Flavoursome

Activity 1

In this activity, students learn how to use “cloning”: an interesting way of comparing two ratios. Cloning (alternatively “duplicating” or “replicating”) can easily be modelled using multilink cubes as materials, as in the following illustration. A different colour is needed for each part of the ratio:

• i. The 5:3 recipe is cloned, and 2 copies made
• ii. The 2 copies are combined to make a 10:6 mix
• iii. The 10:6 mix is used to make three copies of the 3:2 recipe, with 1 measure of apple juice left over.

Have students clone the ratios and record the results:

Ensure that they connect the numbers in the lists with the situation shown in Whina’s method.

Students need to be able to make sense of question 1 if they are to be able to do Activity Two. The extra apple juice shows that recipe 1 has a stronger apple flavour and conversely that recipe 2 has a stronger blueberry flavour.

Question 2 is designed to highlight the fact that Whina kept cloning both recipes until she found a common amount of either apple or blueberry. Without this, she couldn’t compare the ratios. In question 1, she matched the amounts of blueberry; in question 2, she matches the amount of apple:

Question 1 shows that recipe 1 has a stronger apple flavour. Question 2 shows that recipe 2 has a stronger blueberry flavour. It is important that your students understand that these are just different ways of stating the same conclusion. 

Activity 2

Emphasise the phrase “or your own” to encourage your students to use both cloning (with or without multilink cubes) and another strategy to answer these questions.

A second strategy could be to write the proportion of the named flavour in each recipe as a fraction and then to compare the two fractions with the help of a common denominator.

Ask

• “What proportions of recipe A and recipe B are raspberry?”
• “How can we compare these two fractions?”

In question 1, recipe A is 3/7 raspberry and recipe B is 2/5 raspberry. Using 35 as a suitable common denominator, we can write these two equations: 3/7 x 5/5 = 15/35 and 2/5 x 7/7 = 14/35. We can now see that 3/7 is greater than 2/5, which shows that recipe A has the stronger raspberry flavour.

Activity 1

1.

The spare measure tells Whina that the 5:3 recipe has proportionally more apple juice in it than the 3:2 recipe. This means that the 5:3 recipe will have a stronger apple taste and the 3:2 recipe will have a stronger blueberry taste.

2.

Whina wants to match either the amounts of apple juice or the amounts of blueberry juice. By doubling the 5:3 recipe and trebling the 3:2 recipe, she makes the blueberry match (6 measures). If she takes 3 copies of the 5:3 recipe (as suggested) and 5 copies of the 3:2 recipe, she will match the amounts of apple juice. (She will then discover that 3 copies of the first recipe [15:9] will “fit” into the 5 copies of the second recipe [15:10], leaving one “spare” measure of blueberry juice.)

Activity 2

1.

If recipe A is cloned 3 times, recipe B will “fit into” it 4 times, with 1 measure of raspberry left over. This means that recipe A has a stronger raspberry flavour than recipe B.

2.

Recipe D can be cloned 4 times to give a 20:28 mixture. Cloning recipe C 5 times gives 20:25; when the second mixture is fitted into the first, 3 measures of orange are left over. This shows that recipe C has a stronger mango flavour than recipe D.

3.

Recipe E could be cloned 4 times to give 20:24 and recipe F cloned twice to give 14:16. A third clone of recipe F could be obtained if there were just 1 more measure of passionfruit, meaning that recipe F must have a stronger passionfruit flavour than recipe E.