--- title: "Ratio and rate models" subtitle: "Number Foundations · Modelling · Lesson 29" --- # Ratio and rate models **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Painting a room, mixing cordial for a party, filling a pool, sharing the cost of a gift: the maths is easy once you choose the right model and remember what the answer means. :::teacher-note **In one sentence:** Students model practical problems as a ratio or a rate (paint coverage, cordial, fuel, sharing, filling), solve them and interpret the answer in the situation (AC9M8M07, node 1). **Students should be able to say:** I can decide whether a problem needs a ratio or a rate. I can set up and solve a ratio or rate model. I can interpret the answer in the situation, such as rounding up to whole tins. **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 litre of paint covers 12 m². How much paint do you need for a 30 m² wall?** ☐ 0.4 L ☐ 2.5 L ☐ 42 L ☐ 360 L My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 2.5 L: 30 ÷ 12 = 2.5. (360 multiplies the area by the rate; that would be m² × m² per L, which makes no sense.) ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Choosing the model :::keep-together ### Ratio or rate Here is the routine. 1. $\text{need: litres of paint for 20 m}^2$ — Say what you are finding, with units. 2. $\text{12 m}^2 \text{ per L: a rate}$ — Different units, so a rate. 3. $20 \div 12 \approx 1.7 \text{ L}$ — m² ÷ (m² per L) = L. 4. $\text{buy 2 one-litre tins}$ — Interpret: tins are whole, and 1 would not be enough. **Cordial is mixed 1 part cordial to 4 parts water. Is this a ratio or a rate model?** ☐ A rate: litres per litre ☐ A percentage ☐ A ratio: both parts are litres of liquid ☐ Neither ::: :::teacher-note **Answer:** A ratio: both parts are litres of liquid Same kind of quantity, same units: a ratio, 1 : 4. ::: :::keep-together ### Find the mistake **Ana buys paint. Click the line where her answer stops making sense.** ``` 1 Ana needs 2.4 L of paint for her wall. 2 The paint is sold in 1 L tins. 3 2.4 rounds to 2, so she buys 2 tins. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: 2.4 does round to 2, but 2 tins hold only 2 L, not enough. Here she must round up: 3 tins. ::: :::keep-together ### Fuel use **A car uses 7 L of petrol per 100 km. How many litres does a 350 km trip use?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 24.5 350 km is 3.5 lots of 100 km: 3.5 × 7 = 24.5 L. ::: :::typical ## Share, scale, fill **Share a gift.** **Scale a recipe.** **Which model.** **Fill a tank.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Models :::keep-together ### Paint **5 L of paint at 12 m² per litre covers how many square metres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 60 5 × 12 = 60 m². ::: :::keep-together ### Cordial **Cordial is mixed 1 : 4 with water. How many litres of cordial are in 3 L of drink?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 0.6 5 parts make 3 L, so one part is 0.6 L of cordial. ::: :::keep-together ### Buses **A bus seats 45 people. How many buses are needed for 200 people?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5 200 ÷ 45 = 4.4…, and a part bus is still a bus: 5. ::: :::keep-together ### Review: percentage increase **Review: increase $50 by 10%.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 55 50 × 1.1 = $55. ::: ## Make: paint a fence Then say how many 4 L tins to buy, and why. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A recipe uses 2 cups of rice to 3 cups of water. How much water for 5 cups of rice? Is this a ratio or a rate?** {{lines-3}} ::: :::teacher-note **Answer:** A ratio (cups to cups): 5 × 1.5 = 7.5 cups of water. :::