Measurements

Area - Square metres, acres and hectares

By the end of the lesson, the learner should be able to:
- Identify square metre, acre and hectare as units of area
- Convert between square metres, acres and hectares
- Show interest in units of measuring area

In groups, learners are guided to:
- Draw square measuring 1 m by 1 m and find area (1 m²)
- Walk around school compound and identify 1 acre piece of land
- Observe shapes with area of 1 hectare (100 m × 100 m)

What are the units of measuring area?

- Smart Minds Mathematics Learner's Book pg. 106
- Metre rulers
- Tape measures

- Oral questions - Written exercises - Observation

Measurements

Area - Area of a rectangle
Area - Area of a parallelogram

By the end of the lesson, the learner should be able to:
- State the formula for area of a rectangle
- Calculate area of rectangles
- Appreciate the use of area in real life

In groups, learners are guided to:
- Trace and cut out rectangles
- Find area by multiplying length and width
- Complete tables with length, width and area of rectangles

How do we find the area of a rectangle?

- Smart Minds Mathematics Learner's Book pg. 108
- Rectangular cut-outs
- Grid papers
- Smart Minds Mathematics Learner's Book pg. 110
- Paper cut-outs
- Scissors

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of a rhombus
Area - Area of a trapezium

By the end of the lesson, the learner should be able to:
- Derive the formula for area of a rhombus
- Calculate area of rhombuses
- Value accuracy in calculating area

In groups, learners are guided to:
- Cut out square WXYZ and mark point K on line WX
- Cut triangle WKZ and paste on line XY to form rhombus
- Discover: Area = Base length × Perpendicular height

How do we find the area of a rhombus?

- Smart Minds Mathematics Learner's Book pg. 112
- Square cut-outs
- Scissors
- Smart Minds Mathematics Learner's Book pg. 114
- Paper cut-outs
- Rulers

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of circles
Area - Area of borders
Area - Area of combined shapes

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

- Written assignments - Class activities - Oral questions

Measurements

Volume and Capacity - The cubic metre (m³)
Volume and Capacity - Converting m³ to cm³

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

- Oral questions - Practical activities - Observation

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
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 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
- 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
Time, Distance and Speed - Units of measuring time

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

- Written assignments - Class activities - Oral questions

Measurements

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

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
- Smart Minds Mathematics Learner's Book pg. 138
- Stopwatches
- Number cards

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Converting hours and seconds
Time, Distance and Speed - Converting units of distance
Time, Distance and Speed - Speed in km/h

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
- 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
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
Temperature - Converting °C to Kelvin
Temperature - Converting Kelvin to °C

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
- Smart Minds Mathematics Learner's Book pg. 153
- Calculators
- Smart Minds Mathematics Learner's Book pg. 154
- Temperature tables

- Written exercises - Oral questions - Observation

Measurements

Temperature - Temperature changes
Money - Profit

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
- Smart Minds Mathematics Learner's Book pg. 157
- Classroom shop
- Paper money

- Written assignments - Class activities - Oral questions

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
Money - Discount
Money - Percentage discount

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
- Smart Minds Mathematics Learner's Book pg. 164
- Price tags
- Charts
- Smart Minds Mathematics Learner's Book pg. 166

- 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
Money - Mobile money services

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

- Written assignments - Class activities - Oral questions

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
Angles - Angles at a point
Angles - Vertically opposite angles

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
- Smart Minds Mathematics Learner's Book pg. 186
- Paper cut-outs
- Smart Minds Mathematics Learner's Book pg. 187
- Scissors

- Oral questions - Written exercises - 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
Angles - Angles in a parallelogram

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

- Written assignments - Class activities - Oral questions

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
Geometrical Constructions - Measuring angles

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

- Written assignments - Class activities - Oral questions

Geometry

Geometrical Constructions - Bisecting angles
Geometrical Constructions - Constructing 90° angle

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
- Smart Minds Mathematics Learner's Book pg. 210
- Rulers, protractors

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 45° angle
Geometrical Constructions - Constructing 60° angle
Geometrical Constructions - Constructing 30° angle

By the end of the lesson, the learner should be able to:
- Construct an angle of 45° by bisecting 90°
- Verify the constructed angle
- Value accuracy in geometrical constructions

In groups, learners are guided to:
- Draw horizontal line, mark point K
- Construct 90° angle (MKB = 90°)
- Bisect angle MKB: make arcs at S and R, draw arcs to intersect at O, join O to K

How do we construct an angle of 45°?

- Smart Minds Mathematics Learner's Book pg. 211
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 213
- Rulers, protractors
- Smart Minds Mathematics Learner's Book pg. 214

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 120° angle
Geometrical Constructions - Constructing 105° and 75° angles

By the end of the lesson, the learner should be able to:
- Construct an angle of 120° using a pair of compasses and ruler
- Verify the constructed angle
- Show confidence in constructing obtuse angles

In groups, learners are guided to:
- Draw straight line, mark point M
- With centre M, make arc at C, with centre C make arc at E
- With centre E and same radius, make arc at F, join E to M (angle EMB = 120°)

How do we construct an angle of 120°?

- Smart Minds Mathematics Learner's Book pg. 215
- Pair of compasses
- Rulers, protractors
- Smart Minds Mathematics Learner's Book pg. 216
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing equilateral triangles

By the end of the lesson, the learner should be able to:
- Construct equilateral triangles using compasses and ruler
- Verify that all sides and angles are equal
- Appreciate properties of equilateral triangles

In groups, learners are guided to:
- Draw straight line, mark point Y, mark point X 6 cm away
- With Y as centre and radius 6 cm, draw arc above line
- With X as centre and same radius, draw arc to intersect at Z, join Z to Y and X

How do we construct an equilateral triangle?

- Smart Minds Mathematics Learner's Book pg. 218
- Pair of compasses
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing isosceles triangles
Geometrical Constructions - Constructing scalene triangles

By the end of the lesson, the learner should be able to:
- Construct isosceles triangles given side measurements
- Verify that two sides and two angles are equal
- Show confidence in constructing triangles

In groups, learners are guided to:
- Draw straight line, mark point M, mark point N 5 cm away
- With M as centre and radius 7 cm, draw arc above line
- With N as centre and radius 5 cm, draw arc to intersect at P, join points

How do we construct an isosceles triangle?

- Smart Minds Mathematics Learner's Book pg. 219
- Pair of compasses
- Rulers
- Smart Minds Mathematics Learner's Book pg. 220

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing circles

By the end of the lesson, the learner should be able to:
- Construct circles given radius or diameter
- Measure and verify the dimensions of constructed circles
- Appreciate the application of geometrical constructions in real life

In groups, learners are guided to:
- Use pair of compasses to draw circles with different diameters
- Measure diameter of circles drawn
- Calculate radius from diameter (radius = diameter ÷ 2)

How do we construct circles with given measurements?

- Smart Minds Mathematics Learner's Book pg. 221
- Pair of compasses
- Rulers

- Written assignments - Practical activities - Oral questions

Data Handling and Probability

Data Handling - Meaning of data and data collection
Data Handling - Frequency tables

By the end of the lesson, the learner should be able to:
- Define data as information gathered by observation, questioning or measurement
- Collect data through simple activities
- Show interest in collecting data

In groups, learners are guided to:
- Use digital device to find meaning of data
- Select favourite fruit from options (banana, watermelon, orange, mango)
- Write favourite fruit on paper and drop in basket, count responses

What is data?

- Smart Minds Mathematics Learner's Book pg. 222
- Pieces of paper
- Basket
- Smart Minds Mathematics Learner's Book pg. 223
- Class registers
- Frequency table templates

- Oral questions - Written exercises - Observation

Data Handling and Probability

Data Handling - Determining suitable scale
Data Handling - Drawing pictographs
Data Handling - Drawing bar graphs

By the end of the lesson, the learner should be able to:
- Explain the importance of choosing appropriate scale
- Determine suitable scale for vertical and horizontal axes
- Show confidence in selecting scales for graphs

In groups, learners are guided to:
- Compare Anne's and Josephine's graph scales
- Observe that congested scales make graphs hard to interpret
- Use multiples of 2 or 5 to make divisions easy to plot

Why is it important to choose a suitable scale for graphs?

- Smart Minds Mathematics Learner's Book pg. 225
- Graph papers
- Rulers
- Smart Minds Mathematics Learner's Book pg. 226
- Bloating paper
- Scissors, glue
- Smart Minds Mathematics Learner's Book pg. 228
- Rulers, coloured pencils

- Written exercises - Oral questions - Observation

Data Handling and Probability

Data Handling - Interpreting information from bar graphs
Data Handling - Drawing pie charts

By the end of the lesson, the learner should be able to:
- Read and interpret information from bar graphs
- Answer questions based on bar graph data
- Show interest in analyzing data from bar graphs

In groups, learners are guided to:
- Study bar graph showing fruits sold by Bahati in five days
- Identify scale used on vertical and horizontal axes
- Answer questions about highest, lowest values and comparisons

How do we interpret information from bar graphs?

- Smart Minds Mathematics Learner's Book pg. 231
- Bar graph samples
- Worksheets
- Smart Minds Mathematics Learner's Book pg. 233
- Pair of compasses
- Protractors

- Written assignments - Class activities - Oral questions

Data Handling and Probability

Data Handling - Interpreting pie charts
Data Handling - Drawing line graphs
Data Handling - Interpreting travel graphs

By the end of the lesson, the learner should be able to:
- Read and interpret information from pie charts
- Calculate values from pie chart sectors
- Value the use of pie charts in presenting data

In groups, learners are guided to:
- Study pie chart showing how Standa spent monthly salary of sh 30,000
- Calculate values: (sector angle ÷ 360°) × total value
- Answer questions about entertainment, rent, savings, investment

How do we interpret information from pie charts?

- Smart Minds Mathematics Learner's Book pg. 236
- Pie chart samples
- Calculators
- Smart Minds Mathematics Learner's Book pg. 238
- Graph papers
- Rulers
- Smart Minds Mathematics Learner's Book pg. 240

- Written assignments - Class activities - Oral questions