--- title: "Rates" subtitle: "Number Foundations · Rates · Lesson 27" --- # Rates **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Speed limits, the price of petrol, your heart rate and how fast your phone downloads: all rates. Each one says 'this much per one of that'. :::teacher-note **In one sentence:** Students match rates to distances and times on a double number line, tell rates from ratios, find unit rates and convert between rate units such as km/h and m/s (AC9M8M05, node 1). **Students should be able to say:** I can write a rate with its two units. I can find a unit rate by dividing in the right order. I can convert a speed between km/h and m/s, and tell a rate from a ratio. **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 car travels 150 km in 2 hours at a steady speed. How far does it go in 1 hour?** ☐ 2/150 km ☐ 75 km ☐ 152 km ☐ 300 km My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 75 km: 150 ÷ 2 = 75. The car's speed is 75 km per hour. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Rate or ratio :::keep-together ### Rate or ratio Here is the routine. 1. $\text{distance} \div \text{time}$ — Divide what you want "per" by the "one" quantity. 2. $150 \div 2.5 = 60$ — 150 km in 2.5 h. 3. $60 \text{ km/h}$ — Keep both units in the answer. 4. $60 \div 3.6 \approx 16.7 \text{ m/s}$ — To convert km/h to m/s, × 1000 ÷ 3600, which is ÷ 3.6. **Rate or ratio?** Groups: Rate, Ratio - 60 km per hour: {{field-15}} - $3.50 per kg: {{field-15}} - 2 : 3 cordial to water: {{field-15}} - 80 beats per minute: {{field-15}} - 3 boys to 4 girls: {{field-15}} - 7 L per 100 km: {{field-15}} ::: :::teacher-note **Answer:** 60 km per hour → Rate; $3.50 per kg → Rate; 2 : 3 cordial to water → Ratio; 80 beats per minute → Rate; 3 boys to 4 girls → Ratio; 7 L per 100 km → Rate A rate has two different units; a ratio compares the same kind of thing. ::: :::keep-together ### Find the mistake **Mia works out the price of apples per kilogram. Click the line where her working goes wrong.** ``` 1 Mia buys 3 kg of apples for $12. 2 To find the price in dollars per kilogram, she divides 3 by 12: 0.25. 3 So the apples cost $0.25 per kg. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: dollars per kilogram is dollars ÷ kilograms: 12 ÷ 3 = $4 per kg. 3 ÷ 12 = 0.25 kg per dollar, a different rate. ::: :::keep-together ### Convert a speed **Convert 90 km/h to metres per second.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 25 90 × 1000 = 90 000 m in 3600 s: 90 000 ÷ 3600 = 25 m/s. ::: :::typical ## Convert and compare **m/s to km/h.** **Price per kilogram.** **Best buy.** **Heart rate.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Rates :::keep-together ### Speed **A train travels 240 km in 3 hours. What is its speed in km per hour?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 80 240 ÷ 3 = 80 km/h. ::: :::keep-together ### Convert **Convert 36 km/h to metres per second.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 10 36 ÷ 3.6 = 10 m/s. ::: :::keep-together ### Price per kg **A 2 kg bag of flour costs $3.40. What is the price in dollars per kilogram?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1.7 3.40 ÷ 2 = $1.70 per kg. ::: :::keep-together ### Review: ratios **Review: what is the ratio 12 : 18 in simplest form?** ☐ 2 : 3 ☐ 3 : 2 ☐ 6 : 9 ☐ 12 : 18 is already simplest ::: :::teacher-note **Answer:** 2 : 3 Divide both by 6: 2 : 3. ::: ## Make: a long drive Then give the speed in metres per second, to 1 decimal place. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A cyclist rides 45 km in 1.5 hours. Find her speed in km/h and m/s.** {{lines-3}} ::: :::teacher-note **Answer:** 45 ÷ 1.5 = 30 km/h; 30 ÷ 3.6 ≈ 8.3 m/s. :::