--- title: "Modelling with money" subtitle: "Number Foundations · Modelling · Lesson 23" --- # Modelling with money **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A $200 bike is 20% off, and then a coupon takes a further 10% off the new price. Is that the same as 30% off? :::teacher-note **In one sentence:** Students model money problems (discounts, rises, markups, profit and sharing) by formulating what is known and unknown, choosing a representation, solving, and interpreting and justifying the answer in dollars (AC9M7N09, nodes 1 to 3). **Students should be able to say:** I can say what is known and unknown in a money problem and choose how to model it. I can solve problems with fractions, percentages and ratios, including percentages in two steps. I can write my answer in dollars and explain why I chose that representation. **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 Why is 10% of the new price less than 10% of $200? :::keep-together **A $200 bike is 20% off, then a coupon takes 10% off the new price. What is the final price?** ☐ $144 ☐ $160 ☐ $140 ☐ $150 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** $144. 20% off $200 is $160, then 10% off $160 is $144. $140 would be 30% off $200; the 10% is of a smaller amount. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Formulate, solve, interpret :::keep-together ### Say what you know **Known: a $60 jumper is 25% off. Unknown: the sale price. What is it, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 45 25% of $60 = $15, so $45. Or 60 × 0.75 = 45. ::: :::keep-together ### Find the mistake **Ben finds the percentage profit on a scarf. Click the line where his working goes wrong.** ``` 1 A scarf costs $5 to make and sells for $8. 2 Profit = 8 − 5 = $3 3 Percentage profit = 3 ÷ 8 = 0.375 = 37.5% 4 Answer: 37.5% profit. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: profit is a percentage of the cost, the original amount: 3 ÷ 5 = 0.6 = 60%. Ben divided by the selling price. ::: :::keep-together ### Which representation? **Shop A takes $\tfrac{1}{3}$ off a $90 jacket. Shop B takes 30% off. Which is the better deal, and why?** ☐ Shop A: $\tfrac{1}{3}$ is about 33%, more than 30% ☐ They are the same ☐ Shop B: 30 is bigger than 3 ☐ You cannot tell ::: :::teacher-note **Answer:** Shop A: $\tfrac{1}{3}$ is about 33%, more than 30% $\tfrac{1}{3}$ of $90 = $30 off; 30% of $90 = $27 off. Writing both as percentages (33⅓% and 30%) makes the comparison immediate. ::: :::typical ## New money problems **The game.** **A pay rise.** **Markup, then sale.** **Write the price.** **What does it assume?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Money models :::keep-together ### Fractions of a prize **A $240 prize is shared: $\tfrac{1}{4}$ to Ann, and the rest equally among 3 others. How much does each of the other three get, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 60 Ann gets $60, leaving $180. $180 ÷ 3 = $60 each. ::: :::keep-together ### Saving up **A bike costs $400. You have saved 65% of it. How many more dollars do you need?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 140 65% of $400 = $260 saved. $400 − $260 = $140. Or 35% of $400. ::: :::keep-together ### Bulk buying **A pack of 12 pens costs $9, while one pen costs $1. What percentage cheaper is each pen in the pack?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 25 12 singles cost $12; the pack costs $9, so each pen costs 75% as much. That is 25% cheaper. ::: :::keep-together ### Review: sharing **Review: share $84 in the ratio $3 : 4$. What is the bigger share, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 48 3 + 4 = 7 parts. 84 ÷ 7 = 12. The bigger share is 4 × 12 = 48. ::: ## Make: a $75 sale Then write one sentence for a shopper explaining your sale. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A $80 jacket is marked up 25% then sold at 25% off the new price. Is the final price more than, less than or equal to $80? Work it out.** {{lines-3}} ::: :::teacher-note **Answer:** 80 × 1.25 = 100, then 100 × 0.75 = 75: less than $80. :::