Measurements

Area - Area of a regular pentagon

By the end of the lesson, the learner should be able to:
- State the formula for the area of a regular pentagon and explain the relationship between the central triangle and the polygon.
- Calculate the area of a regular pentagon by dividing it into five equal triangles.
- Appreciate the relevance of area of regular polygons in design and architecture.

In groups, learners are guided to:
- Discuss the properties of a regular pentagon and use cut-outs to divide it into triangles.
- Measure the base and height of one triangle, calculate its area and multiply by five.
- Solve real-life problems involving the area of regular pentagons such as pentagonal tiles and floor designs.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 79
- Ruler, protractor and sheets of paper

- Oral questions - Written assignments - Observation

Measurements

Area - Area of a regular hexagon
Area - Surface area of prisms
Area - Surface area of pyramids
Area - Area of a sector and segment of a circle

By the end of the lesson, the learner should be able to:
- Describe how a regular hexagon is divided into six equal triangles to calculate its area.
- Calculate the area of a regular hexagon by summing the areas of six equal triangles.
- Value the use of hexagonal area calculations in real-life applications such as tiling and honeycomb structures.

In groups, learners are guided to:
- Draw a regular hexagon, divide it into six equal triangles and cut them out.
- Measure the base and height of one triangle, calculate its area and multiply by six.
- Explore real-life applications of regular hexagons such as floor tiles, bathroom walls and honey combs.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 81
- Ruler, protractor, sheets of paper
- Oxford Active Mathematics Grade 9 pg. 85
- Triangular and rectangular-based prism models
- Ruler, sheets of paper
- Oxford Active Mathematics Grade 9 pg. 87
- Pyramid models, sheets of paper, ruler
- Oxford Active Mathematics Grade 9 pg. 89
- Pair of compasses, ruler, protractor
- Sheets of paper

- Oral questions - Written assignments - Observation

Measurements

Area - Surface area of a cone
Area - Surface area of a sphere
Volume of Solids - Volume of a triangular-based prism
Volume of Solids - Volume of a rectangular-based prism

By the end of the lesson, the learner should be able to:
- Identify the faces of a cone and state the formula for its total surface area.
- Calculate the surface area of a cone using the formula SA = πr² + πrl.
- Appreciate the relevance of cone surface area in packaging, manufacturing and everyday objects.

In groups, learners are guided to:
- Open a paper cone to form a net, identify the circular base and curved surface.
- Measure the radius and slant height, calculate the area of each part and sum them.
- Collect cone-shaped objects from the environment and calculate their surface areas using the formula.

How do we work out the area of different surfaces?

- Oxford Active Mathematics Grade 9 pg. 93
- Paper cones, scissors, ruler, protractor
- Oxford Active Mathematics Grade 9 pg. 95
- Spherical balls of different sizes
- Ruler and writing materials
- Oxford Active Mathematics Grade 9 pg. 98
- Triangular-based prism models
- Oxford Active Mathematics Grade 9 pg. 100
- Rectangular-based prism models

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Volume of a pyramid

By the end of the lesson, the learner should be able to:
- State the formula for the volume of triangular, rectangular and square-based pyramids.
- Calculate the volume of various pyramids using V = ⅓ × base area × height.
- Appreciate the geometry of pyramids and their significance in architecture and cultural heritage.

In groups, learners are guided to:
- Collect or construct pyramid models, measure the base dimensions and perpendicular height.
- Apply the formula V = ⅓bh to calculate the volumes of pyramids of different shapes.
- Use relevant formulas to compare the volumes of a prism and a pyramid with the same base and height.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 101
- Pyramid models (clay or cut paper)
- Ruler and writing materials

- Written assignments - Oral questions - Observation

Measurements

Volume of Solids - Volume of a cone
Volume of Solids - Volume of a frustum

By the end of the lesson, the learner should be able to:
- State the formula for the volume of a cone and explain each variable.
- Calculate the volume of a cone using the formula V = ⅓πr²h.
- Appreciate the application of cone volume in everyday containers such as funnels, ice cream cones and silos.

In groups, learners are guided to:
- Collect cone-shaped objects such as funnels and party hats, measure the radius and height.
- Apply the formula V = ⅓πr²h to calculate the volume of the cone.
- Compare the volume of a cone with a cylinder of the same base and height and discuss the relationship.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 103
- Cone-shaped models and containers
- Ruler and writing materials
- Oxford Active Mathematics Grade 9 pg. 105
- Pyramid models

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Volume of a sphere
Volume of Solids - Application of volume of solids in real life

By the end of the lesson, the learner should be able to:
- State the formula for the volume of a sphere and explain each term.
- Calculate the volume of a sphere using the formula V = 4/3πr³.
- Appreciate the application of sphere volume in manufacturing spherical tanks, balls and globes.

In groups, learners are guided to:
- Collect balls of different sizes, measure the diameter, calculate the radius and compute volume using V = 4/3πr³.
- Discuss real-life spherical objects and estimate their volumes using the formula.
- Play games involving different-sized balls and work out their volumes using the formula.

How do we use the volume of solids in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 107
- Spherical balls of different sizes
- Ruler and writing materials
- Oxford Active Mathematics Grade 9 pg. 108
- Writing materials
- Internet access

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Conversion of units of mass
Mass, Volume, Weight and Density - Conversion of units of mass: applications

By the end of the lesson, the learner should be able to:
- State the units of mass and explain the relationships between kg, g, mg, Dg, hg and tonne.
- Convert units of mass from one form to another in different situations.
- Appreciate the importance of accurate mass measurement in trade and consumer protection.

In groups, learners are guided to:
- Study and identify different instruments used for measuring mass including balances and scales.
- Discuss the units of mass (kg, g, mg, hg, Dg, t) and their conversion factors using the ×10/÷10 rule.
- Solve problems involving conversion of mass units in real-life contexts such as weighing produce and luggage.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 110
- Beam balance or electronic balance
- Objects of different masses
- Oxford Active Mathematics Grade 9 pg. 111
- Beam balance and electronic balance
- Sand, stones and other materials

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Mass and weight
Mass, Volume, Weight and Density - Mass, volume and density

By the end of the lesson, the learner should be able to:
- Explain the difference between mass and weight and state the formula W = mg.
- Calculate weight from mass using the gravitational constant g = 10 N/kg.
- Value accurate measurement of mass and weight in ensuring consumer protection and health safety.

In groups, learners are guided to:
- Discuss the difference between mass and weight using different objects on a balance.
- Measure the mass of objects, then calculate weight using W = mg.
- Discuss contexts where both mass and weight are used such as weighing luggage, food and body health.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 113
- Beam balance or electronic balance
- Objects of different masses
- Oxford Active Mathematics Grade 9 pg. 114
- Cuboid blocks of different substances
- Beam balance and ruler

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Calculating mass, volume and density
Mass, Volume, Weight and Density - Application of density

By the end of the lesson, the learner should be able to:
- Describe the relationships among mass, volume and density using the formula ρ = m/V.
- Calculate mass, volume and density of different substances using the relevant formula.
- Value the use of density calculations in science, engineering and identifying materials.

In groups, learners are guided to:
- Fill containers of known volume with different substances (water, sand), measure the mass and calculate density.
- Rearrange the density formula to calculate mass (m = ρV) and volume (V = m/ρ) in different problems.
- Solve problems involving mass, volume and density in different real-life situations using IT devices or other resources.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 115
- Cylindrical containers, beam balance
- Sand, water and different substances
- Oxford Active Mathematics Grade 9 pg. 116
- Cylindrical containers, measuring cylinder
- Liquids (water, oil), solid objects

- Written assignments - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density - Application of density in real life
Time, Distance and Speed - Speed in metres per second

By the end of the lesson, the learner should be able to:
- Discuss real-life applications of density including floatation, construction and food science.
- Solve complex problems involving mass, volume, weight and density in different contexts.
- Value the knowledge of density and its applications in making informed daily decisions.

In groups, learners are guided to:
- Investigate whether different objects float or sink in water and relate the observations to their densities.
- Use IT tools to explore how density is measured and applied in industry and food science.
- Discuss with family members situations where density knowledge is applied in solving daily problems.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 117
- Water containers, objects of different densities
- Internet access
- Oxford Active Mathematics Grade 9 pg. 121
- Stopwatches or clocks
- Tape measure

- Written tests - Oral questions - Observation

Measurements

Time, Distance and Speed - Speed in kilometres per hour

By the end of the lesson, the learner should be able to:
- Describe the relationship between speed in m/s and km/h and state the conversion factor.
- Calculate speed in km/h and convert between m/s and km/h accurately.
- Value the application of speed in km/h in road transport, journey planning and road safety.

In groups, learners are guided to:
- Use distance-time graphs to determine speed in km/h for different journeys.
- Calculate speed using distances between real Kenyan towns and actual journey times.
- Solve problems involving journeys between towns and discuss speed limits and road safety.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 122
- Graph paper and ruler
- Writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Average speed
Time, Distance and Speed - Average speed: applications

By the end of the lesson, the learner should be able to:
- Explain the concept of average speed and how it differs from instantaneous speed.
- Calculate average speed for journeys with different speeds over different distances.
- Appreciate the relevance of average speed in planning multi-stage journeys and road safety.

In groups, learners are guided to:
- Analyse scenarios where a vehicle travels at different speeds on different legs of a journey.
- Work out average speed using total distance ÷ total time taken for the whole journey.
- Solve problems involving average speed in real-life transport scenarios such as bus, lorry and cyclist journeys.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 123
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 124
- Graph paper and writing materials

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Velocity
Time, Distance and Speed - Acceleration

By the end of the lesson, the learner should be able to:
- Explain the difference between speed and velocity and define displacement.
- Distinguish between speed and velocity and calculate velocity in given real-life situations.
- Appreciate the precision of velocity in describing motion in physics and engineering.

In groups, learners are guided to:
- Discuss the difference between distance and displacement using diagrams with directional arrows.
- Determine velocity of objects moving in specified directions and compare with speed values.
- Solve problems that distinguish between speed and velocity in real-life contexts.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 125
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 126
- Stopwatch and tape measure

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Longitudes on the globe
Time, Distance and Speed - Longitudes and local time

By the end of the lesson, the learner should be able to:
- Identify and describe longitudes on the globe including the Greenwich Meridian and their labelling.
- Distinguish between longitudes east and west of the Greenwich Meridian using a globe or map.
- Appreciate the global system of longitudes and their role in navigation and geography.

In groups, learners are guided to:
- Study a globe or maps and identify longitudes as imaginary lines running from north to south.
- Identify the Greenwich Meridian and distinguish east (0°–180°E) and west (0°–180°W) longitudes.
- Use a globe and maps to identify the longitudes of different cities in Kenya and across the world.

Why does time vary in different places of the world?

- Oxford Active Mathematics Grade 9 pg. 126
- Globe or map of the world
- Oxford Active Mathematics Grade 9 pg. 127
- Globe, maps
- Digital resources and internet access

- Oral questions - Written assignments - Observation

Measurements

Money - Currencies of other countries
Money - Conversion of currencies

By the end of the lesson, the learner should be able to:
- Identify currencies used in different countries and explain the concept of currency exchange.
- Distinguish between buying and selling rates of currency exchange.
- Appreciate the global nature of currency exchange in international trade and travel.

In groups, learners are guided to:
- Collect cut-outs of different currencies from old newspapers and magazines and match each to its country.
- Use digital devices to search for and list currencies of various countries.
- Visit a nearby bank or financial institution to find out the buying and selling rates of different currencies.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 132
- Old newspapers and magazines
- Digital devices and internet access
- Oxford Active Mathematics Grade 9 pg. 133
- Newspapers with currency exchange rates
- Digital devices

- Oral questions - Written assignments - Observation

Measurements

Money - Conversion of currencies: applications
Money - Import duty and excise duty

By the end of the lesson, the learner should be able to:
- Identify situations where currency conversion is used in international trade and travel.
- Solve real-life problems involving conversion between different world currencies.
- Develop awareness of financial literacy and consumer protection in international transactions.

In groups, learners are guided to:
- Solve multi-step problems converting US dollars, Euros, Pounds, Yen and other currencies to and from Kenya shillings.
- Discuss the effect of exchange rate changes on the cost of imported goods.
- Use IT tools to find current exchange rates and apply them to solve real-life problems.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 134
- Writing materials
- Internet access
- Oxford Active Mathematics Grade 9 pg. 136
- KRA resource materials

- Written tests - Oral questions - Observation

Measurements

Money - Value Added Tax
Money - Export duty and application of taxes in real life

By the end of the lesson, the learner should be able to:
- Define Value Added Tax (VAT) and explain how it is calculated on goods and services.
- Calculate VAT using the formula VAT = rate × (customs value + import duty + excise duty).
- Value the role of VAT in public revenue generation and recognise it on shopping receipts.

In groups, learners are guided to:
- Collect shopping receipts and identify the VAT charged and the rate applied.
- Work out VAT on different items using the given formula and the 16% standard rate.
- Discuss imported and local goods that attract VAT and calculate the total cost of goods inclusive of VAT.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 139
- Shopping receipts
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 140
- KRA resource materials
- Internet access

- Oral questions - Written assignments - Observation

Measurements

Approximations and Errors - Approximation of quantities using arbitrary units

By the end of the lesson, the learner should be able to:
- Define an arbitrary unit and describe its use in approximating measurements of different quantities.
- Approximate lengths, areas, volumes, capacities and masses using arbitrary units.
- Appreciate the role of approximation in everyday measurement when standard tools are unavailable.

In groups, learners are guided to:
- Measure the classroom length in palm lengths, foot lengths and strides and compare results.
- Approximate the area of a surface using small and large squares and record findings.
- Approximate the volume of a box using small and large cubes and the capacity of containers using cups and jugs.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 142
- Sticks, string, cups, jugs
- Small and large squares (cut paper)

- Oral questions - Written assignments - Observation

Measurements

Approximations and Errors - Errors in estimation of measurements
Approximations and Errors - Percentage errors

By the end of the lesson, the learner should be able to:
- Explain the concept of measurement error and how it arises from estimation.
- Calculate the error in a measurement by computing the difference between estimated and actual values.
- Develop a sense of responsibility in minimising errors when measuring quantities.

In groups, learners are guided to:
- Estimate the length of objects using palm lengths then measure with a ruler; record both values.
- Calculate the error = estimated measurement − actual measurement for each object.
- Discuss real-life situations where estimation errors have consequences such as in construction and medicine.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 144
- Ruler, beam balance
- Objects of different sizes
- Oxford Active Mathematics Grade 9 pg. 146
- Ruler, measuring cylinder, beam balance
- Internet access

- Written assignments - Oral questions - Observation

Measurements
Geometry
Geometry
Geometry
Geometry
Geometry

Approximations and Errors - Application of approximations and errors in real life
Coordinates and Graphs - Plotting points on a Cartesian plane
Coordinates and Graphs - Graphs of straight lines
Coordinates and Graphs - Parallel lines and their gradients
Coordinates and Graphs - Perpendicular lines and their gradients
Coordinates and Graphs - Applications of graphs of straight lines

By the end of the lesson, the learner should be able to:
- Identify real-life situations where approximations and errors are relevant such as in trade, science and engineering.
- Solve problems involving approximations and errors in various measurement contexts.
- Value accuracy and precision in measurement as a foundation for consumer protection and scientific inquiry.

In groups, learners are guided to:
- Solve real-life problems involving errors and percentage errors in capacity, mass and length measurements.
- Discuss how errors in measurement affect trade and consumer protection in everyday buying and selling.
- Discuss with family members how knowledge of approximations and errors is applied in their daily work and home activities.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 148
- Writing materials
- Digital resources and internet access
- Oxford Active Mathematics Grade 9 pg. 149
- Graph paper and ruler
- Oxford Active Mathematics Grade 9 pg. 151
- Oxford Active Mathematics Grade 9 pg. 154
- Oxford Active Mathematics Grade 9 pg. 158
- Oxford Active Mathematics Grade 9 pg. 162

- Written tests - Oral questions - Observation