**National curriculum content**

- Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison
- Solve problems involving similar shapes where the scale factor is known or can be found
- Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

**Lesson objectives**

- Use ratio language
- Ratio and fractions
- Introducing the ratio symbol
- Calculating ratio
- Using scale factors
- Ratio and proportion problems
- Ratio and proportion problems (2)

**What we want children to know**

- Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (for example, similar shapes and recipes).
- Understand that a ratio shows the relationship between two values and can describe how one is related to another
- Enlarge shapes to make them 2 or 3 times as big

- Pupils solve problems involving unequal quantities, for example, ‘for every egg you need three spoonfuls of flour’, ‘ 3/5 of the class are boys’. These problems are the foundation for later formal approaches to ratio and proportion.

**What skills we want children to develop**

Use knowledge to solve reasoning and problem solving questions such as:

**Do, then explain**

- Purple paint is made from red and blue paint in the ratio of 3:5. To make 40 litres of purple paint how much would I need of each colour? Explain your thinking.

**What else do you know?**

- 88% of a sum of money = £242. Make up some other statements. Write real life problems for your number sentences.
- In a flower bed a gardener plants 3 red bulbs for every 4 white bulbs. How many red and white bulbs might he plant?

**Undoing**

- I think of a number and then reduce it by 15%. The number I end up with is 306. What was my original number?
- In a sale where everything is reduced by 15% I paid the following prices for three items. £255, £850, £4.25. What was the original selling price?

**Vocabulary/Mathematical Talk**

- How would your sentence change if there were 2 more blue flowers?
- How does this help you work out the fraction?
- What does the denominator of the fraction tell you?
- Why is the order of the numbers important when we write ratios?
- How do we write a ratio that compares three quantities?
- How can we represent this ratio using a bar model?
- What does enlargement mean?
- What does scale factor mean?
- Have the angles changed size?
- What does a scale factor of 2 mean? Can you have a scale factor of 2.5?
- How does this problem relate to ratio?
- What is the same about the ratios?

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