
- Assign variables to unknown quantities in word problems
- Form quadratic equations from statements involving areas, products, and dimensions
- Translate real-life problems involving classrooms, trains, and gardens into quadratic equations

- Measure the length and width of a desk and express the area in terms of x
- Formulate quadratic equations from problems involving consecutive integers, triangles, and rectangular plots
- Form equations from speed, distance, and time relationships

How do we translate real-life problems into quadratic equations?

- Master Core Mathematics Grade 10 pg. 57
- Rulers
- Measuring tapes

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Solving quadratic equations by factorisation

By the end of the lesson, the learner should be able to:
- Rearrange a quadratic equation into standard form ax²+bx+c = 0
- Solve quadratic equations by factorising and setting each factor to zero
- Apply factorisation to find dimensions of real objects such as billboards from their area equations

- Write the equation in standard quadratic form
- Factorise the left-hand side of the equation
- Set each factor equal to zero and solve the resulting linear equations

How do we solve quadratic equations using factorisation?

- Master Core Mathematics Grade 10 pg. 58
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Solving quadratic equations with algebraic fractions

By the end of the lesson, the learner should be able to:
- Eliminate fractions by multiplying through by the LCM of the denominators
- Solve the resulting quadratic equation by factorisation
- Apply the technique to solve equations arising from rate and proportion problems

- Identify the LCM of the denominators in the equation
- Multiply every term by the LCM to clear fractions
- Rearrange and solve the quadratic equation by factorisation

How do we solve quadratic equations that contain algebraic fractions?

- Master Core Mathematics Grade 10 pg. 61
- Charts

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Application of quadratic equations to real-life (ages and dimensions)

By the end of the lesson, the learner should be able to:
- Formulate quadratic equations from word problems involving ages and dimensions
- Solve the equations and interpret the solutions in context
- Use quadratic equations to determine present ages, lengths of playgrounds, and widths of table mats

- Assign variables to unknowns and form equations from given relationships
- Solve the quadratic equations by factorisation
- Check that solutions are reasonable in the context of the problem

How do we use quadratic equations to solve age and dimension problems?

- Master Core Mathematics Grade 10 pg. 62
- Calculators

- Oral questions - Written assignments - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Application of quadratic equations to real-life (speed, distance and area)

By the end of the lesson, the learner should be able to:
- Formulate quadratic equations from problems involving speed, distance, and area
- Solve the equations and select appropriate solutions
- Use quadratic equations to determine cycling speeds, drone heights, and photograph frame widths

- Form equations from speed-distance-time relationships and area problems
- Solve the quadratic equations by factorisation
- Reject solutions that do not make sense in the real-life context

How do we apply quadratic equations to solve speed and area problems?

- Master Core Mathematics Grade 10 pg. 63
- Calculators

- Oral questions - Written assignments - Observation

Measurements and Geometry

Similarity and Enlargement - Centre of enlargement and linear scale factor
Similarity and Enlargement - Image of an object under enlargement (positive scale factor)

By the end of the lesson, the learner should be able to:
- Determine the centre of enlargement and the linear scale factor for similar figures
- Draw lines joining corresponding vertices to locate the centre of enlargement
- Relate the concept of enlargement to everyday applications such as photo enlargement and map reading

- Discuss in a group and review the properties of similar figures and enlargement
- Use an object and its image to establish the centre of enlargement and the ratio of the lengths of corresponding sides (Linear Scale Factor)
- Use digital devices to explore enlargement concepts

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 65
- Graph papers
- Rulers and geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 68
- Squared books

- Observation - Oral questions - Written assignments

Measurements and Geometry

Similarity and Enlargement - Image of an object under enlargement (negative scale factor)

By the end of the lesson, the learner should be able to:
- Construct the image of an object under an enlargement given the centre and a negative linear scale factor
- Draw images on the Cartesian plane using a negative scale factor
- Relate negative enlargement to real-life situations such as inverted images in pinhole cameras

- Draw on the Cartesian plane the images of objects under enlargement given the centres and negative linear scale factors
- Discuss the effect of a negative scale factor on the position of the image relative to the centre of enlargement

How are similarity and enlargement applied in day-to-day life?

- Master Core Mathematics Grade 10 pg. 68
- Graph papers
- Rulers and geometrical set

- Observation - Oral questions - Written assignments