Measurements

Volume of Solids - Volume of a triangular-based prism

By the end of the lesson, the learner should be able to:

- State the formula for the volume of a triangular-based prism and identify its cross-section.
- Calculate the volume of a triangular-based prism using V = cross-sectional area × length.
- Appreciate the use of prism volume calculations in determining the capacity of structures such as roofs and channels.

In groups, learners are guided to:

- Collect models of triangular-based prisms, identify the cross-section and measure its dimensions and the length.
- Calculate the area of the triangular cross-section and multiply by the length to obtain the volume.
- Solve real-life problems involving the volume of triangular-based prisms such as rooftops and swimming channels.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 98
- Triangular-based prism models
- Ruler and writing materials

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Volume of a rectangular-based prism
Volume of Solids - Volume of a pyramid

By the end of the lesson, the learner should be able to:

- Identify the dimensions of a rectangular-based prism and explain the formula for its volume.
- Calculate the volume of rectangular-based prisms (cuboids) by multiplying base area by height.
- Value the application of prism volume in construction, storage and packaging planning.

In groups, learners are guided to:

- Collect and measure cuboid-shaped containers, calculate the base area and multiply by height.
- Verify volume calculations by counting unit cubes packed into a model.
- Solve problems involving the volume of tanks, boxes and rooms in real-life contexts.

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

- Oxford Active Mathematics Grade 9 pg. 100
- Rectangular-based prism models
- Ruler and writing materials
- Oxford Active Mathematics Grade 9 pg. 101
- Pyramid models (clay or cut paper)

- Oral questions - Written assignments - 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

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

- Oral questions - Written assignments - Observation

Measurements

Volume of Solids - Application of volume of solids in real life
Mass, Volume, Weight and Density - Conversion of units of mass

By the end of the lesson, the learner should be able to:

- Identify real-life contexts where volumes of prisms, pyramids, cones, frustums and spheres are applied.
- Solve real-life problems involving volumes of different solids using appropriate formulas.
- Value the knowledge of volume in making practical decisions in construction and manufacturing.

In groups, learners are guided to:

- Solve multi-step problems involving volumes of containers, tanks and structures using relevant formulas.
- Discuss with family members how knowledge of volume is used in construction and packaging.
- Use IT tools to explore and calculate the volumes of different solid objects in engineering contexts.

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

- Oxford Active Mathematics Grade 9 pg. 108
- Writing materials
- Internet access
- Oxford Active Mathematics Grade 9 pg. 110
- Beam balance or electronic balance
- Objects of different masses

- Written tests - Oral questions - Observation

Measurements

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

By the end of the lesson, the learner should be able to:

- Identify practical situations where mass unit conversions are necessary.
- Solve problems requiring conversion of mass units in different real-life situations.
- Value the skill of mass conversion in ensuring accurate measurement and consumer protection.

In groups, learners are guided to:

- Collect and weigh different materials using a beam balance or electronic balance and record masses in different units.
- Convert between units by multiplying or dividing by the appropriate factor and verify answers.
- Solve real-life problems involving mass conversion such as weighing farm produce, ingredients and packages.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 111
- Beam balance and electronic balance
- Sand, stones and other materials
- Oxford Active Mathematics Grade 9 pg. 113
- Beam balance or electronic balance
- Objects of different masses

- Written assignments - Oral questions - Observation

Measurements

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

By the end of the lesson, the learner should be able to:

- Define density and state the formula ρ = m/V.
- Calculate density given the mass and volume of a substance.
- Appreciate the concept of density in explaining why some objects float and others sink.

In groups, learners are guided to:

- Collect cuboid-shaped blocks of different materials, measure their mass using a balance and dimensions using a ruler.
- Calculate the volume of each block and divide by mass to obtain density.
- Compare densities of different materials and discuss why denser objects sink in water.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 114
- Cuboid blocks of different substances
- Beam balance and ruler
- Oxford Active Mathematics Grade 9 pg. 115
- Cylindrical containers, beam balance
- Sand, water and different substances

- Oral questions - Written assignments - Observation

Measurements

Mass, Volume, Weight and Density - Application of density

By the end of the lesson, the learner should be able to:

- Identify real-life situations where density is applied such as in materials science and fluid mechanics.
- Determine the density of different liquids and solids through practical investigation.
- Appreciate the role of density in differentiating substances and making informed materials choices.

In groups, learners are guided to:

- Fill a cylindrical container with water, measure mass and calculate density; repeat with salty water and cooking oil.
- Compare densities of different liquids and discuss floatation using the concept of relative density.
- Solve complex problems involving density, volume and mass of different solid and liquid substances.

How do you weigh materials and objects?

- Oxford Active Mathematics Grade 9 pg. 116
- Cylindrical containers, measuring cylinder
- Liquids (water, oil), solid objects

- Oral questions - Written tests - 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
Time, Distance and Speed - Average speed

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
- Oxford Active Mathematics Grade 9 pg. 123

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Average speed: applications

By the end of the lesson, the learner should be able to:

- Identify situations where average speed calculations are applied in real life.
- Solve multi-step problems involving average speed with stops and different legs of a journey.
- Develop a positive attitude towards using mathematical tools to plan and optimise travel.

In groups, learners are guided to:

- Calculate average speed for journeys with rest stops, different speeds on different sections and return trips.
- Analyse distance-time graphs to determine average speed for each segment of a journey.
- Solve problems involving journeys with multiple speed changes and stops at intermediate points.

How do we observe speed in daily activities?

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

- Written tests - Oral questions - 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

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

- Written tests - Oral questions - Observation

Measurements

Money - Import duty and excise duty
Money - Value Added Tax

By the end of the lesson, the learner should be able to:

- Define import duty, excise duty and customs value and explain when each applies.
- Calculate import duty and excise duty charged on goods using given rates.
- Appreciate the role of import and excise duty in generating government revenue and protecting local industries.

In groups, learners are guided to:

- Visit the Kenya Revenue Authority (KRA) or invite a resource person to discuss import and excise duties.
- Work out import duty from given customs values and rates using the formula: duty = rate × customs value.
- Research goods exempted from import duty in Kenya and discuss the economic rationale.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 136
- KRA resource materials
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 139
- Shopping receipts

- Written assignments - Oral questions - Observation

Measurements

Money - Export duty and application of taxes in real life
Approximations and Errors - Approximation of quantities using arbitrary units

By the end of the lesson, the learner should be able to:

- Define export duty and identify goods that attract export duty.
- Calculate export duty charged on exported goods using given rates.
- Appreciate the importance of paying taxes in supporting national development and public services.

In groups, learners are guided to:

- Discuss and research goods that attract export duty and those that are exempted in Kenya.
- Solve problems calculating export duty using the formula: duty = rate × value of export.
- Discuss with family members the different types of taxes and why paying taxes is important for national development.

How do we determine taxes charged on different goods?

- Oxford Active Mathematics Grade 9 pg. 140
- KRA resource materials
- Internet access
- Oxford Active Mathematics Grade 9 pg. 142
- Sticks, string, cups, jugs
- Small and large squares (cut paper)

- Written tests - Oral questions - Observation

Measurements

Approximations and Errors - Errors in estimation of measurements

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

- Written assignments - Oral questions - Observation

Measurements
Geometry

Approximations and Errors - Percentage errors
Approximations and Errors - Application of approximations and errors in real life
Scale Drawing - Compass and true bearings

By the end of the lesson, the learner should be able to:

- Describe percentage error and explain how it relates the error to the actual measurement.
- Calculate percentage error using the formula: percentage error = (error ÷ actual measurement) × 100%.
- Appreciate the use of percentage error in quality control and scientific measurement contexts.

In groups, learners are guided to:

- Estimate and measure different quantities (length, capacity, mass) and calculate the raw error for each.
- Apply the percentage error formula to each measurement and compare results across different quantities.
- Use IT devices to compute percentage errors and relate findings to consumer protection and quality assurance.

How do we estimate measurements of different quantities?

- Oxford Active Mathematics Grade 9 pg. 146
- Ruler, measuring cylinder, beam balance
- Internet access
- Oxford Active Mathematics Grade 9 pg. 148
- Writing materials
- Digital resources and internet access
- Oxford Active Mathematics Grade 9 pg. 165
- Ruler and protractor

- Written tests - Oral questions - Observation

Geometry

Scale Drawing - Compass bearings: identifying bearing directions
Scale Drawing - True bearings
Scale Drawing - Bearing of one point from another

By the end of the lesson, the learner should be able to:

- Identify compass bearings from diagrams showing multiple directions of travel from a fixed point.
- Measure and state the compass bearing of directions using the four cardinal and four intercardinal compass points.
- Value the global standardisation of compass bearings in ensuring safety in navigation and travel.

- Study diagrams showing directions in which different learners travelled from a common point and identify each compass bearing.
- Measure the angles between compass directions and state each as a compass bearing.
- Solve problems identifying the compass bearing of places shown in navigation diagrams.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 166
- Ruler and protractor
- Oxford Active Mathematics Grade 9 pg. 167
- Oxford Active Mathematics Grade 9 pg. 168
- Ruler, protractor and maps

- Oral questions - Written assignments - Observation

Geometry

Scale Drawing - Locating points using bearing and distance
Scale Drawing - Scale drawing using multi-step bearings

By the end of the lesson, the learner should be able to:

- State the procedure for locating a point on a scale drawing given its bearing and distance.
- Draw scale diagrams to show the positions of points at given bearings and distances from a reference point.
- Appreciate how scale drawing using bearings enables accurate planning in navigation and land management.

In groups, learners are guided to:

- Use a ruler and protractor to make a scale drawing showing the position of a point at a given bearing and distance.
- Use the scale 1 cm represents 10 m (or 100 km) to draw positions of ships, aircraft and landmarks.
- Measure the straight-line distance between points on the scale drawing and convert to actual distance.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 170
- Ruler and protractor
- Graph paper
- Oxford Active Mathematics Grade 9 pg. 171

- Written assignments - Oral questions - Observation

Geometry

Scale Drawing - Identifying the angle of elevation

By the end of the lesson, the learner should be able to:

- Define the angle of elevation and explain how it is formed between the horizontal and the line of sight.
- Identify the angle of elevation in given real-life diagrams and practical scenarios.
- Appreciate the use of angles of elevation in construction, navigation and engineering.

In groups, learners are guided to:

- Stand 5 m from a goal post and hold a stick vertically, then observe and identify the angle from the horizontal to the top.
- Identify the angle of elevation in given diagrams showing towers, mountains and buildings.
- Discuss real-life situations where angles of elevation are used such as observing aircraft, cranes and tall buildings.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 173
- Ruler, stick and string

- Oral questions - Written assignments - Observation

Geometry

Scale Drawing - Determining the angle of elevation
Scale Drawing - Identifying the angle of depression

By the end of the lesson, the learner should be able to:

- Explain the method for determining the angle of elevation using scale drawing.
- Make scale drawings to determine the angle of elevation from given distance and height data.
- Value the precision of scale drawing in finding angles of elevation without direct measurement.

In groups, learners are guided to:

- Lean a ladder against a wall at different positions, measure the height and horizontal distance and make a scale drawing.
- Measure the angle of elevation from the scale drawing and verify with actual measurement.
- Solve real-life problems finding angle of elevation or height of buildings and towers using scale drawing.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 174
- Ruler, protractor, metre rule
- Graph paper
- Object, tape measure and string

- Written assignments - Oral questions - Observation

Geometry

Scale Drawing - Determining angles of depression
Scale Drawing - Application of scale drawing in simple surveying

By the end of the lesson, the learner should be able to:

- Explain the procedure for determining the angle of depression using scale drawing.
- Make scale drawings to determine the angle of depression from given heights and distances.
- Develop accuracy in solving problems involving angles of depression in real-life contexts.

In groups, learners are guided to:

- Make scale drawings representing situations where an observer looks down at an object from a height.
- Measure the angle of depression from the scale drawing and interpret the answer in real-life terms.
- Solve problems involving vertical cliffs, planes and observatories using scale drawing of angles of depression.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 175
- Ruler, protractor
- Graph paper
- Oxford Active Mathematics Grade 9 pg. 177

- Written tests - Oral questions - Observation

Geometry

Scale Drawing - Surveying and area calculation from scale drawing

By the end of the lesson, the learner should be able to:

- Identify the steps involved in calculating the area of a land parcel from a scale drawing and field book.
- Solve problems calculating the area of land parcels using scale drawings and field book measurements.
- Value the knowledge of scale drawing in community development, land allocation and agriculture.

In groups, learners are guided to:

- Use field book data to draw sections of a field and identify all triangular and trapezoidal sections.
- Calculate the area of each section using actual measurements derived from the scale drawing.
- Add the areas of individual sections to find the total area of the land parcel and express in hectares.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 178
- Ruler, protractor
- Graph paper

- Written tests - Oral questions - Observation

Geometry

Similarity and Enlargement - Similar figures and their properties
Similarity and Enlargement - Identifying similar figures: ratios and proportions

By the end of the lesson, the learner should be able to:

- Define similarity and state the properties of similar figures (equal angles, proportional sides).
- Identify similar figures and determine ratios of corresponding sides.
- Appreciate the application of similarity in photography, map-making and architecture.

In groups, learners are guided to:

- Collect objects from the environment, sort them by similarity and discuss what makes them similar.
- Measure corresponding sides of similar triangles and determine the ratios.
- Verify that similar figures have equal corresponding angles and proportional corresponding sides using set squares.

What are similar objects?

- Oxford Active Mathematics Grade 9 pg. 182
- Objects from environment
- Ruler and protractor
- Oxford Active Mathematics Grade 9 pg. 184

- Oral questions - Written assignments - Observation

Geometry

Similarity and Enlargement - Drawing similar figures
Similarity and Enlargement - Properties of enlargement

By the end of the lesson, the learner should be able to:

- Explain the steps for drawing a figure similar to a given figure using a specified ratio.
- Draw figures similar to given objects using a specified ratio of similarity.
- Develop creativity and precision in representing similar shapes at different scales.

In groups, learners are guided to:

- Trace a given triangle, measure its sides and draw a similar triangle where each side is enlarged or reduced by a given scale.
- Use a ruler and geometrical instruments to draw similar rectangles and other geometric shapes.
- Verify the similarity of drawn figures by checking angle equality and side ratios.

What are similar objects?

- Oxford Active Mathematics Grade 9 pg. 186
- Ruler, protractor
- Geometrical instruments
- Oxford Active Mathematics Grade 9 pg. 189
- Ruler and geometrical instruments
- Tracing paper

- Oral questions - Written assignments - Observation

Geometry

Similarity and Enlargement - Centre of enlargement and scale factor

By the end of the lesson, the learner should be able to:

- Identify the centre of enlargement and the scale factor from a given enlargement diagram.
- Determine the centre of enlargement and calculate the scale factor from object and image measurements.
- Value the systematic use of the centre of enlargement in creating accurate scale models and plans.

In groups, learners are guided to:

- Join corresponding vertices of object and image and extend the lines to locate the centre of enlargement.
- Calculate the scale factor by dividing the distance from centre to image vertex by the distance from centre to object vertex.
- Determine the coordinates of image vertices from given scale factors and centres of enlargement.

How do we use enlargement in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 191
- Ruler and geometrical instruments
- Graph paper

- Written assignments - Oral questions - Observation

Geometry

Similarity and Enlargement - Application of properties of enlargement
Similarity and Enlargement - Linear scale factor of similar figures

By the end of the lesson, the learner should be able to:

- Identify real-life contexts where enlargement is applied such as map-making and model design.
- Apply properties of enlargement to draw objects and their images given the centre and scale factor.
- Appreciate how enlargement enables accurate reproduction of shapes at different sizes in design.

In groups, learners are guided to:

- Use IT devices to enlarge and reduce images and discuss the scale factor applied to each dimension.
- Apply enlargement properties to determine coordinates of image vertices from a given centre and scale factor.
- Solve problems involving enlargement in real-life contexts such as making scale models of buildings and printing photographs.

How do we use enlargement in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 195
- Ruler and geometrical instruments
- Digital devices
- Oxford Active Mathematics Grade 9 pg. 196
- Ruler and similar objects
- Writing materials

- Oral questions - Written tests - Observation

Geometry

Trigonometry - Angles and sides of a right-angled triangle
Trigonometry - Trigonometric ratios: sine, cosine and tangent

By the end of the lesson, the learner should be able to:

- Identify the hypotenuse, opposite and adjacent sides of a right-angled triangle relative to a given acute angle.
- Distinguish the three sides of a right-angled triangle with respect to different acute angles.
- Appreciate the foundational role of right-angled triangles in trigonometry and real-life applications.

In groups, learners are guided to:

- Draw right-angled triangles and identify all angles and sides including the hypotenuse.
- Discuss and label the opposite, adjacent and hypotenuse sides relative to each acute angle in the triangle.
- Identify sides in various right-angled triangles relative to different acute angles represented by letters.

What is the relationship between angles and sides in a right-angled triangle?

- Oxford Active Mathematics Grade 9 pg. 199
- Ruler and geometrical instruments
- Oxford Active Mathematics Grade 9 pg. 201
- Ruler
- Writing materials

- Oral questions - Written assignments - Observation

Geometry

Trigonometry - Tables of trigonometric ratios
Trigonometry - Trigonometric ratios using a calculator

By the end of the lesson, the learner should be able to:

- Describe the structure of tables of sines, cosines and tangents including the main, difference and ADD sections.
- Use tables of sines, cosines and tangents to read trigonometric ratios for given angles.
- Appreciate mathematical tables as reliable and accurate tools for reading trigonometric values.

In groups, learners are guided to:

- Study a section of the table of sines and practise navigating the rows, columns and ADD section.
- Read cosine and tangent values from respective tables for given angles including angles with decimals.
- Solve problems that require reading trigonometric ratios directly from mathematical tables.

What is the relationship between angles and sides in a right-angled triangle?

- Oxford Active Mathematics Grade 9 pg. 204
- Mathematical tables (sines, cosines, tangents)
- Oxford Active Mathematics Grade 9 pg. 211
- Scientific calculator
- Mathematical tables

- Oral questions - Written assignments - Observation

Geometry

Trigonometry - Application of sines

By the end of the lesson, the learner should be able to:

- Explain how the sine ratio is used to calculate unknown sides and angles in right-angled triangles.
- Apply the sine ratio to calculate lengths of sides and sizes of angles in real-life situations.
- Appreciate the use of sine in solving real-world problems such as finding heights of buildings and lengths of ramps.

In groups, learners are guided to:

- Use the sine ratio to determine the height a ladder reaches on a wall given its length and the angle it makes with the ground.
- Solve problems involving angles of elevation using the sine ratio and mathematical tables or a calculator.
- Discuss the use of trigonometry in surveying, construction and navigation with reference to real examples.

What is the relationship between angles and sides in a right-angled triangle?

- Oxford Active Mathematics Grade 9 pg. 213
- Scientific calculator
- Mathematical tables

- Written assignments - Oral questions - Observation

Geometry
Data Handling and Probability
Data Handling and Probability
Data Handling and Probability

Trigonometry - Application of cosines and tangents
Data Interpretation (Grouped Data) - Class width
Data Interpretation (Grouped Data) - Frequency distribution tables of grouped data
Data Interpretation (Grouped Data) - Modal class of grouped data

By the end of the lesson, the learner should be able to:

- Identify situations where cosine and tangent ratios are applied to solve right-angled triangle problems.
- Apply cosine and tangent ratios to calculate unknown lengths and angles in real-life situations.
- Value the comprehensive use of trigonometric ratios in engineering, construction and navigation.

In groups, learners are guided to:

- Use the cosine ratio to find horizontal distances and side lengths in right-angled triangle problems.
- Apply the tangent ratio to determine angles and distances in elevation and depression situations.
- Discuss with family members how trigonometry is applied in real-world professions such as architecture, engineering and aviation.

What is the relationship between angles and sides in a right-angled triangle?

- Oxford Active Mathematics Grade 9 pg. 216
- Scientific calculator
- Mathematical tables
- Oxford Active Mathematics Learner's Book Grade 9 pg. 224
- Calculators
- Reference books
- Charts showing sets of data
- Oxford Active Mathematics Learner's Book Grade 9 pg. 227
- Manila paper and charts
- Oxford Active Mathematics Learner's Book Grade 9 pg. 230
- Charts

- Written tests - Oral questions - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) - Mean of grouped data
Data Interpretation (Grouped Data) - Median of grouped data
Data Interpretation (Grouped Data) - Mean and median of grouped data in real-life situations

By the end of the lesson, the learner should be able to:

- State the steps of calculating the mean of grouped data.
- Calculate the mean of grouped data from real-life situations.
- Appreciate the use of the mean in summarising data.

In groups, learners are guided to:
- Discuss how to obtain the midpoint (x) of each class
- Work out fx for each class and the sums of f and fx
- Calculate the mean from different sets of grouped data

How is the mean of grouped data calculated?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 233
- Calculators
- Charts
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 236
- Oxford Active Mathematics Learner's Book Grade 9 pg. 238
- IT devices and calculators
- Internet access

- Written assignment - Oral questions - Observation

Data Handling and Probability

Probability - Experiments involving equal and likely outcomes
Probability - Range of probability of an event
Probability - Identifying mutually exclusive events

By the end of the lesson, the learner should be able to:

- Explain the meaning of equally likely outcomes.
- Perform experiments involving equal and likely outcomes and determine probability.
- Appreciate the occurrence of chance events in real life.

In groups, learners are guided to:
- Discuss the meaning of equally likely outcomes using a coin or a die
- Carry out experiments such as tossing a coin or rolling a die and record the outcomes
- Work out the probability of equally likely outcomes

What does it mean for outcomes to be equally likely?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 242
- Coins
- Dice
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 244
- Oxford Active Mathematics Learner's Book Grade 9 pg. 245

- Practical activity - Observation - Oral questions

Data Handling and Probability

Probability - Experiments involving mutually exclusive events
Probability - Experiments involving independent events
Probability - Tree diagrams for a single outcome

By the end of the lesson, the learner should be able to:

- Describe single-chance experiments involving mutually exclusive events.
- Perform experiments of single chance involving mutually exclusive events.
- Collaborate with peers while carrying out probability experiments.

In groups, learners are guided to:
- Carry out experiments involving mutually exclusive events, for example spinning an arrow
- Determine the probability of mutually exclusive events
- Discuss how the probabilities of mutually exclusive events are added

How do we find the probability of mutually exclusive events?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 246
- Spinners
- Coins and dice
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 247
- Coins
- Dice
- Oxford Active Mathematics Learner's Book Grade 9 pg. 249
- Charts
- IT devices

- Practical activity - Observation - Written exercise