Algebra

Linear Inequalities - Forming and solving linear inequalities in one unknown
Linear Inequalities - Graphical representation of linear inequalities in one unknown

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

- State the meaning of a linear inequality and identify the inequality symbols (>, <, ≥, ≤) and their interpretations.
- Solve linear inequalities in one unknown including cases where the inequality sign reverses.
- Appreciate the use of inequalities in representing real-life constraints such as budgets and resource limits.

In groups, learners are guided to:

- Discuss why resources such as bursary funds are sometimes shared unequally and form inequalities to represent such scenarios.
- Form and solve linear inequalities from real-life word problems involving trophies, school fees and class sizes.
- Work out inequalities involving all four operations and discuss the rule for reversing the sign when multiplying or dividing by a negative number.

How do we form and solve linear inequalities in one unknown?

- Oxford Active Mathematics Grade 9 pg. 72
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 73
- Graph paper and ruler

- Oral questions - Written assignments - Observation

Algebra

Linear Inequalities - Graphical representation of linear inequalities in two unknowns
Linear Inequalities - Graphical representation of inequalities in two unknowns: applications

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

- Describe what a linear inequality in two unknowns represents and how it differs from one in one unknown.
- Draw the boundary line for a linear inequality in two unknowns and identify the correct region.
- Appreciate the power of graphical methods in representing constraints involving two variables simultaneously.

In groups, learners are guided to:

- Form inequalities in two unknowns from contexts such as age comparisons, costs and total capacity of transport.
- Draw a straight line from a table of values for equations such as x+y=5 and determine the region satisfying x+y<5.
- Choose test points on each side of the boundary line, substitute into the inequality and shade the region that satisfies it.

How do we represent linear inequalities in two unknowns graphically?

- Oxford Active Mathematics Grade 9 pg. 74
- Graph paper and ruler
- Writing materials
- Oxford Active Mathematics Grade 9 pg. 75

- Oral questions - Written assignments - Observation

Algebra
Measurements
Measurements
Measurements

Linear Inequalities - Application of linear inequalities in real life
Area - Area of a regular pentagon
Area - Area of a regular hexagon
Area - Surface area of prisms

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

- Identify real-life situations where linear inequalities are used to model constraints and support decisions.
- Solve inequalities from real-life scenarios such as budgeting, capacity limits and resource sharing.
- Appreciate the role of linear inequalities in making informed and equitable decisions in everyday life.

In groups, learners are guided to:

- Solve a real-life budget problem: given a Ksh 600 budget for games and videos, form and solve a two-variable inequality and identify feasible combinations.
- Form and solve inequalities from real-life scenarios involving charity donations, factory workers' hours and county government planning.
- Discuss with family members how the knowledge of linear inequalities is applied to share resources equitably in the community.

How are linear inequalities applied in making real-life decisions?

- Oxford Active Mathematics Grade 9 pg. 77
- Writing materials
- Digital resources and internet access
- Oxford Active Mathematics Grade 9 pg. 79
- Ruler, protractor and sheets of paper
- 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

- Written tests - Oral questions - Observation

Measurements

Area - Surface area of pyramids
Area - Area of a sector and segment of a circle
Area - Surface area of a cone
Area - Surface area of a sphere

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

- Describe the structure of triangular, rectangular and square-based pyramids.
- Calculate the surface area of pyramids by summing the areas of all faces including the base.
- Value the skill of surface area calculation in making architectural models and constructing real structures.

In groups, learners are guided to:

- Open pyramid nets, draw and label all faces including the base and lateral triangular faces.
- Calculate the area of each triangular face and the base, then sum all areas.
- Identify objects from the environment that are pyramid-shaped and calculate their surface areas.

How do we work out the area of different surfaces?

- 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
- 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

- Written tests - Oral questions - Observation

Measurements

Volume of Solids - Volume of a triangular-based prism
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:

- 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
- Oxford Active Mathematics Grade 9 pg. 100
- Rectangular-based prism models
- 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
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

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

- Oral questions - Written assignments - 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
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
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
Approximations and Errors - Errors in estimation of measurements

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)
- Oxford Active Mathematics Grade 9 pg. 144
- Ruler, beam balance
- Objects of different sizes

- Oral questions - Written assignments - Observation

Measurements

Approximations and Errors - Percentage errors
Approximations and Errors - Application of approximations and errors in real life

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

- Written tests - Oral questions - Observation

Geometry

Scale Drawing - Compass and true bearings
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:

- Describe compass bearings and true bearings and explain how they indicate direction.
- Identify compass bearings (N, S, E, W, NE, NW, SE, SW) and measure true bearings clockwise from North.
- Appreciate the use of bearings in navigation on land, sea and air.

In groups, learners are guided to:

- Draw a compass rose and identify the eight compass directions and their relationship to each other.
- Identify and state the compass bearing and true bearing of directions shown in diagrams.
- Relate bearings to real-life navigation contexts such as ships using compasses and pilots flying on given bearings.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 165
- Ruler and protractor
- Oxford Active Mathematics Grade 9 pg. 166
- 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
Scale Drawing - Determining angles 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
- Oxford Active Mathematics Grade 9 pg. 175
- Ruler, protractor
- Graph paper

- Oral questions - Written assignments - Observation

Geometry

Scale Drawing - Application of scale drawing in simple surveying
Scale Drawing - Surveying and area calculation from scale drawing

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

- Describe the method of simple surveying using a field book and perpendicular offsets.
- Use scale drawing to represent a piece of land from field book measurements.
- Appreciate the use of scale drawing in surveying land and in community planning.

In groups, learners are guided to:

- Study field book entries showing survey line measurements and perpendicular offsets.
- Draw the vertical survey line and perpendicular offsets to scale, then join the boundary points.
- Calculate the area of each section (triangles and trapeziums) using the scale drawing measurements.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 177
- Ruler, protractor
- Graph paper
- Oxford Active Mathematics Grade 9 pg. 178

- Oral questions - Written assignments - 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

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

- Oral questions - Written assignments - 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
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
Data Handling and Probability

Trigonometry - Application of sines
Trigonometry - Application of cosines and tangents
Data Interpretation (Grouped Data) - Class width

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
- Oxford Active Mathematics Grade 9 pg. 216
- Oxford Active Mathematics Learner's Book Grade 9 pg. 224
- Calculators
- Reference books
- Charts showing sets of data

- Written assignments - Oral questions - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) - Frequency distribution tables of grouped data
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:

- Describe a frequency distribution table for grouped data.
- Draw a frequency distribution table of grouped data using tallies.
- Appreciate the role of frequency tables in summarising data.

In groups, learners are guided to:
- Discuss how to organise data into classes of equal width
- Tally a set of data and record the frequency for each class
- Draw and complete a frequency distribution table for grouped data

How can grouped data be organised into a frequency distribution table?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 227
- Calculators
- Manila paper and charts
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 230
- Charts
- Oxford Active Mathematics Learner's Book Grade 9 pg. 233
- Oxford Active Mathematics Learner's Book Grade 9 pg. 236

- Written assignment - Observation - Oral questions

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

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

- Practical activity - Observation - Written exercise

Data Handling and Probability

Probability - Tree diagrams for a single outcome

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

- Describe a tree diagram.
- Draw a tree diagram to represent the outcomes of an event.
- Appreciate the probability of events occurring in real-life situations.

In groups, learners are guided to:
- Discuss how a tree diagram represents possible outcomes
- List the possible outcomes of an event and their probabilities
- Draw tree diagrams to represent the outcomes of single events

How can a tree diagram help us represent and find probabilities?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 249
- Charts
- IT devices
- Reference books

- Written exercise - Observation - Oral questions