Algebra

Linear Inequalities - Forming and solving 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

- Oral questions - Written assignments - Observation

Algebra

Linear Inequalities - Graphical representation of linear inequalities in one unknown
Linear Inequalities - Graphical representation of linear inequalities in two unknowns

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

- Describe the graphical representation of linear inequalities and explain the difference between a solid and broken boundary line.
- Draw the boundary line and shade the region that does not satisfy the inequality on a Cartesian plane.
- Value the clarity of graphical methods in displaying the solution set of a linear inequality.

In groups, learners are guided to:

- Draw a Cartesian plane and draw the boundary line for inequalities such as x>2 and y≤3 using a table of values.
- Determine whether the boundary line should be solid (≤,≥) or broken (>,<) and discuss the reason for each.
- Shade the region that does NOT satisfy the inequality and verify by substituting test point coordinates.

How do we represent linear inequalities in one unknown on a Cartesian plane?

- Oxford Active Mathematics Grade 9 pg. 73
- Graph paper and ruler
- Oxford Active Mathematics Grade 9 pg. 74
- Writing materials

- Oral questions - Written assignments - Observation

Algebra

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

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

- Explain the steps for identifying and shading the feasible region for a linear inequality in two unknowns.
- Determine coordinate points in the feasible region that satisfy a given linear inequality.
- Develop confidence in constructing and interpreting graphical representations of two-variable inequalities.

In groups, learners are guided to:

- Represent inequalities in two unknowns such as x+y≥5 and x−y≤3 graphically on a Cartesian plane.
- Determine all coordinate points in the unshaded region and verify that each satisfies the given inequality.
- Solve problems involving school enrolment, transport planning and resource allocation using two-variable graphical inequalities.

How do we identify the feasible region satisfying a linear inequality in two unknowns?

- Oxford Active Mathematics Grade 9 pg. 75
- Graph paper and ruler
- Oxford Active Mathematics Grade 9 pg. 77
- Writing materials
- Digital resources and internet access

- Written assignments - Oral questions - Observation

Measurements

Area - Area of a regular pentagon
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:

- 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
- 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
Volume of Solids - Volume of a cone

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
- Oxford Active Mathematics Grade 9 pg. 103
- Cone-shaped models and containers

- Written assignments - Oral questions - Observation

Measurements

Volume of Solids - Volume of a frustum
Volume of Solids - Volume of a sphere

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

- Describe a frustum and explain how it is derived by cutting a pyramid or cone.
- Calculate the volume of a frustum by subtracting the volume of the smaller solid from the larger one.
- Value the ability to calculate the volume of frustums in real-life containers such as buckets and flower pots.

In groups, learners are guided to:

- Cut a pyramid model into two parts to form a frustum and a smaller pyramid, calculate the volume of each.
- Use the formula: volume of frustum = volume of large pyramid − volume of small pyramid.
- Solve real-life problems involving the volume of frustum-shaped containers and objects.

How do we determine the volume of different solids?

- Oxford Active Mathematics Grade 9 pg. 105
- Pyramid models
- Ruler and writing materials
- Oxford Active Mathematics Grade 9 pg. 107
- Spherical balls of different sizes

- Written tests - Oral questions - 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
Mass, Volume, Weight and Density - Mass, volume and density

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
- Oxford Active Mathematics Grade 9 pg. 114
- Cuboid blocks of different substances
- Beam balance and ruler

- Written assignments - Oral questions - Observation

Measurements

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

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

- Describe the relationships among mass, volume and density using the formula ρ = m/V.
- Calculate mass, volume and density of different substances using the relevant formula.
- Value the use of density calculations in science, engineering and identifying materials.

In groups, learners are guided to:

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

How do you weigh materials and objects?

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

- Written assignments - Oral questions - Observation

Measurements

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

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

- Discuss real-life applications of density including floatation, construction and food science.
- Solve complex problems involving mass, volume, weight and density in different contexts.
- Value the knowledge of density and its applications in making informed daily decisions.

In groups, learners are guided to:

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

How do you weigh materials and objects?

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

- Written tests - Oral questions - Observation

Measurements

Time, Distance and Speed - Speed in kilometres per hour
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
Time, Distance and Speed - Velocity

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
- Oxford Active Mathematics Grade 9 pg. 125
- Writing materials

- Written tests - Oral questions - Observation

Measurements

Time, Distance and Speed - Acceleration
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:

- Define acceleration and state the formula a = (v−u)/t.
- Calculate acceleration and deceleration using given initial velocity, final velocity and time values.
- Value the understanding of acceleration in road safety, sport science and engineering applications.

In groups, learners are guided to:

- Participate in short running events, record the starting and finishing velocities, calculate acceleration.
- Use stopwatch and tape measure to measure time and distance, then determine acceleration.
- Solve problems involving acceleration and deceleration using the formula a = (v−u)/t.

How do we observe speed in daily activities?

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

- Written assignments - Oral questions - 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
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
Scale Drawing - Locating points using bearing and distance

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
- Oxford Active Mathematics Grade 9 pg. 170
- Graph paper

- Oral questions - Written assignments - Observation

Geometry

Scale Drawing - Scale drawing using multi-step bearings
Scale Drawing - Identifying the angle of elevation

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

- Describe the procedure for making scale drawings involving multiple journey legs with different bearings.
- Make scale drawings showing two or more journey legs with different bearings and distances.
- Develop confidence and accuracy in solving navigation problems using multi-step scale drawing.

In groups, learners are guided to:

- Make scale drawings for journeys involving two or more legs (e.g. a ship sailing N to B then on a bearing of 080° to C).
- Measure the straight-line distance between the start and end points on the scale drawing and convert to actual distance.
- Solve problems involving aircraft routes and ship paths using multi-step bearings.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 171
- Ruler and protractor
- Graph paper
- Oxford Active Mathematics Grade 9 pg. 173
- Ruler, stick and string

- Written tests - Oral questions - 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
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
Similarity and Enlargement - Properties of enlargement

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

- Written assignments - Oral questions - Observation

Geometry

Similarity and Enlargement - Centre of enlargement and scale factor
Similarity and Enlargement - Application of properties of enlargement

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
- Oxford Active Mathematics Grade 9 pg. 195
- Digital devices

- Written assignments - Oral questions - 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
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
Data Interpretation (Grouped Data) - Mean 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
- Oxford Active Mathematics Learner's Book Grade 9 pg. 233

- Written tests - Oral questions - Observation

Data Handling and Probability

Data Interpretation (Grouped Data) - Median of grouped data
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

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

- Identify the median class of grouped data.
- Calculate the median of grouped data using the formula.
- Appreciate the median as a measure of central tendency.

In groups, learners are guided to:
- Use cumulative frequencies to determine the median class
- Identify the lower class boundary, class width and frequency of the median class
- Calculate the median from different sets of grouped data

How do we locate and calculate the median of grouped data?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 236
- Calculators
- Charts
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 238
- IT devices and calculators
- Internet access
- Oxford Active Mathematics Learner's Book Grade 9 pg. 242
- Coins
- Dice
- Oxford Active Mathematics Learner's Book Grade 9 pg. 244

- Written assignment - Observation - Oral questions

Data Handling and Probability

Probability - Identifying mutually exclusive events
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:

- Define mutually exclusive events.
- Identify mutually exclusive events in real-life situations.
- Appreciate mutually exclusive events in everyday life.

In groups, learners are guided to:
- Discuss the meaning of mutually exclusive events
- Use real-life examples to identify whether events are mutually exclusive
- Classify given events as mutually exclusive or not

When are two events said to be mutually exclusive?

- Oxford Active Mathematics Learner's Book Grade 9 pg. 245
- Coins
- Dice
- Reference books
- Oxford Active Mathematics Learner's Book Grade 9 pg. 246
- Spinners
- Coins and dice
- Oxford Active Mathematics Learner's Book Grade 9 pg. 247
- Oxford Active Mathematics Learner's Book Grade 9 pg. 249
- Charts
- IT devices

- Oral questions - Written exercise - Observation