This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
multiply fractions by 2 and by 10
multiply and divide with money
In this activity, the students use their knowledge of doubling and of fractions to increase the quantities of a recipe. They also need to work out the cost and profit of selling the honey crunch bars.
The doubling of the quantities is likely to be straightforward for the students, although some may need to rely on diagrams or materials to represent the quantities to help them.
For example, doubling 3/4 can be represented by the following diagram:
2 x 3/4
There are six quarters or 6/4, which is the equivalent to 12/4 or 11/2.
Multiplying the quantities could be treated in a similar way:
10 x 3/4
Moving quarters to fill up circles gives seven full circles and two quarters, which is equivalent to 72/4 or 71/2.
These diagrams should help the students to see the connection between this modelling and the more efficient way of working the quantities out: 10 x 1/4 = 10/4, which is the same as 22/4 or 21/2.
The students should know how to calculate profit (that is, money made minus the costs), but you may want to check this before they start question 3.
Answers to Activity
1. 250 g butter
2/3 cup honey
1 cup brown sugar
11/2 cups wholemeal self-raising flour
11/2 cups plain flour
1/2 tsp coriander
1 tsp cinnamon
1/2 tsp nutmeg
2 pinches ground cloves
1/2 cup raisins
1/2 cup almonds
2. 1.25 kg butter
31/3 cups honey
5 cups brown sugar
71/2 cups wholemeal self-raising flour
71/2 cups plain flour
21/2 tsp coriander
5 tsp cinnamon
21/2 tsp nutmeg
10 pinches ground cloves
21/2 cups raisins
21/2 cups almonds
3. a. $19.50
b. $97.50 if no savings were made from buying larger quantities of ingredients. If savings were made, as is likely, the profit would increase.