Measurements

Pythagorean Relationship - Sides of a right-angled triangle

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

- 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

- Oral questions - Written exercises - Observation

Measurements

Pythagorean Relationship - Establishing the relationship
Pythagorean Relationship - Finding unknown sides

By the end of the lesson, the learner should be able to:
- State the Pythagorean relationship
- Verify Pythagorean relationship by counting squares
- Appreciate the relationship between sides of a right-angled triangle

- Trace and draw right-angled triangle with sides 3 cm, 4 cm and 5 cm
- Draw squares on each side and divide into 1 cm squares
- Count squares and compare: squares on height + squares on base = squares on hypotenuse

What is the Pythagorean relationship?

- Smart Minds Mathematics Learner's Book pg. 91
- Square grids
- Rulers and pencils
- Smart Minds Mathematics Learner's Book pg. 92
- Calculators
- Triangle diagrams

- Written assignments - Class activities - Oral questions

Measurements

Pythagorean Relationship - Real life applications

By the end of the lesson, the learner should be able to:
- Identify real life situations involving Pythagorean relationship
- Solve real life problems using Pythagorean relationship
- Value the application of Pythagorean relationship in daily life

- Solve puzzle finding missing sides marked with letters
- Calculate length of ladder inclined on wall
- Use IT devices to explore applications in construction and surveying

Where do we apply Pythagorean relationship in daily life?

- Smart Minds Mathematics Learner's Book pg. 93
- Puzzles
- Digital devices

- Written assignments - Class activities - Oral questions

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

- 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

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

- 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

- Written assignments - Class activities - Oral questions

Measurements

Length - Subtraction involving length

By the end of the lesson, the learner should be able to:
- Describe the process of subtracting lengths
- Subtract lengths involving Hm, Dm, m, dm and cm
- Show confidence in subtracting lengths

- Make cards with subtraction problems
- Regroup where necessary (borrow from higher unit)
- Solve problems comparing distances covered by Joan and John

How do we subtract lengths with different units?

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

- Written exercises - Oral questions - Observation

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

- 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

- 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

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

- 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

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

- 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

- Written assignments - Class activities - Oral questions

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

- 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

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

How do we find the area of a trapezium?

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

- Written exercises - Oral questions - Observation

Measurements

Area - Area of circles

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

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

How do we find the area of a circle?

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

- Written assignments - Class activities - Oral questions

Measurements

Area - Area of borders

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

- 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

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

- 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

- 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

- 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

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

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

How do we convert cubic centimetres to cubic metres?

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

- Written exercises - Oral questions - Observation

Measurements

Volume and Capacity - Volume of cubes

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

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

How do we find the volume of a cube?

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

- Written assignments - Class activities - Oral questions

Measurements

Volume and Capacity - Volume of cuboids

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

- 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

- 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

- Collect containers of different shapes
- Find volume and convert to capacity in litres
- Solve problems about tanks, tins and pipes

Where do we use volume and capacity in daily life?

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

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Units of measuring time

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

- Observe clock face with hour, minute and second hands
- Read time shown on stopwatches (hours, minutes, seconds)
- Draw clock faces showing different times

How do we read time from a clock face?

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

- Oral questions - Practical activities - Observation

Measurements

Time, Distance and Speed - Converting hours and minutes

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

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

How do we convert hours to minutes?

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

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Converting minutes and seconds

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

- 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

- 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

- Walk and run around athletics field (1 lap = 400 m)
- Record time taken for each activity
- Calculate: Speed = Distance ÷ Time

What is speed in kilometres per hour?

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

- Written assignments - Class activities - Oral questions

Measurements

Time, Distance and Speed - Speed in m/s

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

- Mark 100 m distance in the field
- Run 100 m race and record time using stopwatch
- Calculate speed in m/s

What is speed in metres per second?

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

- Written exercises - Oral questions - Observation

Measurements

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

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

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

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

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

- Written assignments - Class activities - Oral questions

Measurements

Temperature - Temperature in our environment
Temperature - Comparing temperature

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

- Take walk outside classroom and observe temperature
- Discuss temperature conditions as warm, hot or cold
- Record temperature changes at different times of day

What is temperature?

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

- Oral questions - Written exercises - Observation

Measurements

Temperature - Units of measuring temperature

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

- Visit health centre to see thermometer
- Identify °C and K symbols on thermometer
- Measure water temperature before and after heating

What are the units of measuring temperature?

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

- Written exercises - Oral questions - Observation

Measurements

Temperature - Converting °C to Kelvin

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

- Measure water temperature before heating and at boiling point
- Compare readings in °C and Kelvin
- Establish: Kelvin = °C + 273

How do we convert degrees Celsius to Kelvin?

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

- Written assignments - Class activities - Oral questions

Measurements

Temperature - Converting Kelvin to °C

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

- Complete table showing daily temperatures in Kelvin
- Convert to °C by subtracting 273
- Solve problems about melting points and town temperatures

How do we convert Kelvin to degrees Celsius?

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

- Written exercises - Oral questions - Observation

Measurements

Temperature - Temperature changes

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

- 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

- Role-play shopping activities using classroom shop
- Compare buying price and selling price
- Establish: Profit = Selling price - Buying price

What is profit in business?

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

- Oral questions - Written exercises - Observation

Measurements

Money - Percentage profit

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

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

How do we calculate percentage profit?

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

- Written exercises - Oral questions - Observation

Measurements

Money - Percentage loss

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

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

How do we calculate percentage loss?

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

- Written assignments - Class activities - Oral questions

Measurements

Money - Discount

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

- 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

- 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

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

- 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

- Written assignments - Class activities - Oral questions

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

- 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

- 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

- 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

- 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

- 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

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

- 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