Fact Families and the Link Between + and −

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Write the Family 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 are just three numbers: 3, 5 and 8. How many true number sentences do you think we can build using only these three? Have a look and see how many you can spot.

Teacher Notes

Give five seconds of quiet think-time, then take three hands-up answers. Some pupils will offer 3 + 5 = 8; nudge for a take-away too. Don't confirm the full set yet — that is what the lesson builds toward.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Look at the three balance beams. The same three numbers, 3, 5 and 8, appear in three sentences here, and each one keeps the beam level. See how the two parts (3 and 5) sit against the whole (8), and how the beam still balances for a take-away.

Here the beam shows the sentence turned around into a take-away. The whole is on one side, and one part comes off to leave the other part.

There is one more take-away hiding in this family.

Teacher Notes

3 + 5 = 8 — point to the two parts making the whole; ask which number is the biggest.
5 + 3 = 8 — same beam, parts swapped; ask did the answer change?
8 − 3 = 5 — the whole loses a part; ask which number is left. Pause before revealing that it is the other part.

Three of the four facts are on the board; the fourth take-away (8 − 5 = 3) is the one pupils build for themselves next, so ask the class to predict it before you move on. Hold out for pupils naming 8 as the whole every time — that is the number the whole family is built on.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Now we build two fact families together on the balance. First we do the family for 2, 7 and 9. Then we do the family for 6, 4 and 10.

Key point

For each family we build four sentences. We start with one addition. Then we swap the two parts around for the second addition. Then we make a take-away. Last of all we make the other take-away. All four balance, and all four use the same three numbers.

Classmates take turns loading the pans at the board. If you are at your seat, watch closely and call out if you agree or if you would change something.

Fact families for 2, 7, 9 and 6, 4, 10

Teacher Notes

Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.

Start with 2 + 7 = 9. Ask a pupil to load 2 and 7 on the left and 9 on the right, and check the beam is level. Then build 7 + 2, then 9 − 2, then 9 − 7 — each time asking which is the whole, which are the parts? before they load the pans. Repeat with 6, 4, 10. Listen for pupils spotting that the biggest number is always alone on one pan of the take-aways.

+15 XP

4 - Write the Family in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, write all four number sentences in the fact family for 4, 6 and 10 — two additions and two take-aways. Read each one aloud to check it is true.

Teacher Notes

Walk the room, glance for pupils who write only additions and forget the two take-aways — no individual marking, this is whole-class copybook practice, not assessment.

+10 XP

5 - Class Challenge ~7 mins

Now the practice round, four on the balance, one after another.

First we learn how to check whether three numbers make a real fact family. Take 5, 7 and 12. The biggest number should be the whole. Predict: if we put the two smaller numbers on one pan and the biggest on the other, will the beam stay level? Then we check. If it balances, the three numbers make a family of four facts. If it tips, they do not.

The first two challenges are quick warm-ups. We make one addition, then one take-away, from the families we built before.

New challenge

We solve x + 6 = 13. The letter x just stands for a missing number we have to find, so we work out what x must be to level the beam.

The last one uses a take-away to check a family whose whole is 13. Each one is a little trickier, so predict where the beam will settle before we check.

Fact family challenge

Teacher Notes

This is the practice round, pupils take turns at the board, check each answer, and the class confirms before moving on.

Worked check first (LO4), on the board before the interactive: numbers 5, 7, 12. 1) Spot the biggest as the whole (12). 2) Class predicts: will 5 + 7 balance 12? 3) Check: 5 + 7 = 12, yes, beam level, so valid family; write the four facts quickly. 4) Contrast with a tip: swap in 11 as the whole (5, 7, 11); 5 + 7 = 12 ≠ 11, beam tips, not a family. Slip to watch: pupils picking a part as the whole.

Keep the first two challenges brisk; they are warm-ups from Try It Together. Save room for the third: x + 6 = 13. Before anyone slides, ask is the box a part or the whole? and take two answers. The last one checks the family with whole 13 using 13 − 5 = 8. Narrate the Check tick: yes, that levels it.

+15 XP

Pupil practice

Module 10 · Algebra: Patterns, Rules and Number Sentences Mixed

Lesson 115 · Fact Families and the Link Between + and −

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This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

3 - Try It Together ~11 mins

Fact families for 2, 7, 9 and 6, 4, 10

4 - Write the Family in Your Copy ~3 mins

5 - Class Challenge ~7 mins

Fact family challenge

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