GCSE Maths

What are we going to do this week? Ratio Use ratio notation Simplify ratios Divide a given quantity into parts Find amounts given parts of a ratio Proportion Understand and use proportion Solve problems involving proportion Ratio, Proportion, Fractions, Decimals and Percentages Link ratio, proportion, fractions, decimals and percentages

What is ratio? Ratio is a way of comparing amounts of something. It shows how much bigger one thing is than another.

How is ratio written? 4 : 1 This ratio has 5 parts altogether as 4 + 1 = 5. This will be important a bit later on!

What fraction of the shapes are triangles?

Which can be simplified to: Simplifying Ratios The ratio of blue to yellow blocks is blue : yellow = 4 : 2 Which can be simplified to: 4 : 2 ÷2 ÷2 2 : 1

1 : 2 2 : 3 1 : 3 1 : 2 2 : 9 1 : 2 7 : 5 2 : 3 1 : 2 4 : 5 2 : 5

When writing ratio, they must first be converted to the same unit. Write the ratios in their simplest form 1mm : 5cm (b) £3.50 : 70p 15 mins : hour (d) 2mm : 10mm (e) 5.2 litres : 300cl Copyright © AQA and its licensors. All rights reserved. Version 2.0

Expanding ratio

Now you try…

Share €10 between Mandy and Lara in the ratio 3 : 2 Number of equal parts = 3 + 2 = 5 2 2 2 2 2 2 2 2 2 2 Amount in 1 part = 10 ÷ 5 = € 2 Mandy gets = € 2  3 = € 6 Lara gets = € 2  2 = € 4

Number of equal parts = 4 + 3 = 7 A 35 ml orange drink is made by mixing orange juice and water in the ratio 4 : 3. Number of equal parts = 4 + 3 = 7 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Amount in 1 part = 35 ÷ 7 = 5 ml Orange Juice = 5  4 = 20 ml Water = 5  3 = 15 ml

More wordy question…your turn

How would you do these? Work in pairs/small groups, discuss how you would do this question. Prepare to feed your discussion back to the group

Applying skills Apply a technique you feel most comfortable with to answer questions. To get good at maths you must do maths!!

Back to targets Can you now use probability vocabulary, write probabilities as fractions, decimals or percentages?

Lesson 2 Proportion

Proportion This involves things such as recipes, where the mix has to be in multiples to be correct. It is similar to sharing in a ratio. Everything must be multiplied or divided by the same amount to keep all the parts in proportion.

How many portions? What we know

Proportion A recipe to make 4 cup cakes requires the following ingredients: 2 eggs 250g of flour 100g of sugar How much of each ingredient would I need to make 10 cup cakes?

Proportion A fruit punch for 20 glasses requires the following ingredients: 1 litre of orange juice 600ml of apple juice 250ml of cranberry juice 350ml of grapefruit juice I need to make enough for 75 glasses of fruit punch. How much of each ingredient do I need?

Past paper question – 3 marks

Hint…how much of the original has Oliver got? A trickier problem… Hint…how much of the original has Oliver got?

Applying skills Apply a technique you feel most comfortable with to answer questions. To get good at maths you must do maths!!

Back to targets Can you now use probability vocabulary, write probabilities as fractions, decimals or percentages?