Year 9 Mathematics (2015)

9Maths.WC.Pythagoras' Theorem & Trigonometry.2015.docx

Chapter 3 Pythagoras Theorem and Trigonometry (15 lessons). Lesson Title and Introductory

Activities Exercise Proficiency Foundation Standard Advanced Mathletics

1 Pre-Test

2 6.9 Simple operations with surds 368

Exercise 6

I

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2 3a,c,e,g,i,k 4a,c,e,g,i,k,m,o 5 8 -

2a,c 3a,c,e,g,i,k 4a,c,e,g,i,k,m,o 5a,c,e,g,i Q6a,c,e,g 8 -

- 3a,c,e,g,i,k 4a,c,e,g,i,k,m,o 5a,c,e,g,i Q6a,c,e,g Q7a,c,e 8, 9 10a,d,g,j

Square Roots

3 3.1 Pythagoras Theorem 132

Lets start: Matching the area of squares Key ideas Example 1, 2

Exercise 3

A

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2, 4a,c,e,g,i 5a,c,e 6a,c,e 10, 11 15 -

- 4a,c,e,g,i 5a,c,e 6a,c,e 8a,c,e 10, 12 15, 16 -

- 4a,c,e,g,i 5a,c,e 6a,c,e 8a,c,e 11, 13 16, 17 18, 19

Hypotenuse, Adjacent, Opposite

Pythagorean Theorem

4 3.2 Finding the shorter sides 139

Lets start: True or false Key ideas Example 3

Exercise 3

B

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2 3a,c,e 4a,c,e 8, 9 12 -

2 3a,c,e 4a,c,e 6 8, 9, 10 12 -

- 3a,c,e 4a,c,e 6 9, 10, 11 12, 13 14, 15

Pythagoras Theorem

5 3.3 Applying Pythagoras Theorem 144

Lets start: The biggest square Key ideas Example 4

Exercise 3

C

Understanding Fluency Problem Solving Reasoning Enrichment

1 2, 3, 5 7, 8 11 -

2 2, 4, 6 8, 9 11 -

- 2, 4, 6 9, 10 11, 12 13

6 Assessment Task Proving Pythagoras Theorem

7 3.5 Trigonometric ratios 155 Lets start: Constancy of sine, cosine and tangent Key ideas Example 6, 7

Exercise 3

E

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2a,c,e,g 3 4a,c,e,g,i 6 8, 9 12 -

3 4a,c,e,g,i 6, 7 9, 10 12, 13 -

- 4a,c,e,g,i 6, 7 10, 11 13, 14 15

Page 2 of 2

Lesson Title and Introductory Activities

Exercise Proficiency Foundation Standard Advanced Mathletics

8 3.6 Finding side lengths 161 Lets start: Calculator start up Key ideas Example 8, 9, 10

Exercise 3

F

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2, 3 4a,c,e,g,i 5a,c,e,g,i,k,m,o 6, 7 10 -

3a,c,e,g 4a,c,e,g,i 5a,c,e,g,i,k,m,o 6, 8 10 -

- 4a,c,e,g,i 5a,c,e,g,i,k,m,o 7, 9 10, 11 12

9 3.7 Solving for the denominator 165

Lets start: Solution steps Key ideas Example 11, 12

Exercise 3

G

Understanding Fluency Problem Solving Reasoning Enrichment

1a,c,e,g 2a,c,e,g,i 3a,c,e,g,i,k 4a,c,e,g 5, 6 9 -

2a,c,e,g,i 3a,c,e,g,i,k 4a,c,e,g 5, 7 9 -

- 3a,c,e,g,i,k 4a,c,e,g 6, 8 9 10

Find unknown sides

10 3.8 Finding an angle 169 Lets start: Trial and error can be slow Key ideas Example 13, 14

Exercise 3

H

Understanding Fluency Problem Solving Reasoning Enrichment

1, 3a,c,e,g,i 4 5a,c,e,g,i,k 6a,c,e,g,i 7a,c,e,g 8, 10 13 -

4 5a,c,e,g,i,k 6a,c,e,g,i 7a,c,e,g 9, 11 13, 14 -

- 5a,c,e,g,i,k 6a,c,e,g,i 7a,c,e,g 10, 12 14, 15 16

Find unknown angles

Sin A Cos A Tan A

11 3.9 Applying Trigonometry 174

Lets start: Illustrate the situation Key ideas Example 15, 16, 17

Exercise 3

I

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2, 3 4, 6, 8 12, 13 17 -

3 4, 6, 8, 10 12, 14 17 -

- 4, 6, 8, 10 14, 16 17, 18 19, 21

Elevation and depression

12 3.10 Bearings 180 Lets start: Opposite Directions Key ideas Example 18, 19, 20

Exercise 3

J

Understanding Fluency Problem Solving Reasoning Enrichment

1, 2 3a,c,e,g,i, 4, 6 8, 10 13 -

2 3a,c,e,g,i, 4, 6, 7 8, 11 13 -

- 3a,c,e,g,i, 4, 6 10, 12 13, 14 15, 16

True and Compass Bearings

13&14 Revision: RAP Sheet

Mathletics Practice Test

15 Test