Mathematics
Intermediate
50 mins
Teacher/Student led
+65 XP
What you need:
IWB/Projector/Large Screen

Direct Proportion and the Unitary Method

Learn to find the value of one unit by dividing, then multiply up to solve real-world problems about prices, distances and quantities. The unitary method is your key to scaling any amount.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedThree pencils cost 90c in the school shop.

    What would one pencil cost? And how would you work out the price of seven?

    2 - Watch and Notice ~9 mins

    Watch the four function machines. They show the two moves in turn: first divide to find what one costs, then multiply up to the amount we want. Watch for the divide step every time — that is where the price of one comes from.

    3 - Try It Together ~11 mins

    We'll do these together on the machine, one problem at a time. An individual pupil comes to the board for each problem while the rest of the class follows and agrees. Each time, we key in a divide rule first to find the value of one, agree the answer as a class, then switch the same machine to a multiply rule to scale up.

    • Six oranges cost €1.80. Find the price of one orange, then price ten.
    • Five buns cost €2.00. Find the price of one bun, then price eight.
    • A car goes 30 km in 3 hours at a steady speed. Find how far it goes in one hour, then how far in eight hours.

    Each time it's the same two moves: divide to find one, then multiply up.

    Divide to one, then multiply up

    4 - Write the Two Steps in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, take the three problems we just did: six oranges for €1.80, five buns for €2.00, and the car going 30 km in 3 hours. For each one write "÷ to find one: ___" then "× up to find the answer: ___". Box your final answer.

    5 - Class Challenge ~8 mins

    We'll work through these together at the board. Divide to find one, then multiply up:

    • Nine buns cost €4.50. Find the price of one, then price four.
    • A car goes 240 km in 3 hours at a steady speed. How far does it go in 7 hours?
    • Six identical bottles hold 4.5 litres altogether. How much do ten bottles hold?
    • Stretch: eight match tickets cost €60. How much do five cost?
    Tip

    That last one asks for fewer tickets, not more — but the same first move still works. Find the value of one ticket by dividing, then multiply up to five.

    Use the unitary method — divide to find the value of one, then multiply up to find the value of many.

    1. 9 buns cost €4.50. Find the price of one bun.
    2. One bun is 50c. How much do 4 buns cost?
    3. A car goes 240 km in 3 hours. How far in 7 hours?
    4. 6 bottles hold 4.5 litres. How much do 10 bottles hold?

    Ways to start:

    • Nine buns cost €4.50 — find the price of one bun, then price four buns.
    • A car travels 240 km in 3 hours at a steady speed — how far does it go in 7 hours?

    Stretch:

    • Six identical bottles hold 4.5 litres altogether — how much do 10 bottles hold?
    • Eight match tickets cost €60 — how much do five tickets cost? The same divide-first move works even when scaling down: find the value of one ticket, then multiply up to five.
    Answers & strategies (teacher)
    1. 9 buns cost €4.50. Find the price of one bun. — 50c (€0.50)
    2. One bun is 50c. How much do 4 buns cost? — €2.00
    3. A car goes 240 km in 3 hours. How far in 7 hours? — 560 km (80 km per hour × 7)
    4. 6 bottles hold 4.5 litres. How much do 10 bottles hold? — 7.5 litres (0.75 l each × 10)
    • Divide the total by the number given to find the value of one unit.
    • Multiply the value of one by the new number of units.
    • For distance, treat km-per-hour exactly like price-per-item.
    • Even when the answer is for fewer items, still find the value of one first, then multiply up.
    Pupil practice
    Module 4 · Ratio and Proportion Measures
    Lesson 43 · Direct Proportion and the Unitary Method
    Download Activity Book page (PDF)
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