--- title: "Percentage change" subtitle: "Number Foundations · Modelling · Lesson 25" --- # Percentage change **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A shop puts a price up 20% in March and has a 20% sale in April. The sign says 'back to the old price'. Is it? :::teacher-note **In one sentence:** Students model percentage increases and decreases as multipliers, chain two changes, and explain why equal percentages up and down do not cancel (AC9M8N05, node 1). **Students should be able to say:** I can use a multiplier for a percentage increase or decrease. I can work out the result of two changes, one after the other. I can explain why up 20% then down 20% is not back to the start. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **A $100 price goes up 10%, then the new price goes down 10%. What is the final price?** ☐ $101 ☐ $90 ☐ $99 ☐ $100 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** $99. Up 10% makes $110. Then 10% of $110 is $11, so the price falls to $99. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Multipliers :::keep-together ### Multipliers Here is the routine. 1. $\text{up } 20\%$ — \times 1.2 2. $\text{down } 20\%$ — \times 0.8 3. $1.2 \times 0.8 = 0.96$ — Multiply the multipliers. 4. $0.96 = 96\%$ — 4% less than the start: an overall decrease of 4%. **What do you multiply by for a 15% increase?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1.15 100% + 15% = 115% = 1.15. ::: :::keep-together ### Find the mistake **Sam works out the jacket's final price. Click the line where his working goes wrong.** ``` 1 A $200 jacket goes up 10%, then the new price goes down 10%. 2 Up 10% adds 10% of $200, which is $20, so it costs $220. 3 Down 10% takes off $20, so it costs $200 again. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: the 10% decrease is 10% of the new price, $220, which is $22. The jacket costs $198. ::: :::keep-together ### Reading a multiplier **A price is multiplied by 0.85. Has it gone up or down, and by how much?** ☐ Up 15% ☐ Down 15% ☐ Down 85% ☐ Up 85% ::: :::teacher-note **Answer:** Down 15% 0.85 = 85%: 15% has been taken off. ::: :::typical ## Back to the start, and discounts **Undo it.** **Two discounts.** **Up 50, down 50.** **Mark-up.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Percentage change :::keep-together ### Increase **Increase $80 by 15%.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 92 80 × 1.15 = $92. ::: :::keep-together ### Decrease multiplier **What do you multiply by for a 35% decrease?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 0.65 100% − 35% = 65% = 0.65. ::: :::keep-together ### Two steps **A $250 bike goes up 20%, then has a 10% discount. What does it cost now, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 270 250 × 1.2 = 300, then 300 × 0.9 = $270. ::: :::keep-together ### Review: percentage of **Review: what is 15% of 60?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 9 0.15 × 60 = 9. ::: :::keep-together ### GST **A price is $80 before GST. GST adds 10%. What is the price with GST, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 88 80 × 1.1 = $88. ::: ## Make: an overall change Then explain why the order of the two changes does not matter to the final price. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A $60 item is discounted 25%, then the discounted price goes up 25%. What is the final price?** {{lines-3}} ::: :::teacher-note **Answer:** 60 × 0.75 × 1.25 = $56.25. :::