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

1. Add or multiply?
2. Use ratio language
3. Introduction to the ratio symbol
4. Ratio and fractions
5. Scale drawing
6. Use scale factors
7. Similar shapes
8. Ratio problems
9. Proportion problems
10. Recipes

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?