Numbers

Integers - Classification of integers

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

- Identify integers from a set of numbers in different situations
- Distinguish between positive integers, negative integers and zero
- Show interest in the use of integers in real life

In groups, learners are guided to:
- Sort number cards into integers and non-integers
- Identify positive, negative integers and zero from a given set
- Discuss real-life examples: floors above ground (positive), below ground (negative), ground floor (zero)

Where do we use integers in real life situations?

Smart Minds Mathematics Grade 8 pg. 1
- Number cards
- Digital resources

- Oral questions - Observation

Numbers

Integers - Representing integers on a number line
Integers - Addition of integers on a number line

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

- Draw a number line and mark integers at equal intervals
- Represent given integers on a number line correctly
- Appreciate the use of a number line in representing integers

In groups, learners are guided to:
- Draw a number line on the ground with equal intervals
- Mark positive integers to the right of zero and negative integers to the left
- Represent given integers by circling them on a number line
- Play jumping games on the number line

How do we represent integers on a number line?

Smart Minds Mathematics Grade 8 pg. 3
- Number line charts
- Digital resources
Smart Minds Mathematics Grade 8 pg. 6

- Oral questions - Written assignments

Numbers

Integers - Subtraction of integers on a number line

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

- Subtract integers on the number line by moving steps to the left
- Solve subtraction problems involving integers in real life
- Value the importance of integers in everyday contexts

In groups, learners are guided to:
- Use a number line on the ground to demonstrate subtraction by jumping left
- Record ending integers and discuss results
- Solve real-life problems such as temperature differences using a number line

How do we subtract integers using a number line?

Smart Minds Mathematics Grade 8 pg. 6
- Number line charts
- Thermometer chart

- Oral questions - Written assignments

Numbers

Integers - Combined operations of integers on a number line

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

- Perform combined operations of addition and subtraction of integers on a number line
- Apply combined integer operations to real life situations
- Show interest in combined operations of integers

In groups, learners are guided to:
- Perform combined operations: apply addition first (jump right) then subtraction (jump left) from new point
- Record starting point, jumps right, jumps left and ending point in a table
- Discuss examples involving distances and temperatures

How do we perform combined operations of integers on a number line?

Smart Minds Mathematics Grade 8 pg. 6
- Number line charts
- Digital resources

- Written assignments - Oral questions

Numbers

Integers - Integers in real life situations

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

- Apply integers to solve problems in real-life situations
- Use IT or print resources to explore integers further
- Reflect on the use of integers in everyday life

In groups, learners are guided to:
- Solve real-life problems involving integers (bank deposits/withdrawals, temperature, altitude)
- Use IT devices or reference books to explore further applications
- Create and share problems involving integers with classmates

Where do we encounter integers in our daily lives?

Smart Minds Mathematics Grade 8 pg. 6
- Digital resources
- Reference books

- Written tests - Oral questions - Observation

Numbers

Fractions - Combined operations on fractions
Fractions - Combined operations on fractions (continued)

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

- Work out the reciprocal of fractions in different situations
- Carry out combined operations involving fractions
- Show interest in fractions and their applications

In groups, learners are guided to:
- Review fractions and discuss the meaning of reciprocal
- Work out reciprocals of given fractions individually and in pairs
- Carry out combined operations on fractions (addition, subtraction, multiplication, division)

How do we use fractions in real-life situations?

Smart Minds Mathematics Grade 8 pg. 14
- Fraction cards
- Digital resources
- Fraction operation charts

- Oral questions - Written assignments

Numbers

Fractions - Order of operations on fractions

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

- Apply the correct order of operations on fractions
- Solve fraction expressions with brackets, then multiplication/division, then addition/subtraction
- Show confidence when solving multi-step fraction problems

In groups, learners are guided to:
- Practise applying BODMAS order to fraction expressions
- Solve expressions involving brackets, division, multiplication, addition and subtraction of fractions
- Discuss why order of operations gives the correct answer

Why is the order of operations important when working with fractions?

Smart Minds Mathematics Grade 8 pg. 17
- Worked examples chart
- Digital resources

- Written assignments - Oral questions

Numbers

Fractions - Order of operations on fractions (practice)

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

- Work out multi-step fraction expressions using correct order of operations
- Check solutions systematically
- Demonstrate accuracy in solving fraction operations

In groups, learners are guided to:
- Work in pairs to solve multi-step fraction expressions
- Peer-check working and identify errors
- Use IT tools to verify answers and explore further practice

How do we verify our answers when working out fraction operations?

Smart Minds Mathematics Grade 8 pg. 17
- Digital resources
- Reference books

- Written assignments - Peer assessment

Numbers

Fractions - Order of operations on fractions (practice)

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

- Work out multi-step fraction expressions using correct order of operations
- Check solutions systematically
- Demonstrate accuracy in solving fraction operations

In groups, learners are guided to:
- Work in pairs to solve multi-step fraction expressions
- Peer-check working and identify errors
- Use IT tools to verify answers and explore further practice

How do we verify our answers when working out fraction operations?

Smart Minds Mathematics Grade 8 pg. 17
- Digital resources
- Reference books

- Written assignments - Peer assessment

Numbers

Fractions - Operations on fractions in real life situations

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

- Identify situations in real life that involve fractions
- Apply operations on fractions to solve real-life problems
- Promote the use of fractions in real-life situations

In groups, learners are guided to:
- Role-play model shopping: divide items using fractions (e.g., half a kilogram of sugar)
- Solve word problems involving fractions from everyday contexts such as agriculture and cooking
- Discuss how fractions are used in sharing resources fairly

How are fractions used in real-life situations such as shopping and farming?

Smart Minds Mathematics Grade 8 pg. 20
- Shopping props
- Digital resources

- Oral questions - Written assignments - Observation

Numbers

Fractions - Operations on fractions in real life (continued)

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

- Solve complex real-life problems involving combined operations on fractions
- Use IT or other resources to further explore fractions
- Reflect on the importance of fractions in daily activities

In groups, learners are guided to:
- Solve multi-step real-life problems involving fractions (distance, harvests, ingredients)
- Play games on fraction operations using IT devices
- Share solutions and reflect on strategies used

How do combined operations on fractions help solve complex real-life problems?

Smart Minds Mathematics Grade 8 pg. 20
- Digital resources
- Reference books

- Written tests - Oral questions

Numbers

Fractions - Operations on fractions in real life (continued)

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

- Solve complex real-life problems involving combined operations on fractions
- Use IT or other resources to further explore fractions
- Reflect on the importance of fractions in daily activities

In groups, learners are guided to:
- Solve multi-step real-life problems involving fractions (distance, harvests, ingredients)
- Play games on fraction operations using IT devices
- Share solutions and reflect on strategies used

How do combined operations on fractions help solve complex real-life problems?

Smart Minds Mathematics Grade 8 pg. 20
- Digital resources
- Reference books

- Written tests - Oral questions

Numbers

Decimals - Converting fractions to decimals

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

- Convert fractions to decimals by dividing numerator by denominator
- Express fractions as terminating or non-terminating decimals
- Show interest in the relationship between fractions and decimals

In groups, learners are guided to:
- Divide numerator by denominator to convert fractions to decimals
- Record results and identify which fractions give terminating decimals
- Discuss the relationship between fractions and their decimal equivalents

How do we convert fractions to decimals?

Smart Minds Mathematics Grade 8 pg. 22
- Calculators
- Digital resources

- Oral questions - Written assignments

Numbers

Decimals - Non-recurring and recurring decimals

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

- Identify non-recurring decimals in different situations
- Identify recurring decimals and indicate the recurring digit(s)
- Show responsibility in classifying decimals correctly

In groups, learners are guided to:
- Convert fractions to decimals and classify each as non-recurring or recurring
- Indicate recurring digits using dot notation
- Discuss examples of recurring decimals encountered in real life

How do we distinguish between non-recurring and recurring decimals?

Smart Minds Mathematics Grade 8 pg. 24
- Calculators
- Digital resources

- Oral questions - Written assignments

Numbers

Decimals - Non-recurring and recurring decimals

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

- Identify non-recurring decimals in different situations
- Identify recurring decimals and indicate the recurring digit(s)
- Show responsibility in classifying decimals correctly

In groups, learners are guided to:
- Convert fractions to decimals and classify each as non-recurring or recurring
- Indicate recurring digits using dot notation
- Discuss examples of recurring decimals encountered in real life

How do we distinguish between non-recurring and recurring decimals?

Smart Minds Mathematics Grade 8 pg. 24
- Calculators
- Digital resources

- Oral questions - Written assignments

Numbers

Decimals - Converting recurring decimals to fractions

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

- Convert recurring decimals to fractions using the algebraic method
- Verify conversions by performing the reverse operation
- Demonstrate critical thinking in solving recurring decimal problems

In groups, learners are guided to:
- Use the algebraic method (multiply by powers of 10 and subtract) to convert recurring decimals
- Verify answers by converting the fraction back to a decimal
- Work in pairs to practise conversions

How do we convert a recurring decimal to a fraction?

Smart Minds Mathematics Grade 8 pg. 27
- Calculators
- Reference books

- Written assignments - Oral questions

Numbers

Decimals - Converting recurring decimals to fractions

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

- Convert recurring decimals to fractions using the algebraic method
- Verify conversions by performing the reverse operation
- Demonstrate critical thinking in solving recurring decimal problems

In groups, learners are guided to:
- Use the algebraic method (multiply by powers of 10 and subtract) to convert recurring decimals
- Verify answers by converting the fraction back to a decimal
- Work in pairs to practise conversions

How do we convert a recurring decimal to a fraction?

Smart Minds Mathematics Grade 8 pg. 27
- Calculators
- Reference books

- Written assignments - Oral questions

Numbers

Decimals - Rounding off decimal numbers

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

- Round off a decimal number to a required number of decimal places
- Apply rounding off to real-life situations such as measurements
- Appreciate precision and approximation in everyday calculations

In groups, learners are guided to:
- Discuss the rules for rounding off decimal numbers
- Round off numbers to 1, 2 and 3 decimal places
- Apply rounding off to real-life contexts such as prices and measurements

When do we use rounding off of decimals in real life?

Smart Minds Mathematics Grade 8 pg. 29
- Number cards
- Digital resources

- Written assignments - Oral questions

Numbers

Decimals - Significant figures

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

- Express decimal and whole numbers to a required number of significant figures
- Apply significant figures to real-life measurement situations
- Show self-esteem when working with significant figures

In groups, learners are guided to:
- Discuss the rules for identifying significant figures in a number
- Round whole numbers and decimals to given significant figures
- Apply significant figures to scientific and everyday measurement contexts

How do significant figures help us express numbers accurately?

Smart Minds Mathematics Grade 8 pg. 32
- Number charts
- Digital resources

- Written assignments - Oral questions

Numbers

Decimals - Significant figures

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

- Express decimal and whole numbers to a required number of significant figures
- Apply significant figures to real-life measurement situations
- Show self-esteem when working with significant figures

In groups, learners are guided to:
- Discuss the rules for identifying significant figures in a number
- Round whole numbers and decimals to given significant figures
- Apply significant figures to scientific and everyday measurement contexts

How do significant figures help us express numbers accurately?

Smart Minds Mathematics Grade 8 pg. 32
- Number charts
- Digital resources

- Written assignments - Oral questions

Numbers

Decimals - Standard form

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

- Express large and small numbers in standard form
- Convert numbers between ordinary form and standard form
- Appreciate the use of standard form in science and technology

In groups, learners are guided to:
- Write numbers in standard form as a × 10ⁿ where 1 ≤ a < 10
- Convert numbers from ordinary form to standard form and vice versa
- Write standard form on cards and share; discuss examples from science (distance to the moon)

Why do we express numbers in standard form?

Smart Minds Mathematics Grade 8 pg. 37
- Number cards/charts
- Digital resources

- Written assignments - Oral questions

Numbers

Decimals - Standard form (continued)

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

- Carry out operations on numbers expressed in standard form
- Apply standard form to solve problems in different situations
- Show confidence in using standard form

In groups, learners are guided to:
- Work out multiplication and division of numbers in standard form
- Solve problems requiring conversion between ordinary and standard form
- Use IT devices to verify results and explore examples from real contexts

How do we perform operations on numbers written in standard form?

Smart Minds Mathematics Grade 8 pg. 37
- Calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Decimals - Standard form (continued)

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

- Carry out operations on numbers expressed in standard form
- Apply standard form to solve problems in different situations
- Show confidence in using standard form

In groups, learners are guided to:
- Work out multiplication and division of numbers in standard form
- Solve problems requiring conversion between ordinary and standard form
- Use IT devices to verify results and explore examples from real contexts

How do we perform operations on numbers written in standard form?

Smart Minds Mathematics Grade 8 pg. 37
- Calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Decimals - Combined operations on decimals

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

- Carry out combined operations on decimals in the correct order
- Apply combined operations on decimals to real-life situations
- Promote use of decimals in real-life situations

In groups, learners are guided to:
- Work out combined operations on decimals applying BODMAS rule
- Play games involving decimal operations using IT tools
- Discuss and apply decimals to real-life scenarios: budgeting and measurement

How do we carry out combined operations on decimals correctly?

Smart Minds Mathematics Grade 8 pg. 41
- Calculators
- Digital resources

- Written tests - Oral questions

Numbers

Squares and Square Roots - Squares of numbers from tables

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

- Locate and read squares of numbers (1–9.999) from the table of squares
- Work out squares of numbers in range 1–9.999 from tables
- Show curiosity in using mathematical tables

In groups, learners are guided to:
- Familiarise with the layout of the table of squares
- Read squares of numbers directly from the table for numbers between 1 and 9.999
- Practise locating values quickly and accurately

What are squares of numbers and how do we find them from tables?

Smart Minds Mathematics Grade 8 pg. 44
- Mathematical tables
- Digital resources

- Oral questions - Written assignments

Numbers

Squares and Square Roots - Squares of numbers greater than 9.999 and less than 1 from tables

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

- Work out squares of numbers greater than 9.999 from tables using standard form
- Work out squares of numbers less than 1 from tables using standard form
- Apply tables systematically to find squares

In groups, learners are guided to:
- Write numbers greater than 9.999 in standard form before using the table
- Find squares of numbers less than 1 by expressing in standard form first
- Work through examples step by step and compare results

How do we use the table of squares for numbers outside the range 1–9.999?

Smart Minds Mathematics Grade 8 pg. 44
- Mathematical tables
- Digital resources

- Written assignments - Oral questions

Numbers

Squares and Square Roots - Squares of numbers greater than 9.999 and less than 1 from tables

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

- Work out squares of numbers greater than 9.999 from tables using standard form
- Work out squares of numbers less than 1 from tables using standard form
- Apply tables systematically to find squares

In groups, learners are guided to:
- Write numbers greater than 9.999 in standard form before using the table
- Find squares of numbers less than 1 by expressing in standard form first
- Work through examples step by step and compare results

How do we use the table of squares for numbers outside the range 1–9.999?

Smart Minds Mathematics Grade 8 pg. 44
- Mathematical tables
- Digital resources

- Written assignments - Oral questions

Numbers

Squares and Square Roots - Squares of numbers greater than 9.999 and less than 1 from tables

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

- Work out squares of numbers greater than 9.999 from tables using standard form
- Work out squares of numbers less than 1 from tables using standard form
- Apply tables systematically to find squares

In groups, learners are guided to:
- Write numbers greater than 9.999 in standard form before using the table
- Find squares of numbers less than 1 by expressing in standard form first
- Work through examples step by step and compare results

How do we use the table of squares for numbers outside the range 1–9.999?

Smart Minds Mathematics Grade 8 pg. 44
- Mathematical tables
- Digital resources

- Written assignments - Oral questions

Numbers

Squares and Square Roots - Square roots of numbers from tables

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

- Locate and read square roots of numbers from the table of square roots
- Work out square roots of numbers from tables in different situations
- Show confidence in using mathematical tables

In groups, learners are guided to:
- Familiarise with the table of square roots
- Read square roots of numbers from the table
- Verify answers by squaring the result to get back the original number

How do we find square roots of numbers from tables?

Smart Minds Mathematics Grade 8 pg. 51
- Mathematical tables
- Digital resources

- Oral questions - Written assignments

Numbers

Squares and Square Roots - Square roots of all range numbers from tables

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

- Work out square roots of numbers greater than 99.99 and less than 1 using tables
- Apply standard form to find square roots of numbers outside the direct table range
- Appreciate the use of tables in calculations

In groups, learners are guided to:
- Write numbers outside direct table range in standard form
- Use the table of square roots for the mantissa and adjust the exponent
- Solve practice problems involving different magnitudes

How do we find square roots of large numbers or decimals using tables?

Smart Minds Mathematics Grade 8 pg. 51
- Mathematical tables
- Digital resources

- Written assignments - Oral questions

Numbers

Squares and Square Roots - Squares of numbers using a calculator

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

- Work out squares of numbers using a scientific calculator
- Compare answers from a calculator with those from tables
- Show enjoyment in using technology for calculations

In groups, learners are guided to:
- Demonstrate the use of the x² key on a scientific calculator
- Practise finding squares of various numbers using a calculator
- Compare calculator results with table results and discuss any differences

How do we find squares of numbers using a calculator?

Smart Minds Mathematics Grade 8 pg. 56
- Scientific calculators
- Digital resources

- Oral questions - Written assignments

Numbers

Squares and Square Roots - Squares of numbers using a calculator

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

- Work out squares of numbers using a scientific calculator
- Compare answers from a calculator with those from tables
- Show enjoyment in using technology for calculations

In groups, learners are guided to:
- Demonstrate the use of the x² key on a scientific calculator
- Practise finding squares of various numbers using a calculator
- Compare calculator results with table results and discuss any differences

How do we find squares of numbers using a calculator?

Smart Minds Mathematics Grade 8 pg. 56
- Scientific calculators
- Digital resources

- Oral questions - Written assignments

Numbers

Squares and Square Roots - Square roots of numbers using a calculator

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

- Work out square roots of numbers using a scientific calculator
- Apply squares and square roots to real-life situations
- Enjoy using squares and square roots in different contexts

In groups, learners are guided to:
- Demonstrate the use of the √ key on a scientific calculator
- Practise finding square roots of numbers using a calculator
- Solve real-life problems: find side of a square given its area
- Use IT devices to play games involving squares and square roots

Where do we apply squares and square roots in real-life situations?

Smart Minds Mathematics Grade 8 pg. 58
- Scientific calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Squares and Square Roots - Square roots of numbers using a calculator

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

- Work out square roots of numbers using a scientific calculator
- Apply squares and square roots to real-life situations
- Enjoy using squares and square roots in different contexts

In groups, learners are guided to:
- Demonstrate the use of the √ key on a scientific calculator
- Practise finding square roots of numbers using a calculator
- Solve real-life problems: find side of a square given its area
- Use IT devices to play games involving squares and square roots

Where do we apply squares and square roots in real-life situations?

Smart Minds Mathematics Grade 8 pg. 58
- Scientific calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Rates

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

- Define and identify rates in different situations
- Express rates as a quantity per unit
- Show interest in the use of rates in real life

In groups, learners are guided to:
- Time phone calls using different mobile service providers and record call duration
- Compute rates (cost per minute, km per hour) from recorded data
- Role-play comparing calling rates from different providers

How do we use rates in real-life situations?

Smart Minds Mathematics Grade 8 pg. 59
- Stopwatches / phones
- Digital resources

- Oral questions - Observation

Numbers

Rates, Ratios, Proportions and Percentages - Working out rates in real life

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

- Work out rates in real-life situations accurately
- Compare rates to make informed consumer decisions
- Apply rates to consumer awareness contexts

In groups, learners are guided to:
- Solve problems involving rates: speed, unit price and wage rates
- Compare rates from different contexts and discuss which represents better value
- Use IT or reference books to find examples of rates from everyday contexts

How do rates help us make better decisions in daily life?

Smart Minds Mathematics Grade 8 pg. 59
- Calculators
- Price lists / advertisements

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Working out rates in real life

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

- Work out rates in real-life situations accurately
- Compare rates to make informed consumer decisions
- Apply rates to consumer awareness contexts

In groups, learners are guided to:
- Solve problems involving rates: speed, unit price and wage rates
- Compare rates from different contexts and discuss which represents better value
- Use IT or reference books to find examples of rates from everyday contexts

How do rates help us make better decisions in daily life?

Smart Minds Mathematics Grade 8 pg. 59
- Calculators
- Price lists / advertisements

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Expressing fractions as ratios

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

- Express fractions as ratios in real-life situations
- Convert between fractions and ratios correctly
- Appreciate the relationship between fractions and ratios

In groups, learners are guided to:
- Use cut-outs from whole objects to relate fractions to ratios
- Express fractions as ratios in the form a:b
- Discuss and share examples of ratios from real life such as mixing ingredients

How are fractions and ratios related?

Smart Minds Mathematics Grade 8 pg. 61
- Fraction/ratio cut-out cards
- Digital resources

- Oral questions - Written assignments

Numbers

Rates, Ratios, Proportions and Percentages - Expressing fractions as ratios

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

- Express fractions as ratios in real-life situations
- Convert between fractions and ratios correctly
- Appreciate the relationship between fractions and ratios

In groups, learners are guided to:
- Use cut-outs from whole objects to relate fractions to ratios
- Express fractions as ratios in the form a:b
- Discuss and share examples of ratios from real life such as mixing ingredients

How are fractions and ratios related?

Smart Minds Mathematics Grade 8 pg. 61
- Fraction/ratio cut-out cards
- Digital resources

- Oral questions - Written assignments

Numbers

Rates, Ratios, Proportions and Percentages - Comparing ratios

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

- Compare two or more ratios in different situations
- Determine which ratio is greater or equivalent
- Show fairness when comparing ratios

In groups, learners are guided to:
- Discuss and compare ratios from cut-out activities
- Simplify ratios to lowest terms for comparison
- Solve problems requiring comparison of ratios in real-life contexts: recipes and solutions

How do we compare two or more ratios?

Smart Minds Mathematics Grade 8 pg. 61
- Ratio cards
- Digital resources

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Dividing quantities in given ratios

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

- Divide quantities in given ratios in real-life situations
- Share resources fairly using ratios
- Value equitable distribution of resources

In groups, learners are guided to:
- Discuss and share quantities of concrete objects (counters, beans) in given ratios
- Solve word problems: dividing money, land and other resources in given ratios
- Role-play sharing activities using given ratios

How do we divide quantities in given ratios?

Smart Minds Mathematics Grade 8 pg. 61
- Counters / beans
- Digital resources

- Oral questions - Written assignments - Observation

Numbers

Rates, Ratios, Proportions and Percentages - Dividing quantities in given ratios

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

- Divide quantities in given ratios in real-life situations
- Share resources fairly using ratios
- Value equitable distribution of resources

In groups, learners are guided to:
- Discuss and share quantities of concrete objects (counters, beans) in given ratios
- Solve word problems: dividing money, land and other resources in given ratios
- Role-play sharing activities using given ratios

How do we divide quantities in given ratios?

Smart Minds Mathematics Grade 8 pg. 61
- Counters / beans
- Digital resources

- Oral questions - Written assignments - Observation

Numbers

Rates, Ratios, Proportions and Percentages - Increase and decrease of quantities using ratios

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

- Increase quantities using given ratios
- Decrease quantities using given ratios
- Apply increase and decrease by ratios to real-life contexts

In groups, learners are guided to:
- Work out problems requiring increasing a quantity in a given ratio (e.g., scaling up a recipe)
- Work out problems requiring decreasing a quantity in a given ratio (e.g., reducing model dimensions)
- Discuss and solve real-life examples involving scale models and recipes

How do we increase or decrease quantities using ratios?

Smart Minds Mathematics Grade 8 pg. 61
- Calculators
- Recipe cards

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Percentage increase and decrease

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

- Work out percentage increase of given quantities in real-life situations
- Work out percentage decrease of given quantities in real-life situations
- Apply percentage change to consumer and financial contexts

In groups, learners are guided to:
- Discuss percentage increase with examples: price hikes, population growth
- Discuss percentage decrease with examples: discounts, depreciation
- Solve problems involving percentage increase and decrease using a structured method

How do we work out percentage increase and decrease in real life?

Smart Minds Mathematics Grade 8 pg. 73
- Calculators
- Price lists / advertisements

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Percentage increase and decrease

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

- Work out percentage increase of given quantities in real-life situations
- Work out percentage decrease of given quantities in real-life situations
- Apply percentage change to consumer and financial contexts

In groups, learners are guided to:
- Discuss percentage increase with examples: price hikes, population growth
- Discuss percentage decrease with examples: discounts, depreciation
- Solve problems involving percentage increase and decrease using a structured method

How do we work out percentage increase and decrease in real life?

Smart Minds Mathematics Grade 8 pg. 73
- Calculators
- Price lists / advertisements

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Percentage change

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

- Calculate percentage change between two values
- Interpret percentage change in real-life situations
- Show accuracy in computing percentage change

In groups, learners are guided to:
- Determine percentage change using: (change ÷ original) × 100%
- Solve problems involving profit and loss, price changes and statistical data
- Use IT devices to explore percentage change interactively

How is percentage change calculated and applied in everyday situations?

Smart Minds Mathematics Grade 8 pg. 73
- Calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Percentage change

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

- Calculate percentage change between two values
- Interpret percentage change in real-life situations
- Show accuracy in computing percentage change

In groups, learners are guided to:
- Determine percentage change using: (change ÷ original) × 100%
- Solve problems involving profit and loss, price changes and statistical data
- Use IT devices to explore percentage change interactively

How is percentage change calculated and applied in everyday situations?

Smart Minds Mathematics Grade 8 pg. 73
- Calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Percentages in real life

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

- Apply percentages to various real-life contexts
- Solve multi-step problems involving percentages
- Appreciate the role of percentages in financial literacy

In groups, learners are guided to:
- Solve real-life problems involving taxes, discounts, interest and commissions
- Discuss how banks and businesses use percentages
- Work in groups to solve consumer-based percentage problems

How are percentages used in financial and consumer contexts?

Smart Minds Mathematics Grade 8 pg. 73
- Calculators
- Digital resources
- Newspapers

- Written tests - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Direct proportion

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

- Identify direct proportion in real-life situations
- Work out direct proportion in different situations
- Show interest in direct proportion

In groups, learners are guided to:
- Role-play shopping activities to identify direct relationships between quantity and cost
- Tabulate values and identify that doubling one quantity doubles the other
- Solve problems using the unitary method and ratio method

How do we identify and work out direct proportion?

Smart Minds Mathematics Grade 8 pg. 80
- Shopping props
- Calculators

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Direct proportion

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

- Identify direct proportion in real-life situations
- Work out direct proportion in different situations
- Show interest in direct proportion

In groups, learners are guided to:
- Role-play shopping activities to identify direct relationships between quantity and cost
- Tabulate values and identify that doubling one quantity doubles the other
- Solve problems using the unitary method and ratio method

How do we identify and work out direct proportion?

Smart Minds Mathematics Grade 8 pg. 80
- Shopping props
- Calculators

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Direct proportion (continued)

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

- Apply direct proportion to solve complex real-life problems
- Verify solutions using cross multiplication
- Demonstrate confidence in solving direct proportion problems

In groups, learners are guided to:
- Solve multi-step problems involving direct proportion (workers and output, distance and fuel)
- Use cross multiplication to verify proportion solutions
- Discuss real-life contexts where direct proportion applies

How is direct proportion used in everyday work and production?

Smart Minds Mathematics Grade 8 pg. 80
- Calculators
- Digital resources

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Indirect proportion

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

- Identify indirect proportion in real-life situations
- Work out indirect proportion in different situations
- Appreciate the concept of indirect proportion in everyday life

In groups, learners are guided to:
- Use an hourglass or timing activity to show an indirect relationship (more workers, less time)
- Tabulate values and identify that doubling one quantity halves the other
- Solve indirect proportion problems using the unitary method

How do we identify and work out indirect proportion?

Smart Minds Mathematics Grade 8 pg. 80
- Hourglass / stopwatch
- Calculators

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Indirect proportion

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

- Identify indirect proportion in real-life situations
- Work out indirect proportion in different situations
- Appreciate the concept of indirect proportion in everyday life

In groups, learners are guided to:
- Use an hourglass or timing activity to show an indirect relationship (more workers, less time)
- Tabulate values and identify that doubling one quantity halves the other
- Solve indirect proportion problems using the unitary method

How do we identify and work out indirect proportion?

Smart Minds Mathematics Grade 8 pg. 80
- Hourglass / stopwatch
- Calculators

- Written assignments - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Indirect proportion (continued)

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

- Apply indirect proportion to solve complex real-life problems
- Distinguish between direct and indirect proportion in a given problem
- Show critical thinking when choosing the correct type of proportion

In groups, learners are guided to:
- Solve multi-step problems involving indirect proportion (more workers, fewer days)
- Compare direct and indirect proportion problems side by side
- Watch videos on ratios and proportions used in daily activities

How do we decide whether a problem involves direct or indirect proportion?

Smart Minds Mathematics Grade 8 pg. 80
- Calculators
- Digital resources (videos)

- Written tests - Oral questions

Numbers

Rates, Ratios, Proportions and Percentages - Review and application

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

- Apply rates, ratios, proportions and percentages to solve problems in varied real-life situations
- Connect these concepts in problem solving
- Promote use of ratios and proportions in real life

In groups, learners are guided to:
- Solve mixed problems involving rates, ratios, percentages and proportions
- Discuss how these concepts connect to each other in real-life contexts
- Use IT resources to explore further examples and applications

How do rates, ratios, proportions and percentages relate to each other in solving real-life problems?

Smart Minds Mathematics Grade 8 pg. 59
- Calculators
- Digital resources

- Written tests - Oral questions - Observation

Algebra

Algebraic Expressions - Like and unlike terms in algebraic expressions

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

- Identify like and unlike terms in algebraic expressions in different situations
- Group like terms together and simplify algebraic expressions
- Show interest in using algebraic expressions in real life

- Use number cards with algebraic expressions to identify like and unlike terms
- Group like terms together and simplify each expression on the cards
- Discuss: like terms share the same letter(s) raised to the same power; for terms with numbers and letters, the number is written before the letter
- Share work with other learners in class

How do we simplify algebraic expressions?

Smart Minds Mathematics Grade 8 pg. 89
- Algebraic expression cards
- Digital resources

- Oral questions - Observation

Algebra

Algebraic Expressions - Like and unlike terms in algebraic expressions

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

- Identify like and unlike terms in algebraic expressions in different situations
- Group like terms together and simplify algebraic expressions
- Show interest in using algebraic expressions in real life

- Use number cards with algebraic expressions to identify like and unlike terms
- Group like terms together and simplify each expression on the cards
- Discuss: like terms share the same letter(s) raised to the same power; for terms with numbers and letters, the number is written before the letter
- Share work with other learners in class

How do we simplify algebraic expressions?

Smart Minds Mathematics Grade 8 pg. 89
- Algebraic expression cards
- Digital resources

- Oral questions - Observation

Algebra

Algebraic Expressions - Factorisation of algebraic expressions
Algebraic Expressions - Factorisation of algebraic expressions (continued)

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

- Identify the highest common factor in an algebraic expression
- Factorise algebraic expressions correctly in different situations
- Appreciate that factorisation is the reverse of expansion

In groups, learners are guided to:
- Use expression cards (e.g. 2a+2b, 3x+15, 6b−24b²) to identify common factors
- Divide each term by the common factor and write it outside the brackets
- Discuss: factorisation is the reverse process of expansion
- Use IT drag-and-drop tools to group and factorise like terms

How do we factorise algebraic expressions?

Smart Minds Mathematics Grade 8 pg. 90
- Algebraic expression cards
- Digital resources

- Written assignments - Oral questions

Algebra

Algebraic Expressions - Simplification of algebraic fractions

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

- Identify like and unlike terms in numerators and denominators of algebraic fractions
- Simplify algebraic fractions by factorising and cancelling common factors
- Show responsibility in simplifying algebraic fractions correctly

In groups, learners are guided to:
- Study algebraic fraction cards (e.g. (ax+bx)/(ay+by)) and identify like and unlike terms in numerator and denominator
- Factorise numerator and denominator then cancel common factors
- Simplify examples such as (y²−4y)/(y−4) and (x²+5x)/(x+5) step by step

How do we simplify algebraic fractions?

Smart Minds Mathematics Grade 8 pg. 91
- Algebraic fraction cards
- Digital resources

- Written assignments - Oral questions

Algebra

Algebraic Expressions - Simplification of algebraic fractions (continued)

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

- Simplify more complex algebraic fractions using common factors
- Apply simplification of algebraic fractions to real-life contexts
- Demonstrate accuracy in simplifying algebraic fractions

In groups, learners are guided to:
- Simplify algebraic fractions involving expressions such as (3bx−3by)/3b and (2m−mn)/(2−n)
- Apply simplification to real-life contexts: sharing books equally expressed as algebraic fractions
- Use IT tools to practise and verify answers

How are algebraic fractions used in real-life situations?

Smart Minds Mathematics Grade 8 pg. 91
- Algebraic fraction cards
- Digital resources

- Written assignments - Peer assessment