Measurements

Circles - Circumference of a circle

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

- Work out the circumference of a circle using the formula C = πd or C = 2πr
- Apply the circumference formula to real-life situations involving circular objects
- Show integrity when drawing circles and working out their circumference

In groups, learners are guided to:
- Collect cylindrical objects (cups, pipes, tins) and wrap a string around each to measure circumference
- Measure the diameter using set squares and calculate C/d; observe it approximates π (≈ 3.142 or 22/7)
- Use the formula C = πd and C = 2πr to work out circumferences of given circles
- Discuss real-life examples: bicycle wheels, circular tanks, compact discs

How do we determine the circumference of a circle?

Smart Minds Mathematics Grade 8 pg. 104
- Cylindrical objects (cups, tins, pipes)
- String, ruler, set squares
- Digital resources

- Oral questions - Written assignments

Measurements

Circles - Length of an arc of a circle

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

- Identify major arc, minor arc and semicircle in a circle
- Work out the length of an arc using the formula l = (θ/360) × 2πr
- Appreciate the relationship between arc length and the circumference of a circle

In groups, learners are guided to:
- Draw a circle on manila paper, cut into equal parts and measure arc lengths
- Compare ratio of arc length to circumference with ratio of angle at centre to 360°; observe they are equal
- Use cut-outs (semicircle, quarter circle) to relate arc length to fraction of circumference
- Calculate arc lengths given radius and angle subtended at the centre

How do we calculate the length of an arc of a circle?

Smart Minds Mathematics Grade 8 pg. 107
- Manila paper, pair of compasses, scissors
- Ruler, protractor
- Digital resources

- Written assignments - Oral questions

Measurements

Circles - Length of an arc (continued)
Circles - Perimeter of a sector of a circle

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

- Calculate arc length given angle and radius in different situations
- Find unknown values (radius or angle) given the arc length
- Show confidence when applying the arc length formula

In groups, learners are guided to:
- Complete tables relating angle subtended, circumference and arc length
- Calculate arc length when given radius and angle and find angle or radius when arc length is known
- Solve real-life problems: arc length of a clock hand sweep, arc of a circular path

What information is needed to calculate the length of an arc?

Smart Minds Mathematics Grade 8 pg. 107
- Mathematical tables
- Calculators
- Digital resources
Smart Minds Mathematics Grade 8 pg. 110
- Manila paper, pair of compasses, scissors
- Ruler, protractor

- Written assignments - Oral questions

Measurements

Circles - Perimeter of a sector (continued and application)

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

- Solve problems involving perimeter of sectors in real-life contexts
- Find unknown radius or angle given the perimeter of a sector
- Promote use of circles in real-life situations

In groups, learners are guided to:
- Solve problems where perimeter of a sector is given and find radius or angle
- Discuss real-life uses of sectors: fan blades, pie charts, irrigation pivots
- Use IT tools to explore sectors of circles and verify calculations

How are sectors of circles used in real-life situations?

Smart Minds Mathematics Grade 8 pg. 110
- Calculators
- Digital resources
- Reference books

- Written tests - Oral questions

Measurements

Area - Area of a circle

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

- Derive the formula for the area of a circle from a dissected circle activity
- Calculate the area of a circle in different situations
- Apply the area of a circle to real-life situations

In groups, learners are guided to:
- Draw a circle, divide into 16 equal sectors, rearrange into an approximate rectangle; derive A = πr²
- Calculate areas of circles given radius or diameter
- Solve real-life problems: grazing area for a tethered cow, area of a circular field, area of circular plots

How do we use area in real-life situations?

Smart Minds Mathematics Grade 8 pg. 114
- Manila paper, pair of compasses, scissors
- Calculators
- Digital resources

- Oral questions - Written assignments

Measurements

Area - Area of a sector of a circle

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

- Work out the area of a sector using A = (θ/360) × πr²
- Find unknown angle or radius given the area of a sector
- Show critical thinking when solving sector area problems

In groups, learners are guided to:
- Cut out a sector from a circle; relate area of sector to fraction of full circle area using angle/360
- Calculate areas of sectors given angle and radius
- Solve problems: area swept by a clock's minute hand, area swept by a windscreen wiper
- Find angle or radius when area of sector is given

How do we calculate the area of a sector of a circle?

Smart Minds Mathematics Grade 8 pg. 118
- Manila paper, pair of compasses, scissors
- Calculators
- Digital resources

- Written assignments - Oral questions

Measurements

Area - Surface area of cubes and cuboids

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

- Work out the surface area of closed and open cubes in real-life situations
- Work out the surface area of closed and open cuboids in real-life situations
- Appreciate the application of surface area of cubes and cuboids in real life

In groups, learners are guided to:
- Study a cube: count faces (6), find area of each face; establish Surface area = 6l²
- Study a cuboid: identify 3 pairs of rectangular faces; establish Surface area = 2(lw + lh + wh)
- Model cubes and cuboids from clay or cartons and ask peers to find their surface areas
- Solve real-life problems: surface area of dice, cartons, building blocks, tanks

How do we work out the surface area of cubes and cuboids?

Smart Minds Mathematics Grade 8 pg. 116
- Clay/cartons/plasticine
- Ruler
- Digital resources

- Written assignments - Oral questions

Measurements

Area - Surface area of cylinders and triangular prisms

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

- Work out the surface area of closed, open and hollow cylinders
- Determine the surface area of a triangular prism
- Use IT tools and other materials to learn more about surface area

In groups, learners are guided to:
- Collect a cylindrical object, wrap paper around curved surface; open and measure to show curved surface area = 2πrh
- Derive: closed cylinder = 2πr² + 2πrh; open cylinder = πr² + 2πrh; hollow cylinder = 2πrh
- Identify faces of a triangular prism (2 triangles + 3 rectangles) and find total surface area
- Watch videos on surface area of cubes, cuboids, cylinders and prisms
- Solve real-life problems: cylindrical tins, pipes, metal rods, wedge-shaped pieces of wood

How do we calculate the surface area of cylinders and triangular prisms?

Smart Minds Mathematics Grade 8 pg. 116
- Cylindrical objects, manila paper
- Calculators
- Digital resources (videos)

- Written assignments - Oral questions

Measurements

Area - Area of irregular shapes

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

- Estimate the area of irregular shapes using a square grid
- Apply the square grid method to real-life contexts such as land estimation
- Recognise the use of area in real-life situations

In groups, learners are guided to:
- Trace an irregularly shaped object (leaf, palm of hand, foot) onto a unit square grid
- Count complete squares and half-squares; add to estimate total area
- Draw an irregular plot of land on a grid and estimate area in cm²; scale up to find actual area in hectares
- Use IT tools to explore estimation of irregular areas interactively

How do we estimate the area of irregular shapes?

Smart Minds Mathematics Grade 8 pg. 126
- Unit square grid paper
- Leaves/irregular objects
- Calculators
- Digital resources

- Written assignments - Observation - Oral questions

Measurements

Money - Principal and interest

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

- Identify principal and interest in real-life financial situations
- Calculate interest given principal and amount in different situations
- Show interest in consumer awareness and financial responsibility

In groups, learners are guided to:
- Visit or invite a resource person from a financial institution to discuss services, deposits, loans and interest
- Discuss meanings of: principal (money deposited or borrowed), interest (additional charge or earnings), amount (principal + interest)
- Calculate interest and principal from given real-life statements (bank deposits, SACCO loans)
- Write a report and share findings with classmates

What is interest in money?

Smart Minds Mathematics Grade 8 pg. 130
- Resource person (banker/SACCO officer)
- Digital resources
- Reference books

- Oral questions - Observation - Written assignments

Measurements

Money - Simple interest

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

- Calculate simple interest using the formula SI = (P × R × T) / 100
- Calculate the amount after simple interest in real-life situations
- Use calculators to carry out operations related to money

In groups, learners are guided to:
- Discuss the simple interest formula: SI = P × R/100 × T
- Note: rate per annum requires time in years; rate per month requires time in months
- Calculate simple interest and amount for varied principals, rates and time periods
- Complete a table of principal, rate, time, simple interest and amount
- Solve real-life problems: bank loans, SACCO deposits, mobile money lending

How do we calculate simple interest?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources
- Reference books

- Written assignments - Oral questions

Measurements

Money - Simple interest

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

- Calculate simple interest using the formula SI = (P × R × T) / 100
- Calculate the amount after simple interest in real-life situations
- Use calculators to carry out operations related to money

In groups, learners are guided to:
- Discuss the simple interest formula: SI = P × R/100 × T
- Note: rate per annum requires time in years; rate per month requires time in months
- Calculate simple interest and amount for varied principals, rates and time periods
- Complete a table of principal, rate, time, simple interest and amount
- Solve real-life problems: bank loans, SACCO deposits, mobile money lending

How do we calculate simple interest?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources
- Reference books

- Written assignments - Oral questions

Measurements

Money - Simple interest

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

- Calculate simple interest using the formula SI = (P × R × T) / 100
- Calculate the amount after simple interest in real-life situations
- Use calculators to carry out operations related to money

In groups, learners are guided to:
- Discuss the simple interest formula: SI = P × R/100 × T
- Note: rate per annum requires time in years; rate per month requires time in months
- Calculate simple interest and amount for varied principals, rates and time periods
- Complete a table of principal, rate, time, simple interest and amount
- Solve real-life problems: bank loans, SACCO deposits, mobile money lending

How do we calculate simple interest?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources
- Reference books

- Written assignments - Oral questions

Measurements

Money - Simple interest (continued)

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

- Find principal, rate or time when other values are known
- Apply simple interest to varied real-life financial contexts
- Spend money responsibly on needs and leisure

In groups, learners are guided to:
- Rearrange SI formula to find P, R or T when the other values are given
- Solve problems: find principal given SI, rate and time; find rate given SI, principal and time
- Discuss real-life contexts: borrowing from SACCOs, saving in banks, mobile money apps
- Use calculators to verify solutions

How is simple interest used in everyday financial decisions?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources

- Written tests - Oral questions

Measurements

Money - Simple interest (continued)

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

- Find principal, rate or time when other values are known
- Apply simple interest to varied real-life financial contexts
- Spend money responsibly on needs and leisure

In groups, learners are guided to:
- Rearrange SI formula to find P, R or T when the other values are given
- Solve problems: find principal given SI, rate and time; find rate given SI, principal and time
- Discuss real-life contexts: borrowing from SACCOs, saving in banks, mobile money apps
- Use calculators to verify solutions

How is simple interest used in everyday financial decisions?

Smart Minds Mathematics Grade 8 pg. 132
- Calculators
- Digital resources

- Written tests - Oral questions

Measurements

Money - Compound interest

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

- Distinguish between simple interest and compound interest
- Calculate compound interest per annum step by step up to three years
- Appreciate that compound interest grows faster than simple interest

In groups, learners are guided to:
- Invite resource person from a financial institution or watch a video on compound interest
- Discuss: in compound interest the interest earned is added to principal at end of each year; new principal earns interest next year
- Calculate compound interest year by year for up to 3 years using: Interest = P × R/100 × 1 year
- Compare compound interest with simple interest on the same principal

How is compound interest different from simple interest?

Smart Minds Mathematics Grade 8 pg. 134
- Calculators
- Digital resources (videos)
- Resource person

- Written assignments - Oral questions

Measurements

Money - Compound interest (continued)

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

- Work out compound interest and total amount for two and three year periods
- Apply compound interest to real-life savings and loan scenarios
- Show responsibility in financial decision making

In groups, learners are guided to:
- Calculate compound interest step by step for 2-year and 3-year problems
- Find total amount paid or received including compound interest
- Solve real-life problems: SACCO loans, bank savings accounts, cooperative society deposits
- Use calculators to carry out multi-step compound interest calculations

How do we calculate compound interest over multiple years?

Smart Minds Mathematics Grade 8 pg. 134
- Calculators
- Digital resources

- Written tests - Oral questions

Measurements

Money - Compound interest (continued)

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

- Work out compound interest and total amount for two and three year periods
- Apply compound interest to real-life savings and loan scenarios
- Show responsibility in financial decision making

In groups, learners are guided to:
- Calculate compound interest step by step for 2-year and 3-year problems
- Find total amount paid or received including compound interest
- Solve real-life problems: SACCO loans, bank savings accounts, cooperative society deposits
- Use calculators to carry out multi-step compound interest calculations

How do we calculate compound interest over multiple years?

Smart Minds Mathematics Grade 8 pg. 134
- Calculators
- Digital resources

- Written tests - Oral questions

Measurements

Money - Appreciation and depreciation

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

- Explain the meaning of appreciation and identify items that appreciate in value
- Work out appreciation per annum step by step up to three years
- Make informed decisions on goods worth investing in

In groups, learners are guided to:
- Discuss: appreciation = increase in value over time (land, gold, currency); initial value = principal
- Calculate appreciated value year by year: new value = old value + (old value × rate/100)
- Solve problems: commercial plots, buildings, batteries over 2–3 years
- Identify and discuss items in the local environment that appreciate in value

What causes the value of assets to appreciate over time?

Smart Minds Mathematics Grade 8 pg. 138
- Calculators
- Newspaper property pages
- Digital resources

- Written assignments - Oral questions

Measurements

Money - Appreciation and depreciation

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

- Explain the meaning of appreciation and identify items that appreciate in value
- Work out appreciation per annum step by step up to three years
- Make informed decisions on goods worth investing in

In groups, learners are guided to:
- Discuss: appreciation = increase in value over time (land, gold, currency); initial value = principal
- Calculate appreciated value year by year: new value = old value + (old value × rate/100)
- Solve problems: commercial plots, buildings, batteries over 2–3 years
- Identify and discuss items in the local environment that appreciate in value

What causes the value of assets to appreciate over time?

Smart Minds Mathematics Grade 8 pg. 138
- Calculators
- Newspaper property pages
- Digital resources

- Written assignments - Oral questions

Measurements

Money - Depreciation

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

- Explain the meaning of depreciation and identify items that depreciate in value
- Work out depreciation per annum step by step up to three years
- Show critical thinking when comparing appreciation and depreciation

In groups, learners are guided to:
- Visit or compare prices of second-hand items (TV, car, motorcycle) with new prices; observe value loss
- Discuss: depreciation = decrease in value over time (vehicles, machinery, electronics) due to wear and tear
- Calculate depreciated value year by year: new value = old value − (old value × rate/100)
- Compare appreciation and depreciation side by side using examples

How does the value of assets depreciate over time?

Smart Minds Mathematics Grade 8 pg. 138
- Calculators
- Price lists / advertisements
- Digital resources

- Written assignments - Oral questions

Measurements

Money - Depreciation

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

- Explain the meaning of depreciation and identify items that depreciate in value
- Work out depreciation per annum step by step up to three years
- Show critical thinking when comparing appreciation and depreciation

In groups, learners are guided to:
- Visit or compare prices of second-hand items (TV, car, motorcycle) with new prices; observe value loss
- Discuss: depreciation = decrease in value over time (vehicles, machinery, electronics) due to wear and tear
- Calculate depreciated value year by year: new value = old value − (old value × rate/100)
- Compare appreciation and depreciation side by side using examples

How does the value of assets depreciate over time?

Smart Minds Mathematics Grade 8 pg. 138
- Calculators
- Price lists / advertisements
- Digital resources

- Written assignments - Oral questions

Measurements

Money - Hire purchase

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

- Explain the meaning of hire purchase and compare it with cash purchase
- Work out hire purchase price given deposit and monthly instalments
- Recognise why hire purchase price is higher than cash price

In groups, learners are guided to:
- Visit a shop or study a catalogue; enquire about cash price and hire purchase price of items
- Record: deposit, monthly instalment, number of months for different items
- Establish: hire purchase price = deposit + total monthly instalments
- Compare hire purchase price with cash price; discuss why people prefer hire purchase despite higher cost
- Solve problems: find hire purchase price, monthly instalment, deposit or number of months

How do we pay for goods on hire purchase?

Smart Minds Mathematics Grade 8 pg. 144
- Shop catalogues / price lists
- Calculators
- Digital resources

- Written assignments - Oral questions - Observation

Measurements

Money - Hire purchase (continued and application)

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

- Calculate hire purchase price when it is expressed as a percentage more than the marked price
- Find monthly instalments, deposit or number of months from hire purchase terms
- Spend money responsibly by evaluating hire purchase vs cash options

In groups, learners are guided to:
- Solve problems where hire purchase price is a given % above marked price (e.g. 20% more)
- Calculate monthly instalment from: monthly instalments = (HP price − deposit) / number of months
- Complete a table of hire purchase values (price, deposit, monthly instalment, number of months)
- Discuss real-life consumer scenarios: buying a motorcycle, sofa set, water pump on hire purchase

How do we decide whether to buy on hire purchase or cash?

Smart Minds Mathematics Grade 8 pg. 144
- Calculators
- Digital resources
- Reference books

- Written tests - Oral questions

Measurements

Money - Hire purchase (continued and application)

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

- Calculate hire purchase price when it is expressed as a percentage more than the marked price
- Find monthly instalments, deposit or number of months from hire purchase terms
- Spend money responsibly by evaluating hire purchase vs cash options

In groups, learners are guided to:
- Solve problems where hire purchase price is a given % above marked price (e.g. 20% more)
- Calculate monthly instalment from: monthly instalments = (HP price − deposit) / number of months
- Complete a table of hire purchase values (price, deposit, monthly instalment, number of months)
- Discuss real-life consumer scenarios: buying a motorcycle, sofa set, water pump on hire purchase

How do we decide whether to buy on hire purchase or cash?

Smart Minds Mathematics Grade 8 pg. 144
- Calculators
- Digital resources
- Reference books

- Written tests - Oral questions