--- title: "Modelling with ratios" subtitle: "Number Foundations · Modelling · Lesson 24" --- # Modelling with ratios **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A builder mixes mortar as 1 part cement to 3 parts sand. She needs 20 litres of mix. How much of each does she need to buy? :::teacher-note **In one sentence:** Students model practical problems with ratios (mixes, scale drawings, models), say what is known and unknown before calculating, solve by finding one part or the scale factor, and answer in the situation's units (AC9M7M06, nodes 1 and 2). **Students should be able to say:** I can say what is known and unknown in a ratio problem before I calculate. I can solve mixing and scale problems with ratios. I can give my answer with the right units and check that it makes sense. **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 Is the sand more or less than half of the mix? How do you know? :::keep-together **Mortar is cement and sand in the ratio 1 : 3. How many litres of sand are in 20 L of mix?** ☐ 6.7 L ☐ 10 L ☐ 15 L ☐ 60 L My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 15 L. 1 + 3 = 4 parts, each 5 L, and sand is 3 parts. 60 L multiplies the total by 3; 6.7 L divides it by 3. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Formulate first :::keep-together ### Scale **A scale drawing uses the ratio $1 : 50$. A wall is 3 cm long on the drawing. How long is the real wall, in cm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 150 Each 1 cm is 50 cm, so 3 cm is 3 × 50 = 150 cm (1.5 m). ::: :::keep-together ### Find the mistake **Raj mixes fertiliser and water in the ratio 1 : 4 to make 2 L. Click the line where his working goes wrong.** ``` 1 Mix fertiliser and water in the ratio 1 : 4 to make 2 L. 2 Fertiliser = 2 ÷ 4 = 0.5 L 3 Water = 2 − 0.5 = 1.5 L 4 Answer: 0.5 L of fertiliser. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: 2 ÷ 4 divides by the water's number. There are 1 + 4 = 5 parts, so one part is 2 ÷ 5 = 0.4 L: fertiliser 0.4 L and water 1.6 L. ::: :::keep-together ### What first? **Orange paint is red and yellow in the ratio 2 : 3. You need 10 L. What should you do first?** ☐ Multiply 2 × 3 × 10 ☐ Divide 10 by 2 ☐ Say what is known (ratio, total 10 L) and what is unknown (litres of red and yellow) ☐ Start mixing and see ::: :::teacher-note **Answer:** Say what is known (ratio, total 10 L) and what is unknown (litres of red and yellow) Known: ratio 2 : 3 and total 10 L. Unknown: litres of each. Relationship: 5 equal parts of 2 L, so red is 4 L and yellow 6 L. ::: :::typical ## New situations **Orange paint.** **On the map.** **The jug.** **Part to whole.** **The model car.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Ratio models :::keep-together ### Mortar **Mortar is cement and sand in the ratio $1 : 4$. How many kilograms of cement are in 30 kg of mortar?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 1 + 4 = 5 parts. 30 ÷ 5 = 6 kg of cement. ::: :::keep-together ### The plan **A plan uses the scale $1 : 200$. A room is 5 cm long on the plan. How long is the room, in metres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 10 5 × 200 = 1000 cm = 10 m. ::: :::keep-together ### The ship **A model ship is built at the ratio $1 : 50$. The model is 24 cm long. How long is the real ship, in metres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12 24 × 50 = 1200 cm = 12 m. ::: :::keep-together ### Review: sharing **Review: share $48 in the ratio $3 : 5$. What is the bigger share, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 30 3 + 5 = 8 parts. 48 ÷ 8 = 6. The bigger share is 5 × 6 = 30. ::: ## Make: exactly 3 litres Then write what is known, what is unknown, and a check that your two amounts add to the total, with units. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A recipe mixes juice and water 2 : 7. How much juice is in a 900 mL drink?** {{lines-3}} ::: :::teacher-note **Answer:** 2 + 7 = 9 parts. 900 ÷ 9 = 100 mL a part. Juice is 200 mL. :::