# Mathematics Guides for JSS 3 Measurement and Geometry (Shapes and Angles)

**MATHEMATICSÂ **

**THEME â€“ MEASUREMENT AND GEOMETRYÂ **

**TOPIC 1 â€“ AREA OF PLANE FIGURES**

**INSTRUCTIONAL MATERIALS**

1. Triangular shapes

2. Models of parallelogram

3. Models of trapezium

4. Model of circles and sectors

5. Flash cards with word problems

**LEARNING OBJECTIVES **

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

1. find area of triangles.

2. find area of parallelograms.

3. find area of trapezium.

4. find area of circles and sectors.

5. solve word problems involving areas.

6. solve quantitative aptitude problems on areas.

**CONTENTS OF THE LESSON**

**FOCUS LESSONSÂ **

1. Areas of triangles

2. Area of parallelogram

3. Area of trapezium

4. Areas of circles

5. Word problems involving area.

**LESSON PRESENTATION**

TEACHERâ€™S ACTIVITIES1. Leads students to derive formula for areas of triangles.

2. Guides students to use the obtained formula to find the area of triangle.

3. Leads students to derive the formula for area of parallelogram.

4. Guides students to use the derived formula to find the area of parallelogram.

5. Leads students to derive the formula for area of trapezium.

6. Guides students to solve problems on area of trapezium using the derived formula.

7. Leads students to derive the formula for area of circles and the sectors.

8. Guides students to use the derived formula to find the area of circles and sectors.

9. Guides students to interpret and solve word problems involving areas.

10. Guide students to solve quantitative aptitude problem an area of figures.

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STUDENTâ€™S ACTIVITIES1. Derive formula for areas of triangles.

2. Use the formula to find the area of triangle.

3. Derive the formula for area of parallelogram.

4. Use the derived formula to find the area of a parallelogram.

5. Derive the formula to find the area of a trapezium.

6. Find the area of trapezium.

7. Derive the formula for area of circles and sectors.

8. Use the derived formula to find the area of circles.

9. Interpret and solve word problems involving areas.

10. Solve quantitative aptitude problems on areas.

**LESSON EVALUATION**

Students to,

1. find the area of given triangles.

2. find the area of given parallelograms.

3. find areas of given trapezium.

4. find the areas of given circles and sectors.

5. solve given word problems involving area.

**MATHEMATICSÂ **

**THEME â€“ MEASUREMENT AND GEOMETRYÂ **

**TOPIC 2 â€“ CONSTRUCTION OF SIMPLE SHAPES AND ANGLESÂ **

**INSTRUCTIONAL MATERIALS**

Plain sheet of paper and Mathematical set.

**LEARNING OBJECTIVES **

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

1. construct angle 45Â°.

2. construct angles 30Â°.

3. use a pair of compasses to copy a given angle.

4. construct simple shapes.

**CONTENTS OF THE LESSON**

**FOCUS LESSONSÂ **

1. Construction of angle 45Â°

2. Construction of angles 30Â°

3. Copying given angles

3. Construction of simple plane shapes

**LESSON PRESENTATION**

TEACHERâ€™S ACTIVITIES1. Leads students to construct angles 45Â°.

2. Leads students to construct angles 30Â°.

3. Leads students to copy a given angle.

4. Guides students to construct simple plane shapes.

STUDENTâ€™S ACTIVITIES1. Construct angles 45Â°.

2. Construct angles 30Â°.

3. Copy a given angle.

4. Construct simple plane shapes.

**LESSON EVALUATION**

Students to,

1. construct angle 45Â°.

2. construct angles 30Â°.

3. copy a given angle.

4. construct simple plane shapes.

**MATHEMATICSÂ **

**THEME â€“ MEASUREMENT AND GEOMETRYÂ **

**TOPIC 3 â€“ SIMILAR SHAPESÂ **

**INSTRUCTIONAL MATERIALS**

Similar shapes of triangles, rectangles, squares, cubes and cuboids.

**LEARNING OBJECTIVES **

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

1. identify similar figures, triangle, rectangles, squares, cubes and cuboids.

2. identify the presence of similar shapes in the environment.

3. enlarge figures using scale factors.

4. calculate lengths, areas and volumes of similar figures.

5. solve problems on quantitative reasoning involving similar shapes.

**CONTENTS OF THE LESSON**

**FOCUS LESSONSÂ **

1. Similar shapes

2. Enlargements and scale factor

3. Lengths, arears and volumes of similar figures.

**LESSON PRESENTATION**

TEACHERâ€™S ACTIVITIES1. Guides students to identify similar shapes around them.

2. Introduce the meaning of enlargement and scale factor.

3. Guides students to enlarge shapes using scale factor.

4. Leads students to identify that if the length of similar figures are in ratio 1 : k then areas and volumes are in ratios 1 : kÂ² = 1 : kÂ³ respectively.

5. Leads students to solve quantitative aptitude problems involving similar shapes.

STUDENTâ€™S ACTIVITIES1. Identify similar shapes around them.

2. Describe the meaning of enlargement and scale factor.

3. Enlarge shapes using scale factors.

4. Identify that if the length of similar figures are in ratio 1 : k then the areas and volumes are in ratios 1 : kÂ² = 1 : kÂ³ respectively.

5. Solve problems on quantitative aptitude involving similar shape.

**LESSON EVALUATION**

Students to,

1. identify given similar shapes.

2. determine the scale factors of any given figures.

3. enlarge figures using the scale factors.

4. find the lengths areas and volume of given similar figures.

5. solve problems on quantitative aptitude involving similar shape.

**MATHEMATICSÂ **

**THEME â€“ MEASUREMENT AND GEOMETRYÂ **

**TOPIC 4 â€“ TRIGONOMETRYÂ **

**INSTRUCTIONAL MATERIALS**

Model of right angled triangle. Flash cards with different problems.

**LEARNING OBJECTIVES **

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

1. identify sine, cosine and tangent of an acute angle.

2. solve problems on applications of trigonometric ratios to finding distances and lengths.

3. apply trigonometric ratios in solving word problems.

**CONTENTS OF THE LESSON**

**FOCUS LESSONS**

1. The sine, cosine and tangent of an acute angle.

2. Applications of trigonometric ratios.

** LESSON PRESENTATIONÂ **

TEACHERâ€™S ACTIVITIES1. Leads students to observe the sine, cosine, and tangent of an acute angle as ratios of sides of right angled triangle.

2. Leads students to use the trigonometric ratios to solve practical problems involving right-angled triangle.

3. Leads students to apply trigonometric ratios to solve word problems.

STUDENTâ€™S ACTIVITIES1. Identify sine, cosine and tangent of an acute angle as ratios of sides of a right-angled triangle.

2. Use trigonometric ratio to solve practical problems.

3. Apply trigonometric ratios to solve word problems.

**LESSON EVALUATION**

Students to,

1. determine sine, cosine and tangent of an acute angle from given triangles.

2. solve practical problems involving trigonometric ratios.