--- title: "What is a ratio?" subtitle: "Number Foundations · Ratios · Lesson 20" --- # What is a ratio? **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A fruit punch is 2 cups of juice for every 3 cups of lemonade. Swap them and it tastes completely different. How do we write a recipe like that down? :::teacher-note **In one sentence:** Students build ratios from rows of equal blocks, write part-to-part and part-to-whole ratios in the order asked, and link part to whole to a fraction (AC9M7N08, node 1). **Students should be able to say:** I can write a ratio of two quantities in a : b form, in the order asked. I can tell part to part from part to whole. I can write a part-to-whole ratio as a fraction. **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 How many counters are in the bag altogether? :::keep-together **A bag has 2 red counters and 3 blue counters. What is the ratio of red to blue?** ☐ 5 : 2 ☐ 2 : 5 ☐ 2 : 3 ☐ 3 : 2 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 2 : 3. Red comes first, so 2 comes first. 3 : 2 is blue to red; 2 : 5 is red to all the counters. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Part to part, part to whole :::keep-together ### Whole bag **A bag has 2 red and 3 blue counters. The ratio of red to all the counters is $2 : ?$** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5 2 + 3 = 5 counters in all, so red to all is 2 : 5. ::: :::keep-together ### Find the mistake **Pip finds the ratio of apples to all the fruit. Click the line where the working goes wrong.** ``` 1 A bowl has 4 apples and 3 pears. Find the ratio of apples to all the fruit. 2 There are 4 + 3 = 7 pieces of fruit altogether. 3 Apples to all the fruit: 4 : 3 4 So 4 of every 7 pieces are apples. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: 4 : 3 is apples to pears. Apples to all the fruit is 4 : 7, the 7 from line 2. ::: :::keep-together ### Which way round? **A drink has 2 cups of blue cordial and 5 cups of water. What is the ratio of water to cordial?** ☐ 5 : 2 ☐ 7 : 2 ☐ 5 : 7 ☐ 2 : 5 ::: :::teacher-note **Answer:** 5 : 2 Water first: 5, then cordial: 2. The ratio of water to cordial is 5 : 2. ::: :::typical ## Change the bag **Dogs and cats.** **Add the parts.** **As a fraction.** **Strong or weak?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Ratios :::keep-together ### Pencils to pens **A box has 5 pens and 8 pencils. The ratio of pencils to pens is $8 : ?$** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5 Pencils first: 8, then pens: 5. 8 : 5. ::: :::keep-together ### Pens to all **In the same box, the ratio of pens to all the items is $5 : ?$** Answer: {{field-15}} ::: :::teacher-note **Answer:** 13 5 + 8 = 13 items, so pens to all the items is 5 : 13. ::: :::keep-together ### Wins to losses **A team won 7 games and lost 3. The ratio of wins to losses is $7 : ?$** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 Wins first: 7. Losses: 3. 7 : 3. ::: :::keep-together ### Review: estimating **Review: estimate $6.8 \times 31$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 210 6.8 ≈ 7 and 31 ≈ 30, so 7 × 30 = 210. ::: ## Make: a three-colour mix Then write the ratio of the first colour to the whole. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A jar has 4 black and 5 white beads. Write the ratio of black to white, and of black to all the beads.** {{lines-3}} ::: :::teacher-note **Answer:** 4 : 5 and 4 : 9. :::