Sharing a Quantity in a Given Ratio

Warning: Your screen size is quite small for viewing this. Rotate your device into landscape mode if you can.

1 Getting Started
2 Watch and Notice
3 Try It Together
4 Work It in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here 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?

Teacher Notes

Take three hands-up answers, not open call-outs. Don't confirm or correct yet, just collect the thinking. Listen for the common slip of giving €15 and €5 by guessing, versus reasoning it out by counting parts.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~11 mins

Illustration for Watch and Notice

Share 12 in 2:1

Watch the ratio bars. There are 2 + 1 = 3 parts in total. Twelve shared into 3 parts gives 4 in each part. So one person gets 2 parts (8) and the other gets 1 part (4).

Share 20 in 3:1

This time there are 3 + 1 = 4 parts. Twenty shared into 4 parts gives 5 in each part. So the shares are 15 and 5.

Share 24 in 1:2:3

A three-way share now. The parts are 1 + 2 + 3 = 6 in total. Twenty-four shared into 6 parts gives 4 in each part. So the three shares are 4, 8 and 12.

Share €90 in 5:4, then find the difference

Now a question with one extra step. There are 5 + 4 = 9 parts. Ninety shared into 9 parts gives €10 in each part. So the two shares are €50 and €40. To find how much more the older one gets, we take one last step and subtract: €50 − €40 = €10.

Teacher Notes

Walk each example one at a time. Each time, say the order aloud: add the parts, find one part, then build each amount.

12 in 2:1 — point to the two bars and the live values; stress that one part is found by dividing the total by the total parts.
20 in 3:1 — this is the hook's €20 answered; let the class connect it back.
24 in 1:2:3 — the three-way share; emphasise the parts still just add (1+2+3 = 6).
€90 in 5:4 — this one adds a fourth step. Build the shares (€50 and €40) the usual way, then ask how much more the older one gets and subtract aloud (€50 − €40 = €10). Pupils will meet this same difference move in the Class Challenge, so name it clearly here.

👇 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.

Worked example

First we add the parts: 4 + 5 = 9 parts. Notice we divide by 9 parts, not by the 2 people sharing. Next we find one part: 18 ÷ 9 = 2. Then we build each amount: 4 × 2 = 8 and 5 × 2 = 10. Last, we check back: 8 + 10 = 18.

Share 18 in 4:5

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Build the two bars at 4 and 5 first, then set the total to 18. The class should call out: 4 + 5 = 9 parts, 18 ÷ 9 = 2 for one part. Then read each share off the bars (8 and 10). Head off the slip of dividing 18 by 2 because there are two people — the divisor is the total parts (9), not the number of people. Rotate two or three pupils to set and read the bars.

+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

Teacher Notes

Walk the room glancing at the "total parts" and "one part" lines — this is whole-class copybook practice, not marking. The check-back line (shares adding to the total) is the habit to praise.

+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

Teacher Notes

This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

For each one set the two (or three) bars, then enter the total, and read the shares off the live bars. The interactive steps through the four challenges in order; the top-level parts only seed the opening bar (3:1), so just work down the list. The final question is the stretch: the bars set to €50 and €40, but the tool does not do the subtraction — read €50 and €40 off the bars and compute the difference (€10) aloud with the class. Keep stressing the three-step order: add the parts, find one part, build each amount.

+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?

Teacher Notes

Listen for pupils naming the total parts as the divisor — that adding 3 + 1 gives the 4 we divide by, not the 2 people. Revoice a strong answer: so the parts tell us how many equal shares to cut the total into, no matter how many people there are.

+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

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.

Teacher Notes

Close by re-saying the three-step chant one last time: add the parts, find one part, build each amount.

+5 XP

Pupil practice

Module 4 · Ratio and Proportion Measures

Lesson 42 · Sharing a Quantity in a Given Ratio

Download Activity Book page (PDF)

End of lesson

123learn · Online learning platform

Unlock the full learning experience

You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

Hundreds of curriculum-aligned lessons

Interactive activities in every lesson

Printable resources & progress tracking

Get started

Copyright Notice
This lesson is copyright of 123Learn.ie 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~11 mins

Share 12 in 2:1

Share 20 in 3:1

Share 24 in 1:2:3

Share €90 in 5:4, then find the difference

3 - Try It Together ~7 mins

Share 18 in 4:5

4 - Work It in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Sharing challenges

6 - What Did We Notice? ~3 mins

7 - What's Next ~3 mins

Key Takeaways

Coming Up

Unlock the full learning experience

XP