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This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
use doubles and simple proportions to solve problems
This problem page uses ratio, which is a difficult concept for many students. Ratio involves the idea that the relative proportions of two or more things stay constant as the quantities change. For example, someone mixing concrete might use five shovels of builders’ mix to one shovel of cement. This ratio can be expressed as 5:1. Using this “recipe”, the builder might put 20 shovels of builders’ mix and four shovels of cement into the mixer. Although the quantities are 20 shovels to four shovels, the ratio remains the same.
In the case of making Pretend Flying-fish Soup for eight people, the recipe for four people is doubled. The quantity of each ingredient is therefore doubled. Finding two times one and a half can be modelled with regions:
Conversely, for question 2, the recipe quantities are halved. Half of one and a half can be demonstrated by folding one and a half paper circles in half.
So half of one and a half is three-quarters.
Answers to Activity
1. 2 onions
2 tsps curry powder
2 tbsps oil
2 tsps salt
2 tsps pepper
3 cups coconut cream
3 kg fish
2. 1/2 onion
1/2 tsp curry powder
1/2 tbsp oil
1/2 tsp salt
1/2 tsp pepper
3/4 cup coconut cream
3/4 kg (750 grams) fish
3. The students could either multiply the two person recipe by three or add the two-person and the four-person recipes together.