Shopping                                                       Measurement, Level 2

Problem

1. Mary has $5. She decides to buy a Choc Attack bar for $1.10. How much change will she get?
2. Hine has $10. She gets $4.60 change after buying a packet of chocolate biscuits. How much were the biscuits?
3. Tui bought a packet of chips for $1.10 in a vending machine. She also got 90 cents change. How much money did she put into the machine?

Extension

1. Maree has $10 and John has $5. After buying some ginger beer John has $3.30 change. Maree buys 2 sticks of liquorice. She has the same amount of change that John spent. What does one stick of liquorice cost?

What is this problem about?
This is a problem about money and change that looks at the situation from three different perspectives. Whenever a question can be solved using an equation like a - b = c, there are always three ways of posing the question. One way to do things is to give a and b and ask for c. This is the situation in Mary’s part of the problem. Mary has $5 (so a = 5) and buys something for $1.10 (so b = 1.10). Her change is c.

A second way of working is to give a and c and ask for b. This is the way that the problem is posed for Hine. She starts with $10 (a = 10) and ends up with $4.60 change (c = 4.60). Her problem is to find b, the cost of the biscuits.

The third way to pose the problem is to give the values of b and c and to try to find a. Tui is faced with this version.

Generally one of the versions of the problem is harder than the others are. In this case Hine’s problem is probably the hardest because it takes two adjustments. With Mary you only have to look at the problem as a subtraction one – it’s a straightforward use of a – b. Tui can look at her problem as an addition problem - she has to work out b + c. But Hine has to work out that her problem involves calculating a – c. This seems not to be immediately obvious as the other two questions because of the need to swap b and c in the implicit equation of the problem.

Achievement Objectives
Measurement (Level 1)
- give change for sums of money.

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (guess and check, use drawing, use equipment, be systematic, act it out).

Resources
Play money
Picture of Choc attack bar
Blackline master of the problem (English)

Specific Learning Outcomes
The children will be able to:
- give change for sums of money
- solve subtraction problems presented in different forms

1. Introduce the problem by showing the picture of the choc attack bar. Ask:
   How much do you think this bar would cost? Why do you think that?
   How could you pay for it? (with exact change, with a $2, EFT-POS etc)
2. Pose question 1.
3. Ask the children to solve the problem mentally and then share their solutions. Make sure that you allow the children time to think before you ask for the solutions. Value each of the different approaches used, as there is no single correct way to solve this problem mentally. Some children will count on from $1.10, others will first subtract $1 from $5 to make $4 and then subtract another 10c to get $3.90.
4. Let the children work individually to solve questions 2 & 3.
5. Ask the children to share their solutions with a small group.
6. Pose question 4 to the whole class or use it as an extension to the problem.

Solution
This problem can be solved using play money or by using a diagrammatic representation. Some children will be able to solve the problems mentally.

1. With Mary, change is what is left after spending, so she has to take the $1.10 from the $5. This gives $3.90.
2. Hine needs to work out that the biscuits cost the difference between her original $10 and the change she received. So her biscuits cost $10 less $4.60. This is $5.40.
3. Tui knows that what she put into the machine came out partly as chips and partly as change. So the sum of $1.10 and 90 cents is what she started with. So that must have been $1.10 plus $0.90, which equals $2.
4. (Extension) This is roughly a three-step problem and so is more difficult than the earlier three problems. Break it down into steps. First deal with John because we have two pieces of information for him. This is like Hine’s problem so his ginger beer cost $5 less $3.30, a total of $1.70.

Now Maree started with $10 and we now know that her change was $1.70 because this is the same as John spent. So the liquorice sticks cost her $10 minus $1.70, which equals $8.30.

To find the cost of one stick of liquorice we have to divide the cost of two by two. So we have to divide $8.30 by 2. This results in $4.15.