1. Lesson Objective By the end of the lesson you should be able to go backwards through percentage problems to find the starting value.

2. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? Pupil A works out the answer as £27.30 Pupil B works out the answer as £30 Which one is correct?

3. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? Pupil B is correct. But why? What has pupil A done wrong? Pupil A has made the mistake of increasing £21 by 30% to undo the decrease of 30% from the original price. The problem with this is the 30% taken off the original price was not 30% of £21 but 30% of whatever the original price was.

4. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? This problem can be made much simpler if we think of it as multipliers. This is still a percentage decrease problem (why?), what multiplier should we use? 0.7xoriginal price= £21 How can we work out the original price from this?

5. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? This problem can be made much simpler if we think of it as multipliers. This is still a percentage decrease problem (why?), what multiplier should we use? 0.7xoriginal price= £21 ÷ original price = £30

6. Reverse Percentage Problems Whenever you are returning to an original value in a percentage problem you must remember to divide by the multiplier! example 2 – find the missing values in each of these. 35% of N is 24.5 increase M by 12% and you get 100.8 decrease P by 45% and you get 44 N=24.5 ÷ 0.35 = 70 M=100.8 ÷ 1.12 = 90 P=44 ÷ 0.55 = 80

7. Reverse Percentage Problems Your turn. On your worksheet use straight lines to join question numbers to their answers Some lines go over others All lines are either vertical or horizontal

8. Reverse Percentage Problems. 100. 2000. 800. 250. 170. 300. 190. 3000. 1000. 900. 370. 160. 240. 700. 110. 340. 270. 130. 310. 280. 350. 200. 330. 230. 120. 290. 360. 150. 320. 400. 260. 140. 600. 220. 210. 180. 390. 500 100. 984 after a 23% increase 984 ÷ 1.23 = 800 so join 100 to 800

9. Reverse Percentage Problems. 100. 2000. 800. 250. 170. 300. 190. 3000. 1000. 900. 370. 160. 240. 700. 110. 340. 270. 130. 310. 280. 350. 200. 330. 230. 120. 290. 360. 150. 320. 400. 260. 140. 600. 220. 210. 180. 390. 500 800. 5% is 16 16 ÷ 0.05 = 320 Join 800 to 320

10. Reverse Percentage Problems. 100. 2000. 800. 250. 170. 300. 190. 3000. 1000. 900. 370. 160. 240. 700. 110. 340. 270. 130. 310. 280. 350. 200. 330. 230. 120. 290. 360. 150. 320. 400. 260. 140. 600. 220. 210. 180. 390. 500 320 is a dead end Choose another question number (bold numbers are good starting points) Keep going until the maze is complete