Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+80 XP
Teacher-led from the board — pupils need no device
What you need:
IWB/Projector/Large Screen

Sharing a Quantity in a Given Ratio

Learn how to share a quantity fairly according to a given ratio. You'll add the parts, find the value of one share, and build each person's amount, then check your answer.

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    Ratio bars
    Ratio bars

    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is a real one for you. There is €20 to be shared between two children, but not equally: the older child gets three times as much as the younger one. We write that share as the ratio 3:1.

    How would you split the €20 so that the older child really does get three times as much?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~11 mins

    The ratio bars will share each total for you, one example at a time. Watch how the parts are added first, then how the size of one part decides every share.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~7 mins

    Today we work through this one together: share 18 in the ratio 4:5.

    Share 18 in 4:5

    +15 XP

    4 - Work It in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, for each sharing problem write "total parts = ___, one part = ___" then list each person's amount. Check your shares add back to the total.

    Try these:

    • Share 16 in 3:1
    • Share 35 in 2:3
    • Share 24 in 1:2:3
    +10 XP

    5 - Class Challenge ~8 mins

    Today we work through these sharing problems together, each one a step harder than the last:

    • Share 16 in 3:1
    • Share 35 in 2:3
    • Share €48 in 1:2:3
    • Two cousins share €90 in the ratio 5:4 — how much more does the older one get?
    Tip

    The last one has an extra step, just like the €90 share we saw earlier: first find both shares, then subtract the smaller from the bigger to see how much more the older cousin gets.

    Sharing challenges

    +15 XP

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    Why do we add the parts of the ratio together before we share? What would go wrong if we forgot that step?

    +10 XP

    7 - What's Next ~3 mins

    Key Takeaways

    • Add all the parts of a ratio to find how many equal shares the total splits into.
    • Divide the total by the total parts to find the value of one part.
    • Multiply one part by each ratio number to build every person's amount, then check the amounts add back to the total.
    • If a question asks how much more one share is, find both shares first, then subtract.
    Coming up

    Next we meet direct proportion and the unitary method: finding the value of one thing, then scaling up to find the value of many.

    +5 XP
    Pupil practice
    Module 4 · Ratio and Proportion Number
    Lesson 45 · Sharing a Quantity in a Given Ratio
    Download Activity Book page (PDF)
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