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

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

- Written assignments - Oral questions - Observation

Measurements

Mass, Volume, Weight and Density - Application of density
Mass, Volume, Weight and Density - Application of density in real life

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
- Oxford Active Mathematics Grade 9 pg. 117
- Water containers, objects of different densities
- Internet access

- Oral questions - Written tests - Observation

Measurements

Time, Distance and Speed - Speed in metres per second
Time, Distance and Speed - Speed in kilometres per hour

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

- State the formula for speed and explain the relationship between distance, time and speed.
- Calculate speed in metres per second from given distance and time values.
- Appreciate the use of speed calculations in sports, transport and safety planning.

- Run or walk a 100 m race, record the time taken for each learner and calculate speed in m/s.
- Discuss the formula speed = distance ÷ time and solve problems using different units.
- Solve real-life problems involving athletes, vehicles and animals using speed in m/s.

How do we observe speed in daily activities?

- Oxford Active Mathematics Grade 9 pg. 121
- Stopwatches or clocks
- Tape measure
- 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

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

- Oral questions - Written assignments - Observation

Measurements

Time, Distance and Speed - Longitudes and local time
Money - Currencies of other countries

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

- Explain how the earth's rotation relates to time differences across longitudes.
- Calculate the local time of a place given its longitude and the time at another location.
- Appreciate the global significance of time zones in international communication and travel.

In groups, learners are guided to:

- Discuss the relationship between longitudes and time using a globe and a light source.
- Calculate time differences between two places using longitude difference × 4 minutes per degree.
- Use IT devices to explore time zones in different parts of the world and solve real-life time problems.

Why does time vary in different places of the world?

- Oxford Active Mathematics Grade 9 pg. 127
- Globe, maps
- Digital resources and internet access
- Oxford Active Mathematics Grade 9 pg. 132
- Old newspapers and magazines
- Digital devices and internet access

- Written tests - Oral questions - Observation

Measurements

Money - Conversion of currencies
Money - Conversion of currencies: applications

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

- Describe how currency conversion works using buying and selling rates from financial institutions.
- Calculate the amount received when converting currencies using given exchange rates.
- Value accurate currency conversion in protecting consumers during trade and travel.

In groups, learners are guided to:

- Use newspapers or visit financial institutions to find current exchange rates for different currencies.
- Fill in a currency exchange rate table and use it to convert between currencies.
- Solve worked examples converting Kenya shillings to foreign currencies and vice versa.

Why do we change currencies from one form to another?

- Oxford Active Mathematics Grade 9 pg. 133
- Newspapers with currency exchange rates
- Digital devices
- Oxford Active Mathematics Grade 9 pg. 134
- Writing materials
- Internet access

- Oral questions - Written assignments - 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
Scale Drawing - Determining 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
- Oxford Active Mathematics Grade 9 pg. 174
- Ruler, protractor, metre rule
- Graph paper

- Oral questions - Written assignments - Observation

Geometry

Scale Drawing - Identifying the angle of depression

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

- Define the angle of depression and distinguish it from the angle of elevation.
- Identify the angle of depression in given diagrams and practical real-life scenarios.
- Appreciate the application of angles of depression in aviation, navigation and cliff-top surveying.

In groups, learners are guided to:

- Stand at a point above ground level, place an object below eye level and identify the angle formed below the horizontal.
- Identify angles of depression in given diagrams showing cliffs, planes and boats.
- Discuss real-life scenarios where angles of depression are encountered such as pilots viewing runways and guards looking down towers.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 174
- Object, tape measure and string

- Oral questions - Written assignments - 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
Similarity and Enlargement - Similar figures and their properties

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

- Written tests - Oral questions - Observation

Geometry

Similarity and Enlargement - Identifying similar figures: ratios and proportions
Similarity and Enlargement - Drawing similar figures

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

- Describe the conditions for two triangles to be similar (equal angles and proportional corresponding sides).
- Calculate unknown lengths in similar figures using the constant ratio of corresponding sides.
- Value the use of proportional reasoning in solving real-life problems involving similar shapes.

In groups, learners are guided to:

- Study pairs of triangles and determine whether they are similar by checking angle equality and side ratios.
- Calculate unknown side lengths using the constant ratio of corresponding sides.
- Solve real-life problems involving similar shapes such as shadow lengths and map-distance calculations.

What are similar objects?

- Oxford Active Mathematics Grade 9 pg. 184
- Ruler and protractor
- Oxford Active Mathematics Grade 9 pg. 186
- Ruler, protractor
- Geometrical instruments

- Written assignments - Oral questions - Observation

Geometry

Similarity and Enlargement - Properties of enlargement
Similarity and Enlargement - Centre of enlargement and scale factor

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

- Define enlargement and state the key properties of an enlargement transformation.
- Demonstrate the properties of enlargement including the invariance of angles and proportional increase of sides.
- Appreciate the role of enlargement in photography, architecture and digital image processing.

In groups, learners are guided to:

- Use models and tracing paper to demonstrate enlargement from a fixed centre of enlargement.
- Join corresponding vertices of object and image and extend the lines to identify properties.
- Discuss and verify: angles are preserved, sides are in constant ratio, and shape is unchanged in enlargement.

How do we use enlargement in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 189
- Ruler and geometrical instruments
- Tracing paper
- Oxford Active Mathematics Grade 9 pg. 191
- Graph paper

- Oral questions - Written assignments - Observation

Geometry

Similarity and Enlargement - Application of properties of enlargement

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

- Oral questions - Written tests - Observation

Geometry

Similarity and Enlargement - Linear scale factor of similar figures
Trigonometry - Angles and sides of a right-angled triangle

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

- State the meaning of linear scale factor and explain how it relates lengths in similar figures.
- Calculate the linear scale factor of similar figures and use it to find unknown lengths.
- Value the application of linear scale factor in model-making, map reading and photography.

In groups, learners are guided to:

- Measure corresponding sides of two similar objects and calculate the ratio to determine the linear scale factor.
- Use the linear scale factor to calculate unknown dimensions of similar figures.
- Discuss with family members how knowledge of similarity and enlargement is applied in making land plans, house plans and other real-life contexts.

How do we use enlargement in real-life situations?

- Oxford Active Mathematics Grade 9 pg. 196
- Ruler and similar objects
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 199
- Ruler and geometrical instruments

- Written tests - Oral questions - Observation

Geometry

Trigonometry - Trigonometric ratios: sine, cosine and tangent
Trigonometry - Tables of trigonometric ratios

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

- State the definitions of sine, cosine and tangent ratios for acute angles in a right-angled triangle.
- Calculate sine, cosine and tangent ratios for given right-angled triangles.
- Value the precision of trigonometric ratios in describing the relationship between angles and sides.

In groups, learners are guided to:

- Work out the ratios of opposite/hypotenuse, adjacent/hypotenuse and opposite/adjacent for different right-angled triangles.
- Observe that the ratio for each trigonometric function is constant for the same angle across similar triangles.
- Calculate sine, cosine and tangent for given angles using known triangle measurements.

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

- Oxford Active Mathematics Grade 9 pg. 201
- Ruler
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 204
- Mathematical tables (sines, cosines, tangents)

- Oral questions - Written assignments - Observation

Geometry

Trigonometry - Trigonometric ratios using a calculator
Trigonometry - Application of sines

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

- Explain how to use a scientific calculator to find trigonometric ratios for given angles.
- Determine sine, cosine and tangent of angles using a scientific calculator accurately.
- Value the efficiency and accuracy of scientific calculators in computing trigonometric ratios.

In groups, learners are guided to:

- Use a scientific calculator to find sin, cos and tan of various angles by pressing the relevant function keys followed by the angle.
- Read the answers from the screen and express them to four significant figures.
- Verify calculator results against values from mathematical tables to build confidence in both methods.

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

- Oxford Active Mathematics Grade 9 pg. 211
- Scientific calculator
- Mathematical tables
- Oxford Active Mathematics Grade 9 pg. 213

- Oral questions - Written assignments - Observation

Geometry
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

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

- Written tests - Oral questions - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) - Modal class of grouped data
Data Interpretation (Grouped Data) - Mean of grouped data
Data Interpretation (Grouped Data) - Median of grouped data

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

- Define the modal class of grouped data.
- Identify the modal class from a frequency distribution table.
- Value the use of the modal class in interpreting data.

In groups, learners are guided to:
- Discuss the meaning of the modal class
- Draw a frequency distribution table for given data
- Identify the modal class from different frequency distribution tables

Which class in a set of grouped data occurs most frequently?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 230
- Calculators
- Charts
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 233
- Oxford Active Mathematics Learner's Book Grade 9 pg. 236

- Oral questions - Written exercise - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) - Mean and median of grouped data in real-life situations
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 how the mean and median are used to interpret real-life data.
- Use IT devices or other materials to determine the mean and median of grouped data.
- Appreciate data interpretation in real-life situations.

In groups, learners are guided to:
- Collect real-life data, for example distances to nearby health facilities, and group it
- Use IT devices or other materials to determine the mean and median of the data
- Discuss the interpretation of the mean and median in real-life contexts

How are the mean and median useful in interpreting real-life data?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 238
- IT devices and calculators
- Internet access
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 242
- Coins
- Dice
- Oxford Active Mathematics Learner's Book Grade 9 pg. 244
- Oxford Active Mathematics Learner's Book Grade 9 pg. 245

- Practical activity / project - 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