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Ratio and Proportion 1 Simple ratios Overview Objectives Understand, recognise and use simple ratios in a context Scale up or down using simple ratios in context Make two quantities using a given simple ratio For this unit you will need: red and yellow paint, large spoon, two paint palettes, two brushes, interconnecting cubes Watch out for pupils who: think that if 1/3 of cubes are red for example, that the ratio is 1 : 3 rather than 1 : 2; think that if you add the same number to each quantity the ratio will remain the same, rather than multiplying or dividing each quantity by the same number. HSNP © Hamilton 2013 Simmering Term 1 Ratio and Proportion 1 Session 1 Objectives: Understand, recognise and use simple ratios in a context Teacher input with whole class Pour two spoons of red paint and one spoon of yellow paint onto one palette and one spoon of red and two spoons of yellow onto the other. Ask pupils what colour of paint will be made when the paints are mixed on each palette, how the two colours will differ and why. Draw out that the two shades of orange will be different as you have used different ratios of red to yellow paint. Mix each and use them to paint two blobs on a large sheet of paper, writing red : orange under each, and the ratios 2 : 1 and 1 : 2. Say that each palette contained three spoonfuls of paint. Ask how many spoonfuls would be needed of each colour to make a total of 6 spoonfuls of the darker orange and of the paler orange. Record the ratios 4 : 2 and 2 : 4 under the initial ratios. What if we needed to double this amount of paint? Paired pupil work Ask pupils to work in pairs to find equivalent ratios for purple paint, made in the ratio of 3 blue spoonfuls for every 1 spoon of red paint. They copy and complete the following table. Encourage them to add their own rows. Total number of spoons Spoons of blue point Spoons of red point 4 3 1 8 12 20 Teacher input with whole class Discuss the relationship between the numbers in the second and third columns, i.e. that the numbers in the second column are 3 times the number in the third column. If purple paint is made with four spoons of paint, what fraction of the spoonfuls is red? Blue? And if 8 spoons are used using the same ratio? HSNP © Hamilton 2013 Simmering Term 1 Ratio and Proportion 1 Session 2 Objectives: Understand, recognise and use simple ratios in a context; Scale up or down using simple ratios in context Teacher input with whole class Display the following list of ingredients for a berry smoothie: 50g blueberries 100g of raspberries 150g of strawberries one banana 150ml apple juice What is the ratio of raspberries to blueberries? What is the ratio of strawberries to blueberries? Strawberries to raspberries? Say that this recipe serves 2 people and ask pupils what they would need to do to make smoothies for 4 people. They write the new recipe on their whiteboards. What is the ratio of raspberries to blueberries now? Discuss the other ratios and agree that they are the same, and so the smoothie will taste the same. Paired pupil work Ask pupils to work together to adapt the recipe for 6 people, then 3 people, then 5 people. Teacher input with whole class Say that cook is making up diluted squash for the pupils’ café. The squash should be mixed 1 part squash to 4 parts water. Ask pupils how much water needs to be added if she uses 100ml of squash. 300ml? 150ml? Ask how much squash she must have used if she added 800ml of water, 1600ml or 2 litres of water. HSNP © Hamilton 2013 Simmering Term 1 Ratio and Proportion 1 Session 3 Objective: Make two quantities using a given simple ratio Teacher input with whole class Show pupils a stick of 4 red cubes and 2 blue cubes. What is the ratio of red to blue cubes? Discuss how we can write the ratio as 4 : 2 but can simplify it to 2 : 1. Remind pupils that this means that there are twice as many red cubes as blue ones, or that there are 2 red cubes for every one blue cube. Repeat with 6 blue cubes and 2 blue cubes and then with 6 blue cubes and 4 red cubes. Paired pupil work Pupils work in pairs or group of four to make as many different sticks of cubes as they can in 2 minutes such that the ratio of one colour to the other is 3 to 1. Teacher input with whole class What fraction is red? And blue? (Ensure pupils see that ¼ is in one colour and ¾ in the other, not 1/3 and 2/3.) Paired pupil work Pupils write as many pairs of numbers as they can with a ratio of 2 to 1 in one minute, then 4 to 1, then 3 to 2. Simmering Term 1 HSNP © Hamilton 2013 Ratio 1