Numbers and Algebra

Real Numbers - Classification of whole numbers as odd and even

By the end of the lesson, the learner should be able to:
- Define odd and even numbers
- Classify whole numbers as odd or even based on their ones place value
- Relate classification of numbers to everyday situations like grouping items equally

- Discuss with peers the meaning of odd and even numbers
- Take turns to roll a die and classify the number that shows up as odd or even
- Use digital devices to explore classification of numbers

How do we determine if a number is odd or even?

- Mentor Core Mathematics Grade 10 pg. 1
- Dice
- Number cards
- Digital devices

- Oral questions - Observation - Written exercises

Numbers and Algebra

Real Numbers - Application of odd and even numbers
Real Numbers - Classification of prime and composite numbers

By the end of the lesson, the learner should be able to:
- Identify odd and even numbers in a given range
- Solve problems involving classification of odd and even numbers
- Connect odd and even number concepts to real-life situations like dividing items into equal groups

- Determine if items can be divided equally into two groups
- Work out exercises involving classification of numbers
- Apply odd and even number concepts to real-life problems

Why is it important to classify numbers as odd or even?

- Mentor Core Mathematics Grade 10 pg. 1
- Number cards
- Counters
- Mentor Core Mathematics Grade 10 pg. 2
- Factor charts
- Digital devices

- Written assignments - Oral questions - Class activities

Numbers and Algebra

Real Numbers - Application of prime and composite numbers

By the end of the lesson, the learner should be able to:
- Classify numbers as prime or composite
- Apply prime and composite number concepts in problem solving
- Connect prime and composite numbers to practical situations like arranging items in rows

- Work out problems involving prime and composite numbers
- Determine if items can be arranged in multiple ways based on factors
- Use digital devices to verify classification of numbers

How are prime and composite numbers used in everyday life?

- Mentor Core Mathematics Grade 10 pg. 2
- Number cards
- Digital devices

- Written assignments - Class activities - Oral questions

Numbers and Algebra

Real Numbers - Classification of real numbers as rational and irrational

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 and irrational numbers to measurements in construction and design

- Discuss in groups the meaning of real numbers
- Categorise real numbers as rational and irrational
- Use digital devices to explore properties of rational and irrational numbers

How do we distinguish between rational and irrational numbers?

- Mentor Core Mathematics Grade 10 pg. 3
- Number cards
- Calculators
- Digital devices

- Oral questions - Written exercises - Observation

Numbers and Algebra

Real Numbers - Determining reciprocal of real numbers by division

By the end of the lesson, the learner should be able to:
- Define the reciprocal of a number
- Determine the reciprocal of real numbers by division
- Connect reciprocals to real-life applications like calculating rates and unit costs

- Divide 1 by given numbers to get reciprocals
- Verify that the product of a number and its reciprocal is 1
- Work out exercises involving reciprocals

What is the reciprocal of a number and how is it obtained?

- Mentor Core Mathematics Grade 10 pg. 5
- Calculators
- Digital devices

- Written exercises - Oral questions - Class activities

Numbers and Algebra

Real Numbers - Reciprocal of numbers using mathematical tables
Real Numbers - Reciprocal using calculators and application in computations

By the end of the lesson, the learner should be able to:
- Read reciprocals of numbers from mathematical tables
- Determine reciprocals of numbers between 1 and 10 using tables
- Relate use of mathematical tables to efficient problem solving in science and engineering

- Discuss features of reciprocal tables
- Read values of reciprocals from mathematical tables
- Work out tasks using reciprocal tables

How do we use mathematical tables to find reciprocals?

- Mentor Core Mathematics Grade 10 pg. 6
- Mathematical tables
- Calculators
- Mentor Core Mathematics Grade 10 pg. 10
- Calculators
- Digital devices

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Expressing numbers in index form

By the end of the lesson, the learner should be able to:
- Express numbers as products of their prime factors
- Write numbers in index notation
- Relate index notation to compact representation of large numbers in science

- Discuss how to express numbers in index form
- Write numbers in terms of bases and indices
- Share results with peers

Why do we express numbers in index form?

- Mentor Core Mathematics Grade 10 pg. 13
- Number cards
- Digital devices

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices and Logarithms - Deriving and applying multiplication law

By the end of the lesson, the learner should be able to:
- Derive the multiplication law of indices
- Apply the multiplication law in simplifying expressions
- Connect the multiplication law to scientific notation used in physics and chemistry

- Write numbers in expanded form and multiply
- Discuss and generate the multiplication law of indices
- Use the law to simplify expressions

How do we multiply numbers in index form?

- Mentor Core Mathematics Grade 10 pg. 14
- Charts
- Digital devices

- Written exercises - Oral questions - Class activities

Numbers and Algebra

Indices and Logarithms - Deriving and applying division law

By the end of the lesson, the learner should be able to:
- Derive the division law of indices
- Apply the division law in simplifying expressions
- Relate division law to calculations involving ratios and rates in real life

- Write numbers in expanded form and divide
- Discuss and generate the division law of indices
- Use the law to simplify expressions

How do we divide numbers in index form?

- Mentor Core Mathematics Grade 10 pg. 15
- Charts
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Deriving and applying power law
Indices and Logarithms - Zero index and negative indices

By the end of the lesson, the learner should be able to:
- Derive the power law of indices
- Apply the power law in simplifying expressions
- Connect power law to compound interest calculations in finance

- Write expressions with powers in expanded form
- Discuss and generate the power law of indices
- Use the law to simplify expressions

What happens when we raise a power to another power?

- Mentor Core Mathematics Grade 10 pg. 16
- Charts
- Digital devices
- Mentor Core Mathematics Grade 10 pg. 17
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Fractional indices

By the end of the lesson, the learner should be able to:
- Interpret fractional indices as roots
- Evaluate expressions with fractional indices
- Connect fractional indices to root calculations used in engineering and construction

- Express numbers as products of prime factors
- Discuss the relationship between fractional indices and roots
- Evaluate expressions with fractional indices

How do fractional indices relate to roots?

- Mentor Core Mathematics Grade 10 pg. 19
- Calculators
- Digital devices

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Applying laws of indices in problem solving

By the end of the lesson, the learner should be able to:
- Apply combined laws of indices in simplifying expressions
- Solve equations involving indices
- Use indices to solve real-world problems in science, engineering and finance

- Use laws of indices to simplify complex expressions
- Solve equations involving indices
- Apply indices to real-life problems

How do we apply laws of indices to solve problems?

- Mentor Core Mathematics Grade 10 pg. 20
- Calculators
- Digital devices

- Written assignments - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Relating index notation to logarithm notation

By the end of the lesson, the learner should be able to:
- Relate index notation to logarithm notation to base 10
- Convert between index and logarithm forms
- Connect logarithms to measuring earthquake intensity (Richter scale) and sound (decibels)

- Discuss the relationship between index and logarithm notation
- Convert expressions from index form to logarithm form and vice versa
- Use digital devices to explore logarithms

What is the relationship between indices and logarithms?

- Mentor Core Mathematics Grade 10 pg. 22
- Calculators
- Digital devices

- Oral questions - Written exercises - Observation

Numbers and Algebra

Indices and Logarithms - Common logarithms from mathematical tables

By the end of the lesson, the learner should be able to:
- Read logarithms of numbers from mathematical tables
- Determine logarithms of numbers between 1 and 10
- Relate logarithm tables to historical computational methods used before calculators

- Discuss features of logarithm tables
- Read logarithms of numbers from tables
- Work out exercises using logarithm tables

How do we read logarithms from mathematical tables?

- Mentor Core Mathematics Grade 10 pg. 23
- Mathematical tables
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

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

By the end of the lesson, the learner should be able to:
- Determine logarithms of numbers greater than 10 using standard form
- Determine logarithms of numbers less than 1
- Apply logarithms to express very large or very small quantities in science

- Express numbers in standard form
- Use standard form and tables to find logarithms
- Work with bar notation for negative characteristics

How do we find logarithms of very large or very small numbers?

- Mentor Core Mathematics Grade 10 pg. 25
- Mathematical tables
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Antilogarithms from tables and calculators

By the end of the lesson, the learner should be able to:
- Define antilogarithm as the reverse of logarithm
- Read antilogarithms from tables
- Use antilogarithms to find original values from logarithmic calculations

- Discuss the meaning of antilogarithm
- Read antilogarithms from tables
- Use calculators to find antilogarithms

What is an antilogarithm and how is it determined?

- Mentor Core Mathematics Grade 10 pg. 29
- Mathematical tables
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Antilogarithms from tables and calculators

By the end of the lesson, the learner should be able to:
- Define antilogarithm as the reverse of logarithm
- Read antilogarithms from tables
- Use antilogarithms to find original values from logarithmic calculations

- Discuss the meaning of antilogarithm
- Read antilogarithms from tables
- Use calculators to find antilogarithms

What is an antilogarithm and how is it determined?

- Mentor Core Mathematics Grade 10 pg. 29
- Mathematical tables
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Application of logarithms in multiplication and division

By the end of the lesson, the learner should be able to:
- Apply logarithms in multiplication of numbers
- Apply logarithms in division of numbers
- Use logarithms to simplify complex calculations in business and science

- Use logarithms to multiply numbers by adding logarithms
- Use logarithms to divide numbers by subtracting logarithms
- Work out problems involving multiplication and division

How do logarithms simplify multiplication and division?

- Mentor Core Mathematics Grade 10 pg. 33
- Mathematical tables
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Indices and Logarithms - Application of logarithms in powers and roots

By the end of the lesson, the learner should be able to:
- Apply logarithms in evaluating powers of numbers
- Apply logarithms in evaluating roots of numbers
- Use logarithms to solve problems involving compound growth and decay

- Use logarithms to evaluate powers by multiplying logarithms
- Use logarithms to evaluate roots by dividing logarithms
- Work out complex calculations involving powers and roots

How do we use logarithms to evaluate powers and roots?

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

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Application of logarithms in powers and roots

By the end of the lesson, the learner should be able to:
- Apply logarithms in evaluating powers of numbers
- Apply logarithms in evaluating roots of numbers
- Use logarithms to solve problems involving compound growth and decay

- Use logarithms to evaluate powers by multiplying logarithms
- Use logarithms to evaluate roots by dividing logarithms
- Work out complex calculations involving powers and roots

How do we use logarithms to evaluate powers and roots?

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

- Written exercises - Oral questions - Observation

Numbers and Algebra

Indices and Logarithms - Combined operations and problem solving

By the end of the lesson, the learner should be able to:
- Apply logarithms in combined operations
- Solve complex problems using logarithms
- Use logarithms to solve real-world problems in physics, engineering and finance

- Work out problems involving combined operations
- Use logarithms to evaluate complex expressions
- Apply logarithms to real-life situations

How do we use logarithms to solve complex mathematical problems?

- Mentor Core Mathematics Grade 10 pg. 39
- Mathematical tables
- Calculators

- Written assignments - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic expressions from statements

By the end of the lesson, the learner should be able to:
- Define a quadratic expression
- Form quadratic expressions from given statements
- Relate quadratic expressions to calculating areas of rectangular shapes

- Generate quadratic expressions from given statements
- Draw rectangles and express their areas as quadratic expressions
- Share work with peers

What is a quadratic expression?

- Mentor Core Mathematics Grade 10 pg. 42
- Graph paper
- Rulers

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic expressions from real-life situations

By the end of the lesson, the learner should be able to:
- Form quadratic expressions from real-life situations
- Interpret quadratic expressions in context
- Connect quadratic expressions to practical problems like garden design and room carpeting

- Form quadratic expressions from problems involving area
- Work out exercises involving formation of quadratic expressions
- Use digital devices to explore quadratic expressions

How are quadratic expressions formed from real-life situations?

- Mentor Core Mathematics Grade 10 pg. 43
- Graph paper
- Digital devices

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Deriving quadratic identities from concept of area

By the end of the lesson, the learner should be able to:
- Derive the identity (a+b)² = a² + 2ab + b² using area concept
- Apply the identity in expanding expressions
- Relate quadratic identities to calculating areas of combined shapes

- Draw squares and rectangles to derive identities
- Discuss and generate quadratic identities
- Write identities on a chart

How are quadratic identities derived from the concept of area?

- Mentor Core Mathematics Grade 10 pg. 44
- Graph paper
- Charts
- Rulers

- Oral questions - Written exercises - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Deriving more quadratic identities
Quadratic Expressions and Equations - Applying quadratic identities in numerical cases

By the end of the lesson, the learner should be able to:
- Derive the identities (a-b)² and (a+b)(a-b) using area concept
- Apply the identities in expanding expressions
- Use quadratic identities to simplify calculations in construction and design

- Use area models to derive identities
- Discuss and verify quadratic identities
- Work out exercises using identities

What are the different quadratic identities and how are they derived?

- Mentor Core Mathematics Grade 10 pg. 45
- Graph paper
- Charts
- Mentor Core Mathematics Grade 10 pg. 47
- Calculators

- Written exercises - Oral questions - Class activities

Numbers and Algebra

Quadratic Expressions and Equations - Factorising quadratic expressions (coefficient of x² is 1)

By the end of the lesson, the learner should be able to:
- Factorise quadratic expressions where coefficient of x² is 1
- Identify factors that give required sum and product
- Relate factorisation to finding dimensions of rectangular areas

- Discuss methods of factorising quadratic expressions
- Identify pairs of numbers with required sum and product
- Factorise expressions and verify by expansion

How do we factorise quadratic expressions?

- Mentor Core Mathematics Grade 10 pg. 48
- Charts
- Digital devices

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Factorising quadratic expressions (coefficient of x² greater than 1)

By the end of the lesson, the learner should be able to:
- Factorise quadratic expressions where coefficient of x² is greater than 1
- Apply factorisation methods to complex expressions
- Use factorisation to solve practical problems involving areas

- Use the product-sum method for factorisation
- Work out exercises involving factorisation
- Verify solutions by expanding

How do we factorise quadratic expressions with leading coefficient greater than 1?

- Mentor Core Mathematics Grade 10 pg. 49
- Charts
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic equations from given situations

By the end of the lesson, the learner should be able to:
- Form quadratic equations from word problems
- Express real-life situations as quadratic equations
- Relate equation formation to modelling practical problems like profit and area calculations

- Read and interpret word problems
- Form quadratic equations from given situations
- Work out exercises involving equation formation

How do we form quadratic equations from real-life situations?

- Mentor Core Mathematics Grade 10 pg. 51
- Charts
- Digital devices

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Forming quadratic equations from given roots

By the end of the lesson, the learner should be able to:
- Form quadratic equations given the roots
- Determine coefficients a, b, c from given roots
- Connect roots of equations to solutions of practical problems

- Use roots to form factors
- Expand factors to form quadratic equations
- Work out exercises involving formation from roots

How do we form quadratic equations when the roots are given?

- Mentor Core Mathematics Grade 10 pg. 52
- Charts
- Calculators

- Written exercises - Oral questions - 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:
- Solve quadratic equations by factorisation
- Apply the zero product property
- Use solutions of quadratic equations to solve measurement problems

- Factorise quadratic equations
- Apply zero product property to find solutions
- Work out exercises involving solving equations

How do we solve quadratic equations by factorisation?

- Mentor Core Mathematics Grade 10 pg. 53
- Charts
- Calculators

- Written exercises - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Solving more quadratic equations by factorisation

By the end of the lesson, the learner should be able to:
- Solve quadratic equations with leading coefficient greater than 1
- Verify solutions by substitution
- Apply equation solving to find unknown dimensions in practical problems

- Factorise and solve complex quadratic equations
- Verify solutions by substituting back
- Work out various exercises

How do we verify solutions of quadratic equations?

- Mentor Core Mathematics Grade 10 pg. 53
- Charts
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Solving more quadratic equations by factorisation

By the end of the lesson, the learner should be able to:
- Solve quadratic equations with leading coefficient greater than 1
- Verify solutions by substitution
- Apply equation solving to find unknown dimensions in practical problems

- Factorise and solve complex quadratic equations
- Verify solutions by substituting back
- Work out various exercises

How do we verify solutions of quadratic equations?

- Mentor Core Mathematics Grade 10 pg. 53
- Charts
- Calculators

- Written exercises - Oral questions - Observation

Numbers and Algebra

Quadratic Expressions and Equations - Applying quadratic equations to real-life situations

By the end of the lesson, the learner should be able to:
- Apply quadratic equations to solve real-life problems
- Interpret solutions in context
- Use quadratic equations to solve problems involving areas, consecutive numbers and profit

- Form and solve quadratic equations from word problems
- Interpret and validate solutions
- Work out real-life application problems

How are quadratic equations applied in real-life situations?

- Mentor Core Mathematics Grade 10 pg. 54
- Charts
- Digital devices

- Written assignments - Class activities - Oral questions

Numbers and Algebra

Quadratic Expressions and Equations - Problem solving with quadratic equations

By the end of the lesson, the learner should be able to:
- Solve complex word problems using quadratic equations
- Select appropriate solutions based on context
- Connect quadratic equations to practical applications in business, construction and daily life

- Analyse and solve complex word problems
- Discuss validity of solutions in given contexts
- Search for applications of quadratic equations using digital devices

Why are quadratic equations important in solving real-world problems?

- Mentor Core Mathematics Grade 10 pg. 55
- Digital devices
- Charts

- Written assignments - Class activities - Project work

Numbers and Algebra

Quadratic Expressions and Equations - Problem solving with quadratic equations

By the end of the lesson, the learner should be able to:
- Solve complex word problems using quadratic equations
- Select appropriate solutions based on context
- Connect quadratic equations to practical applications in business, construction and daily life

- Analyse and solve complex word problems
- Discuss validity of solutions in given contexts
- Search for applications of quadratic equations using digital devices

Why are quadratic equations important in solving real-world problems?

- Mentor Core Mathematics Grade 10 pg. 55
- Digital devices
- Charts

- Written assignments - Class activities - Project work