Direct and Inverse Proportionality Monday December 13 2021

Direct and Inverse Proportionality Monday, December 13, 2021 Why am I doing this? Objectives 1. Understand the idea 2. Calculate values Grade C - A It is an important idea that has many real life applications A favourite SAT and GCSE question

An example of direct proportionality Rope costs 10 p per metre. Complete the missing values in this table. Length (m) 0 Cost (p) 0 1 10 2 3 30 4 20 150

An example of direct proportionality Rope costs 10 p per metre. Complete the missing values in this table. Length (m) 0 Cost (p) 0 1 2 10 20 3 30 4 15 20 40 150 200

Length (m) 0 Cost (p) p~m p = km 30 = k x 3 30 ÷ 3 = k 10 = k p = 10 m 0 1 2 10 20 3 30 4 15 20 40 150 200

Hours (h) 0 2 Wages (w) 0 14. 50 3 5 40 30 w~h 3 x 7. 25 = 21. 75 w = kh 14. 50 = k x 2 40 x 7. 25 = 290 k = 14. 5 ÷ 2 k = 7. 25 w = 7. 25 h

Hours (h) 0 Wages (w) 0 w~h w = kh 14. 50 = k x 2 k = 14. 5 ÷ 2 k = 7. 25 w = 7. 25 h 2 3 14. 50 21. 75 5 40 30 290

1. The values in the table below are directly proportion so p ~ m. Find the rule that connects p and m and use it to find the missing values. Length (m) Cost (p) 0 0 1 2 50 3 4 5 0 0 1 2 3 4 12. 8 5 0 0 1 2 3 4 5 7. 5

Which of the relationships shown below are directly proportional? Length Weight 3 15 4 21 10 50 Cost 2 5 9 Length 7. 4 18. 5 33. 3 Base Height 2 12. 4 5 31 9 55. 8 15 ÷ 3 = 5 21 ÷ 3 = 7 NO 50 ÷ 10 = 5 7. 4 ÷ 2 = 3. 7 18. 5 ÷ 5 = 3. 7 YES 33. 3 ÷ 9 = 3. 7 12. 4 ÷ 2 = 6. 2 31 ÷ 5 = 6. 2 55. 8 ÷ 9 = 6. 2 YES

Inverse Proportionality

Speed (s) Time (t) 10 20 1 40 100

Speed (s) 10 20 40 100 Time (t) 2 1 ½ (0. 5) 0. 2

Speed (s) 10 Time (t) 20 40 100 1 t = 20 ÷ 10 t=2 t~s t = k/s 1 = k ÷ 20 1 x 20 = k k = 20 t = 20/s t = 20 ÷ 40 t = 0. 5 t = 20 ÷ 100 t = 0. 2

Speed (s) 10 20 40 100 Time (t) 2 1 0. 5 0. 2 t = 20 ÷ 10 t=2 t~s t = k/s 1 = k ÷ 20 1 x 20 = k k = 20 t = 20/s t = 20 ÷ 40 t = 0. 5 t = 20 ÷ 100 t = 0. 2

1. The values in the table below are inversely proportion so t ~ s. Find the rule that connects t and s and use it to find the missing values. Speed (s) 0. 1 0. 5 2 2 2. 5 4 5 0. 1 0. 5 2 2. 5 4 4 5 0. 1 0. 5 40 2 2. 5 4 5 Time (t) Speed (s) Time (t)