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 = ?
- 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?
- 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.
- 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.
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.