Mental Strategies for Addition and Subtraction

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 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

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

Illustration for Watch and Notice

Compensation: 4,997 + 386 (bridge up to a tidy number)

Compensation means we jump up to a tidy number first, because tidy numbers are easy to work with. Watch this one: 4,997 is just 3 away from the tidy number 5,000, so we add 3 to reach 5,000, then we add the 383 that is left. That lands us exactly on the answer.

Round-and-adjust: 8,012 − 1,995 (round the taker, then fix it)

Round-and-adjust means we round one number to a tidy figure to make the sum simple, then fix the answer at the end. Here we take away a tidy 2,000 first because it is easier. But we took 5 too many, so we come forward 5 to land right. Watch the line come back the other way.

Partition: 3,450 + 2,780 (break it into place-value parts)

Partition means we split a number into its place-value parts. This time we add the 2,000, then the 700, then the 80, one jump at a time, building up to the answer.

Teacher Notes

Walk each example aloud, one at a time, tracing the arcs on the board, and say the strategy name as you point to its header.

Compensation, 4,997 + 386 — point to how close 4,997 is to a tidy 5,000; the small jump of 3 is the clever first move, then 383 is added on. No overshoot here — we land exactly on 5,383.
Round-and-adjust, 8,012 − 1,995 — stress we come forward 5 because we took 5 too many. This is where pupils slip. Trace the −2,000 jump leftward, then the +5 clearly rightward (forward).
Partition, 3,450 + 2,780 — show that partitioning never changes the total; the parts just rebuild the same answer.

👇 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

Today we work through these on the line, one at a time: reach 10,000 from each starting number using the fewest jumps you can. Plan your route first — which tidy number do we bridge to before we land on 10,000?

Reach 10,000

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.

Push pupils to plan the route before they touch the line: which tidy number do we bridge to first?

+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

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 ~9 mins

Compensation: 4,997 + 386 (bridge up to a tidy number)

Round-and-adjust: 8,012 − 1,995 (round the taker, then fix it)

Partition: 3,450 + 2,780 (break it into place-value parts)

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

Coming up

Unlock the full learning experience

XP