Measurements

Area - Area of a trapezium
Area - Area of circles

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

- Written exercises - Oral questions - Observation

Measurements

Area - Area of borders

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

- Written exercises - Oral questions - Observation

Measurements

Area - Area of combined shapes
Volume and Capacity - The cubic metre (m³)

By the end of the lesson, the learner should be able to:
- Identify combined shapes
- Calculate area of combined shapes by dividing into simpler shapes
- Appreciate the application of area in real life

In groups, learners are guided to:
- Cut out combined shapes into rectangles, triangles and circles
- Calculate area of each part and add
- Practise with help of parent or guardian at home

How do we find the area of combined shapes?

- Smart Minds Mathematics Learner's Book pg. 121
- Combined shape diagrams
- Calculators
- Smart Minds Mathematics Learner's Book pg. 122
- Metre rule
- Long sticks, strings

- Written assignments - Class activities - Oral questions

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
Volume and Capacity - Volume of cubes

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

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Volume of cuboids

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

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Volume of cylinders
Volume and Capacity - Relating volume to capacity

By the end of the lesson, the learner should be able to:
- State the formula for volume of a cylinder
- Calculate volume of cylinders using πr²h
- Show interest in finding volume of cylinders

In groups, learners are guided to:
- Arrange pile of similar coins to form cylinder
- Measure diameter and height
- Establish: Volume = πr² × height

How do we find the volume of a cylinder?

- Smart Minds Mathematics Learner's Book pg. 128
- Coins, cylindrical objects
- Rulers
- Smart Minds Mathematics Learner's Book pg. 130
- Containers, basin
- Measuring cylinder

- Written assignments - Class activities - Oral questions

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
Time, Distance and Speed - Converting hours and minutes

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

- Oral questions - Practical activities - Observation

Measurements

Time, Distance and Speed - Converting minutes 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

- Written exercises - Oral questions - Observation

Measurements

Time, Distance and Speed - Converting hours and seconds
Time, Distance and Speed - Converting units of distance

By the end of the lesson, the learner should be able to:
- State the relationship between hours and seconds
- Convert hours to seconds and seconds to hours
- Value accuracy in converting time units

In groups, learners are guided to:
- Fill tables showing hours, minutes and seconds
- Establish: 1 hour = 3,600 seconds
- Solve problems about assignments, journeys and power saws

How do we convert hours to seconds?

- Smart Minds Mathematics Learner's Book pg. 140
- Calculators
- Conversion charts
- Smart Minds Mathematics Learner's Book pg. 142
- Maps
- Measuring tapes

- Written assignments - Class activities - Oral questions

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

- Written exercises - Oral questions - Observation

Measurements

Temperature - Temperature in our environment

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

- Oral questions - Written exercises - Observation

Measurements

Temperature - Comparing temperature
Temperature - Units of measuring temperature

By the end of the lesson, the learner should be able to:
- Compare temperature of different objects
- Use warmer, colder, hotter to compare temperature
- Appreciate the importance of temperature in daily life

In groups, learners are guided to:
- Shake hands with partner and compare warmth
- Compare coldness of tap water and ice cubes
- Compare temperature of metallic and wooden objects

How do we compare temperature?

- Smart Minds Mathematics Learner's Book pg. 150
- Ice cubes
- Metallic and wooden objects
- Smart Minds Mathematics Learner's Book pg. 151
- Thermometers
- Sufuria, water

- Written assignments - Class activities - Oral questions

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
Temperature - Temperature changes

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

- Written exercises - Oral questions - Observation

Measurements

Money - Profit

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

- Oral questions - Written exercises - Observation

Measurements

Money - Loss
Money - Percentage profit

By the end of the lesson, the learner should be able to:
- Define loss in business transactions
- Calculate loss given buying and selling prices
- Appreciate the importance of avoiding loss in business

In groups, learners are guided to:
- Compare buying price and selling price in tables
- Identify when selling price is lower than buying price
- Establish: Loss = Buying price - Selling price

What is loss in business?

- Smart Minds Mathematics Learner's Book pg. 159
- Price tables
- Charts
- Smart Minds Mathematics Learner's Book pg. 160
- Tables
- Calculators

- Written assignments - Class activities - Oral questions

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

- Written exercises - Oral questions - Observation

Measurements

Money - Commission and percentage commission

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

- Written exercises - Oral questions - Observation

Measurements

Money - Interpreting bills
Money - Preparing bills

By the end of the lesson, the learner should be able to:
- Identify different types of bills
- Interpret components of bills (date, amount, items)
- Appreciate the importance of bills in transactions

In groups, learners are guided to:
- Look at water bills and electricity bills
- Identify components: billing date, metre number, amount payable
- Use digital devices to search for other types of bills

What are the components of a bill?

- Smart Minds Mathematics Learner's Book pg. 171
- Sample bills
- Digital devices
- Smart Minds Mathematics Learner's Book pg. 172
- Bill formats
- Paper money

- Written assignments - Class activities - Oral questions

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 - 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 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
Angles - Vertically opposite angles

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

- Written assignments - Class activities - Oral questions

Geometry

Angles - Alternate 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

- Written assignments - Class activities - Oral questions

Geometry

Angles - Corresponding angles on a transversal
Angles - Co-interior angles on a transversal

By the end of the lesson, the learner should be able to:
- Identify corresponding angles on a transversal
- State that corresponding angles are equal
- Show interest in properties of corresponding angles

In groups, learners are guided to:
- Draw pair of parallel lines and a transversal
- Mark angles v and r, cut them out
- Compare by placing one on top of the other (corresponding angles are equal)

What are corresponding angles?

- Smart Minds Mathematics Learner's Book pg. 190
- Rulers
- Scissors, protractors
- Smart Minds Mathematics Learner's Book pg. 191

- Written exercises - Oral questions - Observation

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

Geometry

Angles - Interior angles of triangles, rectangles, squares
Angles - Interior angles of rhombus, parallelogram, trapezium, pentagon, hexagon

By the end of the lesson, the learner should be able to:
- Identify interior angles of triangles, rectangles and squares
- Calculate sum of interior angles
- Value the properties of interior angles

In groups, learners are guided to:
- Trace and draw triangle, cut angles a, b, c and make straight line (sum = 180°)
- Trace rectangle and square, measure interior angles
- Establish sum of interior angles is 360° for quadrilaterals

What is the sum of interior angles of a triangle?

- Smart Minds Mathematics Learner's Book pg. 195
- Protractors
- Polygon cut-outs
- Smart Minds Mathematics Learner's Book pg. 197
- Polygon cut-outs
- Protractors

- Written assignments - Class activities - Oral questions

Geometry

Angles - Exterior angles of polygons

By the end of the lesson, the learner should be able to:
- Identify exterior angles of polygons
- State that sum of exterior angles of any polygon is 360°
- Show interest in calculating exterior angles

In groups, learners are guided to:
- Trace and cut out quadrilateral, measure exterior angles A, B, C, D
- Find sum of exterior angles (360°)
- Draw and find sum of exterior angles of pentagon, hexagon

What is the sum of exterior angles of any polygon?

- Smart Minds Mathematics Learner's Book pg. 201
- Polygon cut-outs
- Protractors

- Written assignments - Class activities - Oral questions

Geometry

Geometrical Constructions - Measuring angles

By the end of the lesson, the learner should be able to:
- Use a protractor to measure angles accurately
- Draw angles of given sizes
- Show interest in measuring angles

In groups, learners are guided to:
- Trace and draw figures with angles ABC, BAC, ACB, ACD
- Place protractor with centre at vertex, straight edge along one line
- Read angle measure from correct scale

How do we measure angles using a protractor?

- Smart Minds Mathematics Learner's Book pg. 207
- Protractors
- Rulers

- Oral questions - Practical activities - Observation

Geometry

Geometrical Constructions - Bisecting angles

By the end of the lesson, the learner should be able to:
- Define angle bisector
- Bisect angles using a pair of compasses
- Appreciate the use of bisecting angles

In groups, learners are guided to:
- Trace and draw lines, measure angles ABC, ABD and DBC
- With compasses at point L, mark arcs on lines LK and LM at P and W
- With same radius at P and W, draw arcs to intersect at O, join O to L

What is an angle bisector?

- Smart Minds Mathematics Learner's Book pg. 208
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 90° angle
Geometrical Constructions - Constructing 45° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 90° using a pair of compasses and ruler
- Verify the constructed angle using a protractor
- Show confidence in constructing 90° angles

In groups, learners are guided to:
- Draw horizontal line, mark point A
- With compasses at A, make arcs on line at points X and Y
- With centres X and Y, draw arcs above line to intersect at T, join T to A

How do we construct an angle of 90°?

- Smart Minds Mathematics Learner's Book pg. 210
- Pair of compasses
- Rulers, protractors
- Smart Minds Mathematics Learner's Book pg. 211
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing 60° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 60° using a pair of compasses and ruler
- Verify the constructed angle using a protractor
- Show interest in constructing angles

In groups, learners are guided to:
- Draw straight line, mark point A
- With A as centre, make arc intersecting line at Y
- With Y as centre and same radius, draw arc to intersect first at K, join K to A

How do we construct an angle of 60°?

- Smart Minds Mathematics Learner's Book pg. 213
- Pair of compasses
- Rulers, protractors

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing 30° angle
Geometrical Constructions - Constructing 120° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 30° by bisecting 60°
- Verify the constructed angle
- Appreciate the relationship between 30° and 60° angles

In groups, learners are guided to:
- Draw straight line, mark point Y
- With Y as centre, make arc at D, with D as centre make arc at F
- Join F to Y (angle FYD = 60°), then bisect to get 30°

How do we construct an angle of 30°?

- Smart Minds Mathematics Learner's Book pg. 214
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 215
- Rulers, protractors

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 105° and 75° angles

By the end of the lesson, the learner should be able to:
- Construct angles of 105° and 75°
- Combine construction of 90° and 60° to get 105°
- Value the application of angle constructions

In groups, learners are guided to:
- Draw line MN, mark point T
- Construct 90° angle (NTO = 90°), then construct 60° on other side (angle KTO = 60°)
- Bisect angle KTO to get 30°, thus angle PTN = 90° + 15° = 105°

How do we construct an angle of 105°?

- Smart Minds Mathematics Learner's Book pg. 216
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions