4.0 Geometry

4.3 Similarity and Enlargement - Similar figures
4.3 Similarity and Enlargement - Properties of similar figures (1)
4.3 Similarity and Enlargement - Properties of similar figures (2)
4.3 Similarity and Enlargement - Drawing similar figures

By the end of the lesson, the learner should be able to:
- Define similar figures
- Identify and sort similar figures from collections of objects
- Show interest in recognizing similar figures in the environment
- Identify that corresponding angles of similar figures are equal
- Use properties to determine unknown sides and angles
- Develop interest in applying properties of similar figures

The learner is guided to:
- Collect different objects from the environment
- Sort objects according to similarity
- Discuss criteria used for sorting
- Identify pairs of similar figures from given diagrams
The learner is guided to:
- Measure corresponding angles of similar figures
- Observe that corresponding angles are equal
- Use ratio of sides to find unknown lengths
- Solve problems involving similar figures

What makes two figures similar?
How do we use properties of similar figures?

- Master Mathematics Grade 9 pg. 185
- Various objects
- Cut-outs of shapes
- Charts
- Models
- Master Mathematics Grade 9 pg. 186
- Rulers
- Tracing papers
- Calculators
- Pencils
- Master Mathematics Grade 9 pg. 186
- Protractors
- Rulers
- Calculators
- Practice worksheets
- Master Mathematics Grade 9 pg. 189
- Compasses
- Plain papers

- Observation - Oral questions
- Written tests - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Determining properties of enlargement
4.3 Similarity and Enlargement - Positive scale factor (1)

By the end of the lesson, the learner should be able to:
- Define centre of enlargement and scale factor
- Locate the centre of enlargement and determine scale factor
- Appreciate that enlargements produce similar figures

The learner is guided to:
- Join corresponding points of objects and images
- Locate the centre where lines meet
- Measure distances from centre to object and image
- Calculate the scale factor

What is the relationship between object and image in enlargement?

- Master Mathematics Grade 9 pg. 190
- Rulers
- Compasses
- Tracing papers
- Models
- Master Mathematics Grade 9 pg. 192
- Graph papers
- Pencils

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Positive scale factor (2)

By the end of the lesson, the learner should be able to:
- Describe what happens when scale factor is between 0 and 1
- Draw enlargements with fractional scale factors accurately
- Appreciate comparing enlargements with different positive scale factors

The learner is guided to:
- Draw enlargements with fractional scale factors
- Observe that images are smaller than objects
- Note that object and image remain upright
- Practice with various positive scale factors

What happens when the scale factor is between 0 and 1?

- Master Mathematics Grade 9 pg. 192
- Rulers
- Compasses
- Plain papers
- Models

- Class activities - Written assignments

4.0 Geometry

4.3 Similarity and Enlargement - Negative scale factor (1)
4.3 Similarity and Enlargement - Negative scale factor (2)

By the end of the lesson, the learner should be able to:
- State the properties of enlargement with negative scale factors
- Draw enlargements with negative scale factors and position images correctly
- Show interest in recognizing that images are inverted with negative scale factors

The learner is guided to:
- Observe objects and images with negative scale factors
- Note that they are on opposite sides of centre
- Draw enlargements with negative scale factors
- Observe that images are inverted

What is special about negative scale factors?

- Master Mathematics Grade 9 pg. 196
- Rulers
- Compasses
- Graph papers
- Tracing papers
- Plain papers
- Calculators

- Observation - Oral questions

4.0 Geometry

4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (1)
4.3 Similarity and Enlargement - Enlargement on the Cartesian plane (2)
4.3 Similarity and Enlargement - Linear scale factor of similar figures (1)
4.3 Similarity and Enlargement - Linear scale factor of similar figures (2)

By the end of the lesson, the learner should be able to:
- State the rule (x,y) → (kx, ky) for enlargement with centre at origin
- Plot and enlarge figures accurately with centre at origin
- Develop interest in applying enlargement rules on coordinate axes
- Define linear scale factor
- Calculate linear scale factor from similar figures and use it to find unknown lengths
- Show interest in applying linear scale factor to practical situations

The learner is guided to:
- Plot given points on Cartesian plane
- Apply scale factor to coordinates
- Plot image points and join them
- Verify using measurement from origin
The learner is guided to:
- Measure corresponding sides of similar figures
- Calculate ratios to find linear scale factor
- Use scale factor to determine unknown dimensions
- Apply to practical situations

How do we enlarge figures on coordinate axes?
What is linear scale factor?

- Master Mathematics Grade 9 pg. 198
- Graph papers
- Rulers
- Calculators
- Pencils
- Digital devices
- Master Mathematics Grade 9 pg. 200
- Rulers
- Similar objects
- Calculators
- Models
- Maps
- Scale models
- Real objects

- Observation - Written assignments
- Observation - Oral questions

4.0 Geometry

4.4 Trigonometry - Angles and sides of right-angled triangles
4.4 Trigonometry - Tangent ratio and tables of tangents

By the end of the lesson, the learner should be able to:
- Define hypotenuse, opposite and adjacent sides
- Identify and name sides with reference to given angles
- Show interest in recognizing right-angled triangles in real situations

The learner is guided to:
- Draw right-angled triangles
- Identify the hypotenuse
- Label opposite and adjacent sides for given angles
- Practice with different orientations of triangles

How do we identify sides of a right-angled triangle?

- Master Mathematics Grade 9 pg. 205
- Rulers
- Set squares
- Models of triangles
- Charts
- Master Mathematics Grade 9 pg. 207
- Mathematical tables
- Calculators
- Right-angled triangles

- Observation - Oral questions

4.0 Geometry

4.4 Trigonometry - Sine and cosine ratios, tables of sines and cosines

By the end of the lesson, the learner should be able to:
- Define sine and cosine of an angle
- Calculate sine and cosine ratios and read values from mathematical tables
- Develop interest in observing that cosine values decrease as angles increase

The learner is guided to:
- Work out ratios of opposite to hypotenuse (sine)
- Work out ratios of adjacent to hypotenuse (cosine)
- Read values from tables of sines and cosines
- Observe that values in cosine tables are subtracted

How are sine and cosine different from tangent?

- Master Mathematics Grade 9 pg. 211
- Mathematical tables
- Rulers
- Calculators
- Models

- Observation - Written assignments

4.0 Geometry
5.0 Data Handling and Probability
5.0 Data Handling and Probability
5.0 Data Handling and Probability

4.4 Trigonometry - Using calculators and applications of trigonometric ratios
5.1 Data Interpretation (Grouped Data) - Determining appropriate class width for grouping data
5.1 Data Interpretation (Grouped Data) - Drawing frequency distribution tables of grouped data
5.1 Data Interpretation (Grouped Data) - Identifying the modal class of grouped data

By the end of the lesson, the learner should be able to:
- Explain how to use calculators to find trigonometric ratios
- Apply trigonometric ratios to calculate unknown sides and angles
- Appreciate using trigonometry to solve real-life problems

The learner is guided to:
- Use calculator buttons for sin, cos, tan
- Find inverse trigonometric ratios
- Calculate unknown lengths in right-angled triangles
- Solve problems involving heights, distances and angles

How do we use trigonometry to solve real-life problems?

- Master Mathematics Grade 9 pg. 217
- Scientific calculators
- Rulers
- Protractors
- Real-life problem scenarios
- Master Mathematics Grade 9 pg. 224
- Writing materials
- Calculators
- Chart papers
- Digital devices
- Master Mathematics Grade 9 pg. 226
- Tally sheets
- Data sets
- Pencils
- Master Mathematics Grade 9 pg. 228
- Frequency distribution tables
- Reference materials

- Written tests - Practical activities

5.0 Data Handling and Probability

5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (1)
5.1 Data Interpretation (Grouped Data) - Calculating the mean of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (1)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (2)
5.1 Data Interpretation (Grouped Data) - Determining the median of grouped data (3)
5.2 Probability - Experiments involving equally and likely outcomes

By the end of the lesson, the learner should be able to:
- Explain the process of finding mean of grouped data
- Calculate midpoints of classes
- Show interest in organizing data to find the mean
- Explain the formula for calculating median of grouped data
- Identify L, N, cf₁, fm and C from given data
- Appreciate the components of the median formula

The learner is guided to:
- Group given data into classes
- Add class limits and divide by 2 to get midpoints
- Work out products of midpoints and frequencies (fx)
- Find the sum of fx values
The learner is guided to:
- Discuss the median formula and its components
- Identify the lower class boundary (L) of median class
- Determine cumulative frequency of class above median class
- Identify frequency of median class and class width

How do we find the mean of grouped data?
How do we use the median formula?

- Master Mathematics Grade 9 pg. 230
- Calculators
- Frequency tables
- Writing materials
- Mathematical tables
- Data sets
- Charts
- Master Mathematics Grade 9 pg. 232
- Reference materials
- Digital devices
- Master Mathematics Grade 9 pg. 234
- Calculators
- Formula charts
- Frequency tables
- Master Mathematics Grade 9 pg. 236
- Data sets
- Writing materials
- Practice worksheets
- Master Mathematics Grade 9 pg. 239
- Coins
- Dice
- Triangular pyramids
- Baskets and pens

- Observation - Written tests
- Class activities - Oral questions - Written assignments

5.0 Data Handling and Probability

5.2 Probability - Range of probability of an event
5.2 Probability - Identifying mutually exclusive events

By the end of the lesson, the learner should be able to:
- State that the sum of all probabilities equals 1
- Determine the range of probability as 0 ≤ P(A) ≤ 1
- Show interest in understanding that P(A) + P(A') = 1

The learner is guided to:
- Toss a coin and work out probability of head and tail
- Add probabilities of all outcomes
- Use dice to determine probabilities of all faces
- Discuss that probability ranges from 0 to 1

What is the range of probability?

- Master Mathematics Grade 9 pg. 241
- Coins
- Dice
- Calculators
- Charts showing probability range
- Master Mathematics Grade 9 pg. 243
- Pictures of referees
- Real-life scenarios
- Charts

- Class activities - Written tests - Oral questions

5.0 Data Handling and Probability

5.2 Probability - Experiments of single chance involving mutually exclusive events
5.2 Probability - Experiments involving independent events

By the end of the lesson, the learner should be able to:
- Explain the addition law of probability P(A or B) = P(A) + P(B)
- Calculate probabilities of mutually exclusive events
- Show interest in applying the addition law to solve problems

The learner is guided to:
- Pick pens from a closed bag and note colors
- Work out probabilities using the word "OR"
- Apply the formula P(A or B) = P(A) + P(B)
- Solve problems involving mutually exclusive events

How do we calculate probabilities of mutually exclusive events?

- Master Mathematics Grade 9 pg. 244
- Colored pens
- Bags
- Dice
- Number cards
- Calculators
- Master Mathematics Grade 9 pg. 246
- Coins
- Colored balls
- Baskets

- Class activities - Written tests - Practical exercises

5.0 Data Handling and Probability

5.2 Probability - Drawing tree diagrams for single outcomes

By the end of the lesson, the learner should be able to:
- Explain what a tree diagram represents
- Draw tree diagrams showing probability outcomes on branches
- Show interest in verifying that sum of probabilities on branches equals 1

The learner is guided to:
- Identify possible outcomes from tossing a coin
- Draw branches and fill in outcomes
- Determine probabilities and place on branches
- Verify that sum of probabilities equals 1
- Draw tree diagrams for various probability situations

How do we represent probability using tree diagrams?

- Master Mathematics Grade 9 pg. 248
- Drawing materials
- Coins
- Calculators
- Chart papers
- Rulers

- Class activities - Written tests - Practical activities