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
Volume and Capacity - Converting cm³ to m³

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

- Written assignments - Class activities - Oral questions

Measurements

Volume and Capacity - Volume of cubes
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 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
- Smart Minds Mathematics Learner's Book pg. 126
- Clay, cartons
- Rulers

- Written assignments - Class activities - Oral questions

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

- 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
Time, Distance and Speed - Speed in km/h

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

- Written exercises - Oral questions - Observation

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
Temperature - Units of measuring 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
- Smart Minds Mathematics Learner's Book pg. 151
- Sufuria, water

- Oral questions - Written exercises - Observation

Measurements

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

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

- Written assignments - Class activities - Oral questions

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

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
Geometry
Geometry

Money - Mobile money transactions
Angles - Angles on a straight line
Angles - Angles at a point

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
- Smart Minds Mathematics Learner's Book pg. 184
- Protractors
- Rulers
- Smart Minds Mathematics Learner's Book pg. 186
- Paper cut-outs

- Written assignments - Class activities - Oral questions

Geometry

Angles - Vertically opposite angles
Angles - Alternate angles on a transversal

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
- Smart Minds Mathematics Learner's Book pg. 188
- Rulers

- Written exercises - Oral questions - Observation

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
Angles - Interior angles of triangles, rectangles, squares

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

- Written exercises - Oral questions - Observation

Geometry

Angles - Interior angles of rhombus, parallelogram, trapezium, pentagon, hexagon
Angles - Exterior angles of polygons

By the end of the lesson, the learner should be able to:
- Identify interior angles of various polygons
- Calculate sum of interior angles using formula (n-2) × 180°
- Appreciate the relationship between sides and interior angles

In groups, learners are guided to:
- Trace and cut out rhombus, parallelogram, trapezium
- Measure interior angles and find sums
- Sub-divide pentagon into 3 triangles, hexagon into 4 triangles

How do we calculate sum of interior angles of any polygon?

- Smart Minds Mathematics Learner's Book pg. 197
- Polygon cut-outs
- Protractors
- Smart Minds Mathematics Learner's Book pg. 201

- Written exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Measuring angles
Geometrical Constructions - Bisecting 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
- Smart Minds Mathematics Learner's Book pg. 208
- Pair of compasses

- Oral questions - Practical activities - Observation

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
Geometrical Constructions - Constructing 30° 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
- Smart Minds Mathematics Learner's Book pg. 214
- Rulers

- Practical exercises - Oral questions - Observation

Geometry

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

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
- Smart Minds Mathematics Learner's Book pg. 218

- Practical exercises - Oral questions - Observation

Geometry

Geometrical Constructions - Constructing isosceles 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

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing scalene triangles

By the end of the lesson, the learner should be able to:
- Construct scalene triangles given three side measurements
- Verify that all sides and angles are different
- Value accuracy in triangle constructions

In groups, learners are guided to:
- Draw straight line, mark point A, mark point B 6 cm away
- With A as centre and radius 5 cm, draw arc
- With B as centre and radius 8 cm, draw arc to intersect at C, join points

How do we construct a scalene triangle?

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

- Practical exercises - Oral questions - Observation

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
Data Handling - Determining suitable scale

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
- Smart Minds Mathematics Learner's Book pg. 225
- Graph papers
- Rulers

- Oral questions - Written exercises - Observation

Data Handling and Probability

Data Handling - Drawing pictographs
Data Handling - Drawing bar graphs

By the end of the lesson, the learner should be able to:
- Define a pictograph
- Draw pictographs to represent data
- Value the use of pictures in representing data

In groups, learners are guided to:
- Study chart showing wild animals at Masai Mara National Park
- Trace and cut out animals, stick under suitable category
- Use symbols to represent quantities (key: 1 symbol = specific value)

What is a pictograph?

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

- Written assignments - Practical activities - Oral questions

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