--- title: "Percentages of amounts" subtitle: "Number Foundations · Fractions and decimals · Lesson 14" --- # Percentages of amounts **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A jacket is $80, and the sign says 15% off. Before you reach the counter, can you work out what you will pay? :::teacher-note **In one sentence:** Students use a percentage bar to find a percentage of an amount, apply increases and decreases (in two steps and with one multiplier), and express one amount as a percentage of another (AC9M7N06, node 3). **Students should be able to say:** I can find a percentage of an amount, mentally and with a decimal. I can increase or decrease an amount by a percentage, including with one multiplier. I can write one amount as a percentage of another. **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 10% of $80 is $8. What is 5%? :::keep-together **A jacket costs $80. It is 15% off. What do you pay?** ☐ $68 ☐ $65 ☐ $12 ☐ $92 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** $68. 15% of $80 is $12, and $80 − $12 = $68. $12 is the discount, not the price; $65 takes 15 dollars off, not 15%. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Of, off and out of :::keep-together ### Find it, then use it Here is each kind with $80. 1. $10\% \text{ of } 80 = 8, \quad 5\% \text{ of } 80 = 4$ — Mental: 10% is a tenth, 5% is half of that. 2. $15\% \text{ of } 80 = 0.15 \times 80 = 12$ — Or as a decimal: 15% = 0.15. 3. $80 - 12 = 68 \quad \text{or} \quad 80 \times 0.85 = 68$ — A decrease: take it off, or keep 85% in one step. 4. $80 \times 1.15 = 92$ — An increase: 100% + 15% = 115%, so × 1.15. 5. $18 \div 24 = 0.75 = 75\%$ — What percentage: divide, then × 100. Now try one: 35% of 60. **Find 35% of 60.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 21 10% of 60 is 6, so 30% is 18, and 5% is 3: 21. Or 0.35 × 60 = 21. ::: :::keep-together ### Find the mistake **Grace finds the sale price of a $50 game that is 20% off. Click the line where her working goes wrong.** ``` 1 A $50 game is 20% off. Find the sale price. 2 20% = 0.2 3 Sale price = 50 × 0.2 4 = $10 ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: 50 × 0.2 is the discount ($10), not the price. What is left is 80%: 50 × 0.8 = $40. ::: :::keep-together ### Out of **Ari scored 18 out of 24. What percentage is that?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 75 18 ÷ 24 = 0.75 = 75%. ::: :::typical ## One change at a time **GST.** Each task changes one thing. **Increase.** **Decrease.** **What percentage?.** **Up, then down.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Percentages :::keep-together ### A friendly percentage **Find 12.5% of 64. (12.5% is $\tfrac{1}{8}$.)** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8 12.5% = 1/8, and 64 ÷ 8 = 8. ::: :::keep-together ### A multiplier **What do you multiply by to decrease an amount by 30%?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 0.7 100% − 30% = 70% = 0.7. ::: :::keep-together ### Growth **A plant 120 mm tall grows 5% taller. How tall is it now, in mm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 126 5% of 120 = 6, so 126 mm. Or 120 × 1.05 = 126. ::: :::keep-together ### Review: multiplying fractions **Review: work out $\tfrac{2}{3} \times \tfrac{3}{4}$ in simplest form.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1/2 6/12 = 1/2. ::: ## Make: save $15 Then find the pair with the lowest sale price. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A $40 shirt is 35% off. Find the sale price.** {{lines-3}} ::: :::teacher-note **Answer:** 35% of $40 = $14, so $26. Or 40 × 0.65 = 26. :::