*Back to TRC basics*

## Problem solving with money

**Linked from:** Number and Algebra: Money and financial mathematics 115-124

### Prerequisites

- Subtraction strategies (Concept builder)
- Understanding money amounts (Concept builder)
- Addition of small amounts of money (Concept builder)
- Change from $1 and $2 (Concept builder)
- Change from larger amounts (Concept builder)

### Key concepts and skills

- Interpreting the presented scenario to find the correct mathematical procedure and operation
- Expressing change in dollars and cents

### Common errors and misconceptions

- Not correctly identifying that 100 cents makes $1
- Misunderstanding that change is the amount left after paying
- Arithmetic errors
- Misunderstanding of what the question is asking, due to the multi-step nature

### Concept builders

*Finding change*

- Provide students with a small collection of coins; for example, 20c, 20c, 50c and 5c. Ask students to find the total value of the coins and then the change from $2.
- Have students complete the process and record their working as they wish.
- As a group, ask students to share their strategies with the group to find the value of the change.
- Repeat with a different set of coins.
- To extend the activity, have items that students need to find the total value of and the relevant change. Students could use a calculator for amounts of cents that cannot be modelled with coins, such as 26 cents.

*Solving problems*

- Provide students with a problem, such as 'I bought 5 apples that cost 25c each. How much change did I get from $2?'
- Have students model the activity, with fruit, price labels and coins.
- Have students complete the transaction with money and then with recording.

For example, 5 lots of 25 cents is $1.25. $2.00 – $1.25 = 75c. 75c is the amount of change.

- Repeat with a number of examples, working initially with amounts ending in 10 cents and then moving to those ending with 5 cents, keeping below $2.
- Strategies such as underlining or recording key information in the question could also be visited.
- To vary the activity, extend to include values to the cent, e.g. $1.14, and finding change from values such as $10 and $20. Students should be taught to round values to the nearest 5 cents.

### Further reading

- McClure, L. (2013). Problem solving and the new curriculum. Retrieved from http://nrich.maths.org/10367

### Example questions

- Interpret sale information involving percentage to calculate cost (Skill illustration)
- Identify items with a given total cost (Skill illustration)
- Work out the extra needed to buy an item (Skill illustration)
- Identify the total cost of two items (Skill illustration)
- PAT Maths Plus, Test 8, Q3 (Annotated question)
- PAT Maths 4th Ed, Test 4, Q6 (Annotated question)
- PAT Maths Plus, Test 9, Q1 (Annotated question)
- PAT Maths 4th Ed, Test 4, Q4 (Annotated question)
- PAT Maths 4th Ed, Test 9, Q9 (Annotated question)