Using materials

Put one student or a pair of students in charge of recording purchases at the layby counter. Give them a pile of $1 and $10 notes and the modelling book.
Problem: Margaret has $8. She wants to buy a birthday present for her Mum that costs $15, so she goes to the layby counter. She asks to put the item on layby and deposits her $8. Ask the layby clerk to record the transaction and tell her how much she owes. A negative integer will show how much money she owes and a positive integer will show how much money she has.

Record ⁺8 – ⁺15 = ?
Discuss how this shows that Margaret started with $8, purchased a $15 item, and now owes $7.
We show that the $7 is owed by recording it as a negative integer: ⁻7.
Margaret owes $7. When she comes in to pay the rest, the clerk will record: ⁻7 + ⁺7 = 0.
She will owe nothing.

Examples: Pose pocket money and bills stories for: ⁺5 – ⁺7, ⁺10 – ⁺13, ⁺2 – ⁺5, ⁺9 – ⁺2, ⁺5 – ⁺8, ⁺5 – ⁺11, ⁺12 – ⁺25 …

Using imaging and number properties

Students need to repeat this kind of problem, at first by imaging the money, until they can predict the answer and explain their reasoning without using, or referring to, materials. Pose problems about a student’s saving and spending.

Examples: ⁺48 – ⁺99, ⁺150 – ⁺225, ⁺1 000 – ⁺1 450, ⁺995 – ⁺1 025 … Students who are unable to solve the problems by imaging and/or number properties may need to fold back to “Using materials”. Note: These problems could also be solved using the context of temperature.