Geometry

Similarity and Enlargement - Similar figures and properties

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

Identify similar figures and their properties;
Measure corresponding sides and angles of similar figures;
Appreciate the concept of similarity in real-life objects.

Learners study diagrams of similar cross-sections.
Learners measure the corresponding sides of the cross-sections and find the ratio between them.
Learners measure all the corresponding angles and discover that they are equal.

What makes two figures similar?

-KLB Mathematics Grade 9 Textbook page 203
-Ruler
-Protractor
-Cut-out shapes
-Charts showing similar figures
-Manila paper

-Oral questions -Observation -Written exercise -Checklist

Geometry

Similarity and Enlargement - Identifying similar objects
Similarity and Enlargement - Drawing similar figures

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

Identify similar objects in the environment;
Determine if given figures are similar;
Value the concept of similarity in everyday life.

Learners collect and classify objects according to similarity.
Learners identify pairs of similar figures from given diagrams.
Learners discuss real-life examples of similar objects and their properties.

How do we recognize similar objects in our environment?

-KLB Mathematics Grade 9 Textbook page 204
-Ruler
-Protractor
-Various geometric objects
-Charts with examples
-Worksheets with diagrams
-KLB Mathematics Grade 9 Textbook page 206
-Pair of compasses
-Drawing paper
-Calculator

-Oral questions -Group work -Written exercise -Observation

Geometry

Similarity and Enlargement - Properties of enlargement
Similarity and Enlargement - Negative scale factors

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

Determine properties of enlargement of different figures;
Locate the center of enlargement and find scale factors;
Value the application of enlargement in real-life situations.

Learners trace diagrams showing an object and its enlarged image.
Learners draw lines through corresponding points to find where they intersect (center of enlargement).
Learners find the ratios of corresponding lengths to determine the scale factor.

How do we determine the center and scale factor of an enlargement?

-KLB Mathematics Grade 9 Textbook page 209
-Ruler
-Tracing paper
-Colored pencils
-Grid paper
-Charts showing enlargements
-Diagrams for tracing
-KLB Mathematics Grade 9 Textbook page 211
-Charts showing negative scale factor enlargements

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Similarity and Enlargement - Drawing images of objects
Similarity and Enlargement - Linear scale factor

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

Apply properties of enlargement to draw similar objects and their images;
Use scale factors to determine dimensions of images;
Enjoy creating enlarged images of objects.

Learners trace a given figure and join the center of enlargement to each vertex.
Learners multiply each distance by the scale factor to locate the image points.
Learners locate the image points and join them to create the enlarged figure.

How do we draw the image of an object under an enlargement with a given center and scale factor?

-KLB Mathematics Grade 9 Textbook page 214
-Ruler
-Grid paper
-Colored pencils
-Charts showing steps of enlargement
-Manila paper
-KLB Mathematics Grade 9 Textbook page 216
-Calculator
-Similar objects of different sizes
-Charts with examples
-Worksheets

-Oral questions -Practical activity -Written exercise -Peer assessment

Geometry

Similarity and Enlargement - Using coordinates in enlargement
Similarity and Enlargement - Applications of similarity

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

Find the coordinates of images under enlargement;
Determine the center of enlargement and scale factor from given coordinates;
Appreciate the use of coordinates in describing enlargements.

Learners plot figures and their images on a grid.
Learners find the center of enlargement by drawing lines through corresponding points.
Learners calculate the scale factor using the coordinates of corresponding points.

How do we use coordinate geometry to describe and perform enlargements?

-KLB Mathematics Grade 9 Textbook page 218
-Grid paper
-Ruler
-Colored pencils
-Calculator
-Charts with coordinate examples
-KLB Mathematics Grade 9 Textbook page 219
-Drawing paper
-Charts with real-life applications
-Manila paper for presentations

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Angles and sides of right-angled triangles
Trigonometry - Sine ratio

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

Identify angles and sides of right-angled triangles in different situations;
Distinguish between the hypotenuse, adjacent side, and opposite side;
Appreciate the relationship between angles and sides in right-angled triangles.

Learners draw right-angled triangles with acute angles and identify the longest side (hypotenuse).
Learners identify the side which together with the hypotenuse forms the angle θ (adjacent side).
Learners identify the side facing the angle θ (opposite side).

How do we identify different sides in a right-angled triangle?

-KLB Mathematics Grade 9 Textbook page 220
-Ruler
-Protractor
-Set square
-Drawing paper
-Charts with labeled triangles
-Colored markers
-KLB Mathematics Grade 9 Textbook page 222
-Calculator
-Charts showing sine ratio
-Manila paper

-Oral questions -Observation -Written exercise -Checklist

Geometry

Trigonometry - Cosine ratio
Trigonometry - Tangent ratio

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

Identify cosine ratio from a right-angled triangle;
Calculate cosine of angles in right-angled triangles;
Enjoy solving problems involving cosine ratio.

Learners draw triangles with specific angles and sides.
Learners calculate ratios of adjacent side to hypotenuse for different angles and discover the cosine ratio.
Learners find the cosine of marked angles in various right-angled triangles.

What is the cosine of an angle and how do we calculate it?

-KLB Mathematics Grade 9 Textbook page 223
-Ruler
-Protractor
-Calculator
-Drawing paper
-Charts showing cosine ratio
-Worksheets
-KLB Mathematics Grade 9 Textbook page 225
-Charts showing tangent ratio
-Manila paper

-Oral questions -Practical activity -Written exercise -Observation

Geometry

Trigonometry - Reading tables of sines
Trigonometry - Reading tables of cosines and tangents

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

Read tables of trigonometric ratios of acute angles;
Find the sine values of different angles using tables;
Value the importance of mathematical tables in finding trigonometric ratios.

Learners study a part of the table of sines.
Learners use the table to look for specific angles and find their sine values.
Learners find sine values of angles with decimal parts using the 'ADD' column in the tables.

How do we use mathematical tables to find the sine of an angle?

-KLB Mathematics Grade 9 Textbook page 227
-Mathematical tables
-Calculator
-Worksheets
-Chart showing how to read tables
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 229-231

-Oral questions -Practical activity -Written exercise -Assessment rubrics

Geometry

Trigonometry - Using calculators for trigonometric ratios
Trigonometry - Calculating lengths using trigonometric ratios

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

Determine trigonometric ratios of acute angles using calculators;
Compare values obtained from tables and calculators;
Value the use of calculators in finding trigonometric ratios.

Learners use calculators to find trigonometric ratios of specific angles.
Learners compare values obtained from calculators with those from mathematical tables.
Learners use calculators to find sine, cosine, and tangent of various angles.

How do we use calculators to find trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 233
-Scientific calculators
-Mathematical tables
-Worksheets
-Chart showing calculator keys
-Sample exercises
-KLB Mathematics Grade 9 Textbook page 234
-Ruler
-Drawing paper
-Charts with examples

-Oral questions -Practical activity -Written exercise -Checklist

Geometry

Trigonometry - Calculating angles using trigonometric ratios
Trigonometry - Application in heights and distances
Trigonometry - Application in navigation
Trigonometry - Review and mixed applications

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

Use trigonometric ratios to calculate angles in right-angled triangles;
Apply inverse trigonometric functions to find angles;
Enjoy solving problems involving trigonometric ratios.

Learners consider right-angled triangles with known sides.
Learners calculate trigonometric ratios using the known sides and use tables or calculators to find the corresponding angles.
Learners solve problems involving finding angles in right-angled triangles.

How do we find unknown angles in right-angled triangles using trigonometric ratios?

-KLB Mathematics Grade 9 Textbook page 235
-Scientific calculators
-Mathematical tables
-Ruler
-Drawing paper
-Charts with examples
-Worksheets
-KLB Mathematics Grade 9 Textbook page 237
-Charts with real-life examples
-Manila paper
-KLB Mathematics Grade 9 Textbook page 238
-Protractor
-Maps
-Charts with navigation examples
-KLB Mathematics Grade 9 Textbook page 240
-Past examination questions

-Oral questions -Group work -Written exercise -Observation