Measurements

Area - Area of a trapezium

By the end of the lesson, the learner should be able to:
- Derive the formula for area of a trapezium
- Calculate area of trapezia
- Appreciate the application of area in land measurement

In groups, learners are guided to:
- Trace and cut out figure ABCD, mark point M on line AB
- Cut triangle ADM to form trapezium
- Discover: Area = ½(a + b) × h where a and b are parallel sides

How do we find the area of a trapezium?

- Smart Minds Mathematics Learner's Book pg. 114
- Paper cut-outs
- Rulers

- Written exercises - Oral questions - Observation

Measurements

Area - Area of circles

By the end of the lesson, the learner should be able to:
- Derive the formula for area of a circle
- Calculate area of circles using πr²
- Show interest in finding area of circles

In groups, learners are guided to:
- Draw circle with radius 7 cm and divide into 16 sectors
- Cut and rearrange sectors to form rectangle
- Discover: Length = πr, Width = r, Area = πr²

How do we find the area of a circle?

- Smart Minds Mathematics Learner's Book pg. 116
- Pair of compasses
- Manila paper

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of borders
Area - Area of combined shapes

By the end of the lesson, the learner should be able to:
- Define the area of a border
- Calculate area of borders (shaded regions)
- Value accuracy in calculating area of borders

In groups, learners are guided to:
- Read story of Mary putting picture in frame
- Calculate: Area of border = Area of larger shape - Area of smaller shape
- Solve problems about picture frames, carpets and swimming pools

How do we find the area of a border?

- Smart Minds Mathematics Learner's Book pg. 119
- Picture frames
- Diagrams
- Smart Minds Mathematics Learner's Book pg. 121
- Combined shape diagrams
- Calculators

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - The cubic metre (m³)

By the end of the lesson, the learner should be able to:
- Identify the cubic metre as a unit of measuring volume
- Make a model of a 1 metre cube
- Show interest in measuring volume

In groups, learners are guided to:
- Use metre rule, long sticks and strings to measure and cut 12 sticks of 1 m each
- Join sticks using strings to form a 1 metre cube
- Observe safety when using panga to cut sticks

What is a cubic metre?

- Smart Minds Mathematics Learner's Book pg. 122
- Metre rule
- Long sticks, strings

- Oral questions - Practical activities - Observation

Measurements

Volume and Capacity - Converting m³ to cm³

By the end of the lesson, the learner should be able to:
- State the relationship between m³ and cm³
- Convert cubic metres to cubic centimetres
- Appreciate the use of volume conversions

In groups, learners are guided to:
- Use the 1 metre cube made in previous lesson
- Calculate volume in m³ (1×1×1) and in cm³ (100×100×100)
- Establish: 1 m³ = 1,000,000 cm³

How do we convert cubic metres to cubic centimetres?

- Smart Minds Mathematics Learner's Book pg. 123
- 1 metre cube model
- Calculators

- Written assignments - Class activities - Oral questions

Measurements

Volume and Capacity - Converting cm³ to m³

By the end of the lesson, the learner should be able to:
- Explain conversion of cm³ to m³
- Convert cubic centimetres to cubic metres
- Show confidence in converting units of volume

In groups, learners are guided to:
- Make number cards with volumes in cm³ (2,000,000 cm³, 7,000,000 cm³)
- Convert to m³ by dividing by 1,000,000
- Solve problems about oil tankers and water tanks

How do we convert cubic centimetres to cubic metres?

- Smart Minds Mathematics Learner's Book pg. 124
- Number cards
- Calculators

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Volume of cubes

By the end of the lesson, the learner should be able to:
- State the formula for volume of a cube
- Calculate volume of cubes
- Value accuracy in calculating volume

In groups, learners are guided to:
- Draw cube and colour one face (cross-sectional area)
- Establish: Volume = Side × Side × Side
- Model cubes using clay, plasticine or manila paper

How do we find the volume of a cube?

- Smart Minds Mathematics Learner's Book pg. 125
- Clay, plasticine
- Manila paper

- Written assignments - Class activities - Oral questions

Measurements

Volume and Capacity - Volume of cuboids
Volume and Capacity - Volume of cylinders

By the end of the lesson, the learner should be able to:
- State the formula for volume of a cuboid
- Calculate volume of cuboids
- Appreciate the use of volume in real life

In groups, learners are guided to:
- Draw cuboid and shade one face (cross-sectional area)
- Establish: Volume = Length × Width × Height
- Model cuboids using locally available materials

How do we find the volume of a cuboid?

- Smart Minds Mathematics Learner's Book pg. 126
- Clay, cartons
- Rulers
- Smart Minds Mathematics Learner's Book pg. 128
- Coins, cylindrical objects

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Relating volume to capacity

By the end of the lesson, the learner should be able to:
- State the relationship between cm³, m³ and litres
- Convert between cm³, m³ and litres
- Value the relationship between volume and capacity

In groups, learners are guided to:
- Make model cube 10 cm × 10 cm × 10 cm
- Immerse in water and measure displaced water
- Establish: 1,000 cm³ = 1 litre, 1 m³ = 1,000 litres

What is the relationship between volume and capacity?

- Smart Minds Mathematics Learner's Book pg. 130
- Containers, basin
- Measuring cylinder

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Application of volume and capacity

By the end of the lesson, the learner should be able to:
- Calculate capacity of containers in litres
- Solve problems involving volume and capacity
- Appreciate the application of volume and capacity in daily life

In groups, learners are guided to:
- Collect containers of different shapes
- Find volume and convert to capacity in litres
- Solve problems about tanks, tins and pipes

Where do we use volume and capacity in daily life?

- Smart Minds Mathematics Learner's Book pg. 132
- Various containers
- Digital devices

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Units of measuring time

By the end of the lesson, the learner should be able to:
- Identify units of measuring time
- Read time from clock faces and stopwatches
- Show interest in reading time

In groups, learners are guided to:
- Observe clock face with hour, minute and second hands
- Read time shown on stopwatches (hours, minutes, seconds)
- Draw clock faces showing different times

How do we read time from a clock face?

- Smart Minds Mathematics Learner's Book pg. 134
- Clock faces
- Stopwatches

- Oral questions - Practical activities - Observation

Measurements

Time, Distance and Speed - Converting hours and minutes

By the end of the lesson, the learner should be able to:
- State the relationship between hours and minutes
- Convert hours to minutes and minutes to hours
- Appreciate the use of time conversions

In groups, learners are guided to:
- Make clock face using paper cut-out
- Move minute hand clockwise to complete one turn (60 minutes)
- Establish: 1 hour = 60 minutes

How do we convert hours to minutes?

- Smart Minds Mathematics Learner's Book pg. 136
- Paper clock faces
- Stopwatches

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Converting minutes and seconds
Time, Distance and Speed - Converting hours and seconds

By the end of the lesson, the learner should be able to:
- State the relationship between minutes and seconds
- Convert minutes to seconds and seconds to minutes
- Show confidence in converting time units

In groups, learners are guided to:
- Use stopwatch to observe seconds in different minutes
- Establish: 1 minute = 60 seconds
- Solve problems about water pumps, walking distances

How do we convert minutes to seconds?

- Smart Minds Mathematics Learner's Book pg. 138
- Stopwatches
- Number cards
- Smart Minds Mathematics Learner's Book pg. 140
- Calculators
- Conversion charts

- Written exercises - Oral questions - Observation

Measurements

Time, Distance and Speed - Converting units of distance

By the end of the lesson, the learner should be able to:
- State the relationship between kilometres and metres
- Convert kilometres to metres and metres to kilometres
- Appreciate the use of distance conversions

In groups, learners are guided to:
- Estimate distances to nearby places in kilometres
- Convert estimated distances to metres
- Establish: 1 km = 1,000 m

How do we convert kilometres to metres?

- Smart Minds Mathematics Learner's Book pg. 142
- Maps
- Measuring tapes

- Written exercises - Oral questions - Observation

Measurements

Time, Distance and Speed - Speed in km/h

By the end of the lesson, the learner should be able to:
- Define speed as distance covered per unit time
- Calculate speed in kilometres per hour
- Show interest in calculating speed

In groups, learners are guided to:
- Walk and run around athletics field (1 lap = 400 m)
- Record time taken for each activity
- Calculate: Speed = Distance ÷ Time

What is speed in kilometres per hour?

- Smart Minds Mathematics Learner's Book pg. 144
- Athletics field
- Stopwatches

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Speed in m/s

By the end of the lesson, the learner should be able to:
- Calculate speed in metres per second
- Solve problems involving speed in m/s
- Value the application of speed in real life

In groups, learners are guided to:
- Mark 100 m distance in the field
- Run 100 m race and record time using stopwatch
- Calculate speed in m/s

What is speed in metres per second?

- Smart Minds Mathematics Learner's Book pg. 145
- Measuring tape
- Stopwatches

- Written exercises - Oral questions - Observation

Measurements

Time, Distance and Speed - Converting km/h to m/s and vice versa

By the end of the lesson, the learner should be able to:
- Explain conversion of speed units
- Convert km/h to m/s and m/s to km/h
- Appreciate the importance of speed in daily activities

In groups, learners are guided to:
- Read story of school driver observing traffic rules
- Convert distance from km to m, time from hours to seconds
- Practice converting speed between km/h and m/s

How do we convert speed from km/h to m/s?

- Smart Minds Mathematics Learner's Book pg. 146
- Conversion charts
- Digital devices

- Written assignments - Class activities - Oral questions

Measurements

Temperature - Temperature in our environment
Temperature - Comparing temperature

By the end of the lesson, the learner should be able to:
- Define temperature as degree of hotness or coldness
- Describe temperature conditions as warm, hot or cold
- Show interest in learning about temperature

In groups, learners are guided to:
- Take walk outside classroom and observe temperature
- Discuss temperature conditions as warm, hot or cold
- Record temperature changes at different times of day

What is temperature?

- Smart Minds Mathematics Learner's Book pg. 149
- Thermometers
- Charts
- Smart Minds Mathematics Learner's Book pg. 150
- Ice cubes
- Metallic and wooden objects

- Oral questions - Written exercises - Observation

Measurements

Temperature - Units of measuring temperature

By the end of the lesson, the learner should be able to:
- Identify Celsius (°C) and Kelvin (K) as units of temperature
- Read temperature from thermometers
- Show confidence in reading temperature

In groups, learners are guided to:
- Visit health centre to see thermometer
- Identify °C and K symbols on thermometer
- Measure water temperature before and after heating

What are the units of measuring temperature?

- Smart Minds Mathematics Learner's Book pg. 151
- Thermometers
- Sufuria, water

- Written exercises - Oral questions - Observation

Measurements

Temperature - Converting °C to Kelvin

By the end of the lesson, the learner should be able to:
- State the relationship between °C and Kelvin
- Convert temperature from degrees Celsius to Kelvin
- Value accuracy in temperature conversions

In groups, learners are guided to:
- Measure water temperature before heating and at boiling point
- Compare readings in °C and Kelvin
- Establish: Kelvin = °C + 273

How do we convert degrees Celsius to Kelvin?

- Smart Minds Mathematics Learner's Book pg. 153
- Thermometers
- Calculators

- Written assignments - Class activities - Oral questions

Measurements

Temperature - Converting Kelvin to °C

By the end of the lesson, the learner should be able to:
- Explain conversion of Kelvin to degrees Celsius
- Convert temperature from Kelvin to degrees Celsius
- Appreciate the use of temperature conversions

In groups, learners are guided to:
- Complete table showing daily temperatures in Kelvin
- Convert to °C by subtracting 273
- Solve problems about melting points and town temperatures

How do we convert Kelvin to degrees Celsius?

- Smart Minds Mathematics Learner's Book pg. 154
- Temperature tables
- Calculators

- Written exercises - Oral questions - Observation

Measurements

Temperature - Temperature changes

By the end of the lesson, the learner should be able to:
- Calculate rise or drop in temperature
- Solve problems involving temperature changes
- Show interest in temperature changes in daily life

In groups, learners are guided to:
- Record temperature at different times (8:00 a.m., 2:00 p.m.)
- Calculate temperature rise: Final temp - Initial temp
- Calculate temperature drop: Initial temp - Final temp

How do we calculate temperature changes?

- Smart Minds Mathematics Learner's Book pg. 155
- Thermometers
- Digital devices

- Written assignments - Class activities - Oral questions

Measurements

Money - Profit
Money - Loss

By the end of the lesson, the learner should be able to:
- Define profit in business transactions
- Calculate profit given buying and selling prices
- Show interest in calculating profit

In groups, learners are guided to:
- Role-play shopping activities using classroom shop
- Compare buying price and selling price
- Establish: Profit = Selling price - Buying price

What is profit in business?

- Smart Minds Mathematics Learner's Book pg. 157
- Classroom shop
- Paper money
- Smart Minds Mathematics Learner's Book pg. 159
- Price tables
- Charts

- Oral questions - Written exercises - Observation

Measurements

Money - Percentage profit

By the end of the lesson, the learner should be able to:
- Define percentage profit
- Calculate percentage profit
- Show confidence in calculating percentage profit

In groups, learners are guided to:
- Draw tables with buying price, selling price and profit
- Work out percentage profit = (Profit ÷ Buying price) × 100%
- Solve problems about shirts, books and goods

How do we calculate percentage profit?

- Smart Minds Mathematics Learner's Book pg. 160
- Tables
- Calculators

- Written exercises - Oral questions - Observation

Measurements

Money - Percentage loss

By the end of the lesson, the learner should be able to:
- Define percentage loss
- Calculate percentage loss
- Value the importance of minimizing loss in business

In groups, learners are guided to:
- Draw tables with buying price, selling price and loss
- Work out percentage loss = (Loss ÷ Buying price) × 100%
- Solve problems about mattresses, dresses and sheep

How do we calculate percentage loss?

- Smart Minds Mathematics Learner's Book pg. 162
- Tables
- Calculators

- Written assignments - Class activities - Oral questions

Measurements

Money - Discount

By the end of the lesson, the learner should be able to:
- Define discount as reduction from marked price
- Calculate discount given marked price and selling price
- Appreciate the benefit of discounts to buyers

In groups, learners are guided to:
- Read story of Regina bargaining for shoes in shop
- Establish: Discount = Marked price - Selling price
- Solve problems about blouses, blankets and bicycles

What is a discount?

- Smart Minds Mathematics Learner's Book pg. 164
- Price tags
- Charts

- Written exercises - Oral questions - Observation

Measurements

Money - Percentage discount

By the end of the lesson, the learner should be able to:
- Define percentage discount
- Calculate percentage discount
- Show interest in calculating discounts

In groups, learners are guided to:
- Complete tables with marked price, selling price and discount
- Work out percentage discount = (Discount ÷ Marked price) × 100%
- Solve problems about motorcycles, cars and blankets

How do we calculate percentage discount?

- Smart Minds Mathematics Learner's Book pg. 166
- Tables
- Calculators

- Written assignments - Class activities - Oral questions

Measurements

Money - Commission and percentage commission
Money - Interpreting bills

By the end of the lesson, the learner should be able to:
- Define commission as payment for selling goods
- Calculate commission and percentage commission
- Value the role of commission in business

In groups, learners are guided to:
- Read story of Mzee Mambo Leo's motor vehicle firm
- Study table showing Dansam's weekly commission
- Calculate: % Commission = (Commission ÷ Value of goods sold) × 100%

What is commission in business?

- Smart Minds Mathematics Learner's Book pg. 167
- Commission tables
- Calculators
- Smart Minds Mathematics Learner's Book pg. 171
- Sample bills
- Digital devices

- Written exercises - Oral questions - Observation

Measurements

Money - Preparing bills

By the end of the lesson, the learner should be able to:
- Explain the use of symbols @ and 'for' in bills
- Prepare bills for items purchased
- Show confidence in preparing bills

In groups, learners are guided to:
- Read story of Gillian buying items from kiosk
- Prepare bill showing items, quantities and prices
- Calculate total cost and balance

How do we prepare a bill?

- Smart Minds Mathematics Learner's Book pg. 172
- Bill formats
- Paper money

- Written exercises - Oral questions - Observation

Measurements

Money - Postal charges

By the end of the lesson, the learner should be able to:
- Identify postal services and charges
- Calculate cost of sending letters, parcels and postcards
- Appreciate postal services in communication

In groups, learners are guided to:
- Visit nearby post office to gather information
- Prepare chart showing postal charges by mass limits
- Calculate costs for different letters and parcels

How do we calculate postal charges?

- Smart Minds Mathematics Learner's Book pg. 173
- Postal charge tables
- Charts

- Written assignments - Class activities - Oral questions

Measurements

Money - Mobile money services

By the end of the lesson, the learner should be able to:
- Identify mobile money services (deposit, withdraw, transfer, save, borrow)
- Explain the importance of mobile money services
- Value the convenience of mobile money

In groups, learners are guided to:
- Read story of Mr Mamboleo using mobile money in his shop
- Identify services: pay bill, transfer, save, withdraw, borrow
- Complete word puzzle circling mobile money services

What are mobile money services?

- Smart Minds Mathematics Learner's Book pg. 178
- Word puzzles
- Charts

- Written exercises - Oral questions - Observation

Measurements

Money - Mobile money services

By the end of the lesson, the learner should be able to:
- Identify mobile money services (deposit, withdraw, transfer, save, borrow)
- Explain the importance of mobile money services
- Value the convenience of mobile money

In groups, learners are guided to:
- Read story of Mr Mamboleo using mobile money in his shop
- Identify services: pay bill, transfer, save, withdraw, borrow
- Complete word puzzle circling mobile money services

What are mobile money services?

- Smart Minds Mathematics Learner's Book pg. 178
- Word puzzles
- Charts

- Written exercises - Oral questions - Observation

Measurements

Money - Mobile money services

By the end of the lesson, the learner should be able to:
- Identify mobile money services (deposit, withdraw, transfer, save, borrow)
- Explain the importance of mobile money services
- Value the convenience of mobile money

In groups, learners are guided to:
- Read story of Mr Mamboleo using mobile money in his shop
- Identify services: pay bill, transfer, save, withdraw, borrow
- Complete word puzzle circling mobile money services

What are mobile money services?

- Smart Minds Mathematics Learner's Book pg. 178
- Word puzzles
- Charts

- Written exercises - Oral questions - Observation

Measurements

Money - Mobile money transactions

By the end of the lesson, the learner should be able to:
- Interpret mobile money transaction tables
- Calculate transfer costs, withdrawal costs and interest on loans
- Appreciate the efficiency of mobile money transactions

In groups, learners are guided to:
- Study Uwezo Mobile Money transaction tables
- Calculate costs for different transaction ranges
- Calculate interest on loans and savings from mobile lending apps

How do we calculate mobile money transaction costs?

- Smart Minds Mathematics Learner's Book pg. 179
- Transaction tables
- Calculators

- Written assignments - Class activities - Oral questions

Geometry

Angles - Angles on a straight line

By the end of the lesson, the learner should be able to:
- Identify angles formed on a straight line
- State that angles on a straight line add up to 180°
- Show interest in learning about angles

In groups, learners are guided to:
- Go outside classroom and identify angles made by objects in relation to ground
- Draw line AB and mark point P, measure angle APB using protractor
- Draw lines LP and KP and measure angles APL, LPK, KPB

What is the sum of angles on a straight line?

- Smart Minds Mathematics Learner's Book pg. 184
- Protractors
- Rulers

- Oral questions - Written exercises - Observation

Geometry

Angles - Angles at a point

By the end of the lesson, the learner should be able to:
- Identify angles formed at a point
- State that angles at a point add up to 360°
- Appreciate the relationship between angles at a point

In groups, learners are guided to:
- Trace and cut out diagram with angles ACB, ACD and BCD
- Use protractor to measure each angle
- Find sum of angles and establish they add up to 360°

What is the sum of angles at a point?

- Smart Minds Mathematics Learner's Book pg. 186
- Protractors
- Paper cut-outs

- Written assignments - Class activities - Oral questions

Geometry

Angles - Vertically opposite angles

By the end of the lesson, the learner should be able to:
- Identify vertically opposite angles
- State that vertically opposite angles are equal
- Show confidence in working with vertically opposite angles

In groups, learners are guided to:
- Trace and cut out figure with angles a, b, c and d
- Use protractor to measure each angle
- Compare angles: a = c, b = d (vertically opposite angles are equal)

What are vertically opposite angles?

- Smart Minds Mathematics Learner's Book pg. 187
- Protractors
- Scissors

- Written exercises - Oral questions - Observation

Geometry

Angles - Alternate angles on a transversal
Angles - Corresponding angles on a transversal

By the end of the lesson, the learner should be able to:
- Define a transversal
- Identify alternate angles on a transversal
- Value the properties of alternate angles

In groups, learners are guided to:
- Draw two parallel lines and a transversal crossing them
- Mark angles d and f, cut them out using scissors
- Place angle f on top of angle d and compare (alternate angles are equal)

What are alternate angles?

- Smart Minds Mathematics Learner's Book pg. 188
- Rulers
- Scissors
- Smart Minds Mathematics Learner's Book pg. 190
- Scissors, protractors

- Written assignments - Class activities - Oral questions

Geometry

Angles - Co-interior angles on a transversal

By the end of the lesson, the learner should be able to:
- Identify co-interior angles on a transversal
- State that co-interior angles add up to 180°
- Appreciate the relationship between co-interior angles

In groups, learners are guided to:
- Draw pair of parallel lines and a transversal
- Mark angles n and p, cut them out
- Place two angles on a straight line and observe they add up to 180°

What is the sum of co-interior angles?

- Smart Minds Mathematics Learner's Book pg. 191
- Rulers
- Scissors, protractors

- Written assignments - Class activities - Oral questions

Geometry

Angles - Angles in a parallelogram

By the end of the lesson, the learner should be able to:
- Identify properties of angles in a parallelogram
- State that opposite angles are equal and interior angles add up to 360°
- Show confidence in working with parallelogram angles

In groups, learners are guided to:
- Use 4 straws and string to form rectangular shape
- Push top straw sideways to form parallelogram
- Measure angles a, b, c, d and find that opposite angles are equal

What are the properties of angles in a parallelogram?

- Smart Minds Mathematics Learner's Book pg. 193
- Straws, string
- Protractors

- Written exercises - Oral questions - Observation