Thursday, August 29, 2019 Direct Proportion Find a final equation for variables linked by direct proportion Key Words Express relationships using proportional notation and the general equation for those variables directly proportional square cube root equation substitute Find equations for variables directly proportional to squares, cubes or roots variable diagonal Thursday, August 29, 2019 Direct Proportion Express relationships using proportional notation and the general equation for those variables Starter Task Which exchange rate would be best for my trip to France? Find a final equation for variables linked by direct proportion Find equations for variables directly proportional to squares, cubes or roots MoneyCo. £1 = €1.28 XchangeIt £5 = €6.35 FXX £25=€31.25 TraveX £20 = €26 Key Words How many Euros can I get for £400 at the best available price? directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Direct Proportion Express relationships using proportional notation and the general equation for those variables Unitary Method £1 Which exchange rate would be best for my trip to France? Find a final equation for variables linked by direct proportion MoneyCo. £1 = €1.28 XchangeIt £5 = €6.35 ÷5 €1.27 FXX £25=€31.25 ÷ 25 €1.25 €1.28 €1.30 ÷ 20 £20 = €26 TravEX Find equations for variables directly proportional to squares, cubes or roots No change Key Words How many Euros can I get for £400 at the best available price? directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Direct Proportion Express relationships using proportional notation and the general equation for those variables LCM Method LCM =£100 Which exchange rate would be best for my trip to France? Find a final equation for variables linked by direct proportion Find equations for variables directly proportional to squares, cubes or roots MoneyCo. £1 = €1.28 × 100 €128 XchangeIt £5 = €6.35 × 20 €127 FXX £25=€31.25 ×4 €125 TravEX ×5 £20 = €26 €130 Key Words How many Euros can I get for £400 at the best available price? directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Direct Proportion Express relationships using proportional notation and the general equation for those variables If two variables are directly proportional that means that if one doubles the other doubles Find a final equation for variables linked by direct proportion If one is halved the other is halved The two variables are linked by a constant (k) Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Express relationships using proportional notation and the general equation for those variables Direct Proportion Example1: 𝑆 is directly proportional to 𝑇. When 𝑆 = 30 𝑇 = 5. Write an equation linking 𝑆 and 𝑇 𝑆∝𝑇 𝑆 = 𝑘𝑇 Find a final equation for variables linked by direct proportion 30 = 𝑘 × 5 30 ÷ 5 = 𝑘 6=𝑘 𝑆 = 6𝑇 The final equation is Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Express relationships using proportional notation and the general equation for those variables Direct Proportion Example2: 𝑆 is directly proportional to the square of 𝑇. When 𝑆 = 50 𝑇 = 5. Write an equation linking 𝑆 and 𝑇 𝑆 ∝ 𝑇2 𝑆 = 𝑘𝑇 2 Find a final equation for variables linked by direct proportion 50 = 𝑘 × 52 50 ÷ 25 = 𝑘 2=𝑘 𝑆 = 2𝑇 2 The final equation is Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Express relationships using proportional notation and the general equation for those variables Direct Proportion Example3: 𝐶 is directly proportional to the square root of 𝐷. When C = 18 𝐷 = 36. Write an equation linking 𝐶 and 𝐷 C∝ 𝐷 Find a final equation for variables linked by direct proportion C=𝑘 𝐷 18 = 𝑘 × 36 18 ÷ 6 = 𝑘 3=𝑘 Find equations for variables directly proportional to squares, cubes or roots C=3 𝐷 Key Words The final equation is directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Worksheet Express relationships using proportional notation and the general equation for those variables Find a final equation for variables linked by direct proportion Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Answers Express relationships using proportional notation and the general equation for those variables Find a final equation for variables linked by direct proportion Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Answers Express relationships using proportional notation and the general equation for those variables Find a final equation for variables linked by direct proportion Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Express relationships using proportional notation and the general equation for those variables Home Problem Solving for next time Before next lesson consider this problem: You should use direct proportion to find a solution. Look up the building online….. I dropped a stone from the top of the Shard in London. The distance the stone falls is directly proportional to the square of the time it has been falling. After 5 seconds the stone has fallen 122.50 metres. How far will it have fallen after 8 seconds? Find a final equation for variables linked by direct proportion Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal Thursday, August 29, 2019 Express relationships using proportional notation and the general equation for those variables Direct Proportion Exit Task 4 people can paint a fence in 3 hours. How long will it take 6 people to paint it? (Assume everyone works at the same rate) Find a final equation for variables linked by direct proportion Is this a Direct Proportion question? How do you know? How might we describe the link? Key Words Find equations for variables directly proportional to squares, cubes or roots directly proportional square cube root equation substitute variable diagonal
