Mental Strategies for Addition and Subtraction

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Note Your Strategy 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 quick one to do in your head: what is 1,998 + 2,005?

Now the real question. Would you ever reach for a pencil to work that out, or is there a faster way in your head? What did you do to it to make it easy?

Teacher Notes

Give five seconds of quiet think-time, then take three hands-up answers, not open call-outs.

Listen for pupils who rounded 1,998 up to 2,000 and adjusted, or who added 2,000 + 2,000 and fixed the small bits. Revoice the rounding move as the hook for today's strategies.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

The number line shows three ways to add and subtract big numbers: compensation, round-and-adjust, and partition. Look at the jumps on each number line and notice which numbers are chosen to make each one tidy.

Teacher Notes

Compensation 4,997 + 386: point out 4,997 is only 3 from a tidy 5,000; jump 3 to reach 5,000, then add the remaining 383. No overshoot, lands exactly on 5,383.

Round-and-adjust 8,012 - 1,995: take away a tidy 2,000 first (jump left), then come forward 5 because we took 5 too many. This is where pupils slip. Trace the -2,000 leftward, then the +5 clearly rightward. Lands on 6,017.

Partition 3,450 + 2,780: split into parts and add one jump at a time, 2,000 then 700 then 80. Stress partitioning never changes the total; the parts just rebuild it. Lands on 6,230.

Say each strategy name as you point to its header.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

First we work this one out together on the empty number line on screen: 5,996 + 247. We will say the clever first jump aloud before we draw it. Then, on the board beside it, we will trace two more by hand: 7,003 − 1,996 and 2,560 + 3,470, naming the strategy for each before we start.

Work it out on the line

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud. The on-screen interactive is set up for the first calculation only; trace the other two on a hand-drawn line beside it.

Before each calculation, ask the class which strategy fits: is one number close to a tidy figure (compensation or round-and-adjust), or do we want to break it into parts (partition)? Say the first jump aloud before anyone draws.

5,996 + 247 (on the interactive line) — compensation: jump 4 to reach 6,000, then add 243.
7,003 − 1,996 (teacher-traced) — round-and-adjust: take 2,000, then come forward 4.
2,560 + 3,470 (teacher-traced) — partition into 3,000, then 400, then 70.

Watch for the take-away slip where pupils subtract the adjustment instead of coming forward.

+15 XP

4 - Note Your Strategy in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, write each of these calculations and beside it note the mental strategy you used: compensation, partition, or round-and-adjust. Then circle your answer.

4,997 + 386
8,012 − 1,995
3,450 + 2,780

Teacher Notes

The three strategy names are still on the board from Watch and Notice — leave them visible so pupils can match a calculation to a name. Walk the room, glancing at whether the named strategy matches the working — no individual marking, this is whole-class copybook practice, not assessment.

+10 XP

5 - Class Challenge ~8 mins

First we solve one full calculation together and name the strategy: 6,998 + 457. We plan the jumps, draw them, and check we land on the right total. Then we work through these on the line, one at a time: reach 10,000 from each starting number using only the jump sizes shown, in as few jumps as you can. Plan your route first, which tidy number do we bridge to before we land on 10,000? After each one, name the strategy your jumps show (partition, compensation or round-and-adjust).

Reach 10,000

Teacher Notes

Worked example first (board talk-through, not on the interactive): 6,998 + 457, compensation. Jump 2 to reach 7,000, then add the remaining 455. Lands on 7,455. Say the strategy name before the first jump.

These are the practice questions, 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.

Push pupils to plan the route before they touch the line: which tidy number do we bridge to first? After each check, ask which strategy the jumps match.

Watch for pupils who fire off allowed jumps with no plan, or who cannot name the strategy their route used.

+15 XP

6 - What Did We Notice? ~2 mins

MATHS TALK

One pupil says a mental strategy is always quicker than the column method. Another says it is riskier and the column method is safer. Who is right, and how would you settle it?

Teacher Notes

Listen for pupils naming when each is better — mental wins when a number is close to a tidy figure; columns win when nothing rounds neatly. Revoice a strong answer: so it is not about which is always faster, it is about choosing the strategy that fits the numbers.

+10 XP

7 - What's Next ~3 mins

Today we

added and subtracted in our heads using partition, compensation and round-and-adjust
drew our thinking as jumps on an empty number line
decided when a mental strategy beats the column method

Coming up

Next we keep the decimal points lined up and add and subtract decimals all the way to thousandths.

Teacher Notes

Close by reminding pupils that the empty number line is a tool for thinking, not just a place to write the answer.

+5 XP

Pupil practice

Module 2 · Operations and Computational Fluency Number

Lesson 13 · Mental Strategies for Addition and Subtraction

Download Activity Book page (PDF)

End of lesson

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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

Work it out on the line

4 - Note Your Strategy in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Reach 10,000

6 - What Did We Notice? ~2 mins

7 - What's Next ~3 mins

Today we

Unlock the full learning experience

XP