Geometry

Scale Drawing - Compass and true bearings
Scale Drawing - Compass bearings: identifying bearing directions
Scale Drawing - True bearings

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.
- 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.

- 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.
- 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. 165
- Ruler and protractor
- Oxford Active Mathematics Grade 9 pg. 166
- Ruler and protractor
- Oxford Active Mathematics Grade 9 pg. 167

- Oral questions - Written assignments - Observation

Geometry

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:
- Explain how to determine the bearing of one point from another given a diagram.
- Calculate the bearing of one point from another from given diagrams and measurements.
- Value the application of bearing calculations in locating positions of towns, ships and aircraft.

In groups, learners are guided to:
- Study diagrams showing positions of points and determine compass and true bearings of each from given reference points.
- Use the Kenya map to determine the true bearings between named towns.
- Solve problems involving two planes or ships taking off in different directions from the same point.

How do we use scale drawing in real life?

- Oxford Active Mathematics Grade 9 pg. 168
- Ruler, protractor and maps
- Oxford Active Mathematics Grade 9 pg. 170
- Ruler and protractor
- Graph paper

- Written assignments - Oral questions - Observation

Geometry

Scale Drawing - Scale drawing using multi-step bearings

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

- Written tests - Oral questions - Observation

Geometry

Scale Drawing - Identifying the angle of elevation

By the end of the lesson, the learner should be able to:
- Define the angle of elevation and explain how it is formed between the horizontal and the line of sight.
- Identify the angle of elevation in given real-life diagrams and practical scenarios.
- Appreciate the use of angles of elevation in construction, navigation and engineering.

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

How do we use scale drawing in real life?

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

- Oral questions - Written assignments - Observation

Geometry

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

By the end of the lesson, the learner should be able to:
- Explain the method for determining the angle of elevation using scale drawing.
- Make scale drawings to determine the angle of elevation from given distance and height data.
- Value the precision of scale drawing in finding angles of elevation without direct measurement.
- 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:
- 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.
- 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
- Ruler, protractor, metre rule
- Graph paper
- Oxford Active Mathematics Grade 9 pg. 174
- Object, tape measure and string

- Written assignments - Oral questions - Observation
- 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

By the end of the lesson, the learner should be able to:
- Identify the steps involved in calculating the area of a land parcel from a scale drawing and field book.
- Solve problems calculating the area of land parcels using scale drawings and field book measurements.
- Value the knowledge of scale drawing in community development, land allocation and agriculture.

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

How do we use scale drawing in real life?

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

- Written tests - Oral questions - Observation

Geometry

Similarity and Enlargement - Similar figures and their properties

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

- Oral questions - Written assignments - 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.
- 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:
- 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.
- 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. 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
- Oral questions - Written assignments - Observation

Geometry

Similarity and Enlargement - Centre of enlargement and scale factor

By the end of the lesson, the learner should be able to:
- Identify the centre of enlargement and the scale factor from a given enlargement diagram.
- Determine the centre of enlargement and calculate the scale factor from object and image measurements.
- Value the systematic use of the centre of enlargement in creating accurate scale models and plans.

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

How do we use enlargement in real-life situations?

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

- Written assignments - Oral questions - Observation

Geometry

Similarity and Enlargement - Application of properties of enlargement

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

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

- Written tests - Oral questions - Observation

Geometry

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

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.
- 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:
- 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.
- 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. 199
- Ruler and geometrical instruments
- 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

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

- Oral questions - Written assignments - Observation

Geometry

Trigonometry - Application of sines

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

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

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

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

- Written assignments - Oral questions - Observation

Geometry
Data Handling and Probability

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

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

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

By the end of the lesson, the learner should be able to:
- 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.
- 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:
- 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
- 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 can grouped data be organised into a frequency distribution table?
How do we locate and calculate the median of grouped data?

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

- Written assignment - Observation - Oral questions

Data Handling and Probability

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

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

What does it mean for outcomes to be equally likely?

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

- Practical activity - Observation - Oral questions

Data Handling and Probability

Probability - Identifying mutually exclusive events
Probability - Experiments involving mutually exclusive events

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

- Oral questions - Written exercise - Observation

Data Handling and Probability

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 independent events.
- Perform experiments involving independent events and determine their probability.
- Avoid harmful practices such as gambling when applying probability.

In groups, learners are guided to:
- Discuss the meaning of independent events
- Carry out experiments involving independent events, for example tossing two coins
- Work out the probability of independent events by multiplying their probabilities

How does the outcome of one event affect another in independent events?

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

- Practical activity - Observation - Written exercise