--- title: "Using rates" subtitle: "Number Foundations · Rates · Lesson 28" --- # Using rates **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** How much will it cost to fill the car? How long is the drive to the coast? How many dollars for your holiday money? Each answer comes from one rate, used the right way round. :::teacher-note **In one sentence:** Students use rates both ways (total = rate × amount, amount = total ÷ rate) for petrol, speed, water and exchange rates, letting the units decide multiply or divide (AC9M8M05, node 2). **Students should be able to say:** I can use a rate to find a total or an amount. I can use distance, speed and time in any order. I can check an answer with its units and its size. **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 **Petrol costs $2.05 per litre. How much do 40 litres cost?** ☐ $8.20 ☐ $19.51 ☐ $82 ☐ $42.05 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** $82: 40 × $2.05 = $82. (40 ÷ 2.05 = 19.51 would be how many litres $40 buys.) ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Multiply or divide :::keep-together ### Time Here is the routine. 1. $\text{time} = \text{distance} \div \text{speed}$ — Choose by the units: km ÷ km/h = h. 2. $200 \div 80 = 2.5$ — Divide: 200 km at 80 km/h. 3. $2.5 \text{ h} = 2 \text{ h } 30 \text{ min}$ — Interpret: half an hour is 30 minutes. 4. $80 \times 2.5 = 200$ — Check by going back. **How long does it take to drive 270 km at 90 km/h, in hours?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 270 ÷ 90 = 3 hours. ::: :::keep-together ### Find the mistake **Leo works out a journey time. Click the line where his working goes wrong.** ``` 1 Leo drives 150 km at 60 km/h. How long does it take? 2 Time = distance × speed = 150 × 60. 3 So it takes 9000 hours. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: time = distance ÷ speed. 150 ÷ 60 = 2.5 hours. Units check: km ÷ km per h = h. ::: :::keep-together ### Exchange rates **Say the exchange rate is 1 Australian dollar = 0.65 US dollars. How many US dollars do you get for 200 Australian dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 130 200 × 0.65 = 130 US dollars. ::: :::typical ## Race, shower, money back **Catch up.** **Money back.** **A shower.** **A dripping tap.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Using rates :::keep-together ### Cost **Grapes cost $4.20 per kg. How much do 3.5 kg cost, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 14.7 3.5 × 4.20 = $14.70. ::: :::keep-together ### Distance **A bus averages 85 km/h for 2.5 hours. How far does it go, in km?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 212.5 85 × 2.5 = 212.5 km. ::: :::keep-together ### Time **A cyclist rides 45 km at 15 km/h. How many hours does it take?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 45 ÷ 15 = 3 hours. ::: :::keep-together ### Review: m/s **Review: convert 72 km/h to metres per second.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 20 72 ÷ 3.6 = 20 m/s. ::: :::keep-together ### Pay **A part-time job pays $18.50 per hour. How much is 6.5 hours of work, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 120.25 18.50 × 6.5 = $120.25. ::: :::keep-together ### Run rate **A cricket team needs 120 runs off the last 15 overs. What run rate (runs per over) does it need?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8 120 ÷ 15 = 8 runs per over. ::: ## Make: plan a drive Then say whether your speed is a sensible average for a country drive with a stop, and what the model leaves out. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A plane flies 2100 km at 700 km/h. How long does it take?** {{lines-3}} ::: :::teacher-note **Answer:** 2100 ÷ 700 = 3 hours. :::