Georgia has $5. She buys a nut bar for $1.10.

How much change does she get?

Aria has $10. She gets $4.60 change after buying a packet of rice biscuits.

How much do the biscuits cost?

Oliver pays for $1.10 for two apples. He gets 90 cents change.

How much money did he give to the person at the checkout?

Students are involved in solving three types of subtraction problems for which there are different approaches to find the unknown amount:

Result unknown: a - b = ? This is a straight forward subtraction problem.

Change unknown a - ? = c The approach to this type of problem is likely to be a - c = ? or c + ? = a.

Start unknown: ? - b = c The approach to this type of problem is likely to be c + b = ?

### The Problem

- Georgia has $5. She buys a nut bar for $1.10. How much change does she get?
- Aria has $10. She gets $4.60 change after buying a packet of rice biscuits. How much do the biscuits cost?
- Oliver pays for $1.10 for two apples. He gets 90 cents change. How much money did he give to the person at the checkout?

### Lesson Sequence

- Pose several scenarios in which a student in the class buys a lunch item and receives change. Model/act out with items and money as appropriate.
- Discuss and record solution methods that students share.
- Read the problems one at a time, establishing what each is asking students to find out.
- As students work individually or in pairs ask them to explain their thinking and recording so far.
- Conclude by having a selection of students demonstrate their solutions and respond to any questions classmates may have.
- Pose the Extension as and when appropriate.

#### Extension

- Maree has $6 and John has $5. John buys some juice for $1.40. Maree buys 2 bananas. She has the same amount of change as John. What does one banana cost?
- Discuss with the students each of the kinds of problems they have been solving:

Result unknown: a - b = ?

Change unknown a - ? = c

Start unknown: ? - b = c .

Have them write for another student to solve, a shopping problem of their own using one of these problem types.

### Solution

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

- The calculation for Georgia's change is $5 - $1.10 =
**$3.90.** - The calculation for cost of Aria's biscuits is $10 - $4.60 =
**$5.40**, or $4.60 +**$5.40**= $10. - The calculation for the amount that Oliver gave the person at checkout is $1.10 + 90c =
**$2**

#### Solution to the Extension.

Students need to approach this problem by working step by step. John's juice costs $1.40, so his change is $5 - $1.40, or $3.60. Maree starts with $6 and her change is the same as John's, $3.60. So the two bananas cost her $6 - $3.60, which equals $2.40. Therefore the cost of one banana is $2.40 divided by 2, which equals $1.20.