Measurements

Pythagorean Relationship - Sides of a right-angled triangle
Pythagorean Relationship - Establishing the relationship

By the end of the lesson, the learner should be able to:
- Identify the sides of a right-angled triangle
- Name the base, height and hypotenuse of a right-angled triangle
- Show interest in learning about right-angled triangles

In groups, learners are guided to:
- Read story of Linda and Methuselah using a ladder to climb a fruit tree
- Draw figure formed between tree, ladder and ground
- Identify the longest side (hypotenuse) and two shorter sides (base and height)

What are the sides of a right-angled triangle?

- Smart Minds Mathematics Learner's Book pg. 89
- Ladders
- Right-angled triangle models
- Smart Minds Mathematics Learner's Book pg. 91
- Square grids
- Rulers and pencils

- Oral questions - Written exercises - Observation

Measurements

Pythagorean Relationship - Finding unknown sides
Pythagorean Relationship - Real life applications

By the end of the lesson, the learner should be able to:
- Explain how to use Pythagorean relationship to find unknown sides
- Calculate unknown sides using a² + b² = c²
- Show confidence in applying the relationship

In groups, learners are guided to:
- Use formula c² = a² + b² to find hypotenuse
- Use formula a² = c² - b² to find shorter sides
- Solve problems like finding length of ramp and ladder

How do we find unknown sides using Pythagorean relationship?

- Smart Minds Mathematics Learner's Book pg. 92
- Calculators
- Triangle diagrams
- Smart Minds Mathematics Learner's Book pg. 93
- Puzzles
- Digital devices

- Written exercises - Oral questions - Observation

Measurements

Length - Converting units of length

By the end of the lesson, the learner should be able to:
- Identify units of length (cm, dm, m, Dm, Hm)
- Convert units of length from one form to another
- Show interest in converting units of length

In groups, learners are guided to:
- Study Washika going up stairs labelled cm, dm, m, Dm, Hm
- Note that each step is 10 times the previous
- Generate conversion tables: 1 Hm = 10 Dm = 100 m = 1000 dm = 10000 cm

Why do we convert units of length?

- Smart Minds Mathematics Learner's Book pg. 94
- Conversion charts
- Metre rulers

- Oral questions - Written exercises - Observation

Measurements

Length - Addition involving length
Length - Subtraction involving length

By the end of the lesson, the learner should be able to:
- Explain the process of adding lengths with different units
- Add lengths involving Hm, Dm, m, dm and cm
- Appreciate the use of addition of length in real life

In groups, learners are guided to:
- Study map showing distances between home, school and shopping centre
- Add lengths and regroup where necessary
- Solve problems like Munyao walking from home to market to school

How do we add lengths with different units?

- Smart Minds Mathematics Learner's Book pg. 96
- Maps
- Number cards
- Smart Minds Mathematics Learner's Book pg. 98
- Number cards
- Charts

- Written assignments - Class activities - Oral questions

Measurements

Length - Multiplication involving length
Length - Division involving length

By the end of the lesson, the learner should be able to:
- Explain how to multiply lengths by whole numbers
- Multiply lengths involving Hm, Dm, m, dm and cm
- Value accuracy in multiplication of lengths

In groups, learners are guided to:
- Read story of Natasha fetching water from river twice daily
- Multiply each unit and regroup where necessary
- Solve problems about Jared's daily distance to school

How do we multiply lengths by whole numbers?

- Smart Minds Mathematics Learner's Book pg. 99
- Word problems
- Calculators
- Smart Minds Mathematics Learner's Book pg. 100
- Charts

- Written assignments - Class activities - Oral questions

Measurements

Length - Perimeter and circumference of circles

By the end of the lesson, the learner should be able to:
- Define perimeter and circumference
- Calculate perimeter of plane figures and circumference of circles
- Appreciate the use of perimeter and circumference in real life

In groups, learners are guided to:
- Measure distance around chalkboard, door and window
- Measure circumference and diameter of circular objects
- Establish relationship: Circumference ÷ Diameter = π (3.14 or 22/7)

How do we find the circumference of a circle?

- Smart Minds Mathematics Learner's Book pg. 101
- Circular objects
- Tape measures

- Written assignments - Class activities - Oral questions

Measurements

Area - Square metres, acres and hectares
Area - Area of a rectangle

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

- Oral questions - Written exercises - Observation

Measurements

Area - Area of a parallelogram
Area - Area of a rhombus

By the end of the lesson, the learner should be able to:
- Derive the formula for area of a parallelogram
- Calculate area of parallelograms
- Show confidence in finding area of parallelograms

In groups, learners are guided to:
- Cut out rectangle ABCD and mark point E on line AD
- Cut triangle ABE and paste on line DC to form parallelogram
- Discover: Area = Base length × Perpendicular height

How do we find the area of a parallelogram?

- Smart Minds Mathematics Learner's Book pg. 110
- Paper cut-outs
- Scissors
- Smart Minds Mathematics Learner's Book pg. 112
- Square cut-outs

- Written exercises - Oral questions - Observation

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
Area - Area of borders

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

- Written assignments - Class activities - Oral questions

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
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
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

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

- Written assignments - Class activities - Oral questions

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

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
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

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
Money - Percentage loss

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
- Smart Minds Mathematics Learner's Book pg. 162

- Written exercises - Oral questions - Observation

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
Money - Commission and percentage commission

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
- Smart Minds Mathematics Learner's Book pg. 167
- Commission tables

- Written assignments - Class activities - Oral questions

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 - 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
Geometry

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

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

- Written assignments - Class activities - Oral questions

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
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

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
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

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

- Written assignments - Practical activities - Oral questions

Geometry

Geometrical Constructions - Constructing 30° 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

- 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

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

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

- Oral questions - Written exercises - Observation

Data Handling and Probability

Data Handling - Frequency tables
Data Handling - Determining suitable scale

By the end of the lesson, the learner should be able to:
- Define a frequency table
- Represent data using tally marks and frequency
- Appreciate the use of frequency tables in organizing data

- Ask class teacher to show class register
- Identify number of learners present each day
- Record findings using tally marks in frequency table

How do we represent data in a frequency table?

- Smart Minds Mathematics Learner's Book pg. 223
- Class registers
- Frequency table templates
- Smart Minds Mathematics Learner's Book pg. 225
- Graph papers
- Rulers

- Written assignments - Class activities - Oral questions

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

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

- Written assignments - Class activities - Oral questions

Data Handling and Probability

Data Handling - Drawing pie charts
Data Handling - Interpreting pie charts

By the end of the lesson, the learner should be able to:
- Define a pie chart as a circle divided into sectors
- Calculate angles for each sector
- Draw pie charts to represent data

In groups, learners are guided to:
- Read story of Ndole the bus driver spending salary on fees, savings, food
- Draw circle and shade fractions (1/2, 1/4, 1/4)
- Calculate sector angles: (value ÷ total) × 360°

How do we draw a pie chart?

- Smart Minds Mathematics Learner's Book pg. 233
- Pair of compasses
- Protractors
- Smart Minds Mathematics Learner's Book pg. 236
- Pie chart samples
- Calculators

- Written exercises - Practical activities - Observation

Data Handling and Probability

Data Handling - Drawing line graphs

By the end of the lesson, the learner should be able to:
- Define a line graph as showing relationship between two quantities
- Draw line graphs to represent data
- Appreciate the use of line graphs in showing trends

In groups, learners are guided to:
- Study table showing packets of milk and cost in shillings
- Choose appropriate scale, draw and mark axes
- Plot points using table values, join points with straight line

How do we draw a line graph?

- Smart Minds Mathematics Learner's Book pg. 238
- Graph papers
- Rulers

- Written exercises - Practical activities - Observation

Data Handling and Probability

Data Handling - Interpreting travel graphs

By the end of the lesson, the learner should be able to:
- Draw and interpret travel graphs
- Calculate distance, time and speed from travel graphs
- Show interest in using graphs to represent journeys

In groups, learners are guided to:
- Study table showing Lugai's journey from town A to town B
- Draw travel graph with time on horizontal axis and distance on vertical axis
- Calculate distance at specific times, total time and average speed

How do we use travel graphs to show journeys?

- Smart Minds Mathematics Learner's Book pg. 240
- Graph papers
- Calculators

- Written assignments - Class activities - Oral questions