What you will learn
- Add quickly by finding compatible numbers that make 10, 100 or 1 000.
- Multiply in your head using place value, factoring and tens then units.
- Choose the best strategy for a sum and explain it.
Mental maths means working things out in your head, without writing a column sum. Good mental mathematicians do not count faster. They know some clever tricks and pick the right one. Here are six strategies to try.

1. Compatible numbers
Compatible numbers are pairs that are easy to add, such as numbers that make 10, 100 or 1 000. Look for them first.
Worked example 1
36 + 58 + 64
Show me how
Spot 36 + 64 = 100.
100 + 58 = 158.
So 36 + 58 + 64 = 158.
Other pairs: 250 + 750 = 1 000, 45 + 55 = 100, 7 + 3 = 10.
2. Place value
Say the tens or hundreds as words. 4 × 20 is 4 × 2 tens = 8 tens = 80. 3 × 300 is 3 × 3 hundreds = 9 hundreds = 900. 120 ÷ 4 is 12 tens ÷ 4 = 3 tens = 30.
3. Tens then units
Split a number into tens and units (ones). Work with the tens first, then the units, then put them together.
Worked example 2
7 × 23
Show me how
7 × 20 = 140.
7 × 3 = 21.
140 + 21 = 161.
This works for adding too: 47 + 35 is 40 + 30 = 70, and 7 + 5 = 12, so 82.
4. Factoring and doubling
Break a number into factors and multiply in steps. 6 × 8 is 6 × 2 × 4: 12 × 4 = 48. To multiply by 4, double and double again: 4 × 35 is 70, then 140.
Worked example 3
5 × 18
Show me how
18 = 2 × 9.
5 × 2 = 10.
10 × 9 = 90.
5. Equal addends
Equal addends are numbers that are the same. 25 + 25 + 25 + 25 is 4 × 25 = 100. Doubles near doubles help too: 26 + 25 is 25 + 25 + 1 = 51.
Watch out! A common mistake
Do not try one strategy for everything. For 299 + 145, it is quicker to think 300 + 145 = 445, then take 1 away to get 444. Stop and look at the numbers first.
6. Facts to 10 × 10
All of these strategies need your times tables. Keep practising your facts to 10 × 10 in Lesson 11 so that they come quickly.
Try it
TRY ITMental maths trainer
Pick a strategy. Each question shows the quick way after you answer. Try Name the strategy when you are ready.
Let’s practise
Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.
1. Work out 27 + 45 + 73.
Hint
Which two make 100?
Show answer
27 + 73 = 100, so 145.
2. What is 6 × 30?
Hint
6 × 3 tens.
Show answer
18 tens = 180
3. What is 800 ÷ 4?
Hint
8 hundreds ÷ 4.
Show answer
2 hundreds = 200
4. Work out 6 × 14 using tens then units.
Hint
6 × 10 and 6 × 4.
Show answer
60 + 24 = 84
5. Work out 4 × 45 by doubling.
Hint
Double 45, then double again.
Show answer
90, then 180
6. What is 15 + 15 + 15 + 15?
Hint
4 equal addends.
Show answer
4 × 15 = 60
7. Work out 499 + 238.
Hint
Think of 500.
Show answer
500 + 238 = 738, take 1: 737
8. Which strategy would you use for 125 + 368 + 875? Why?
Hint
Look for a pair that makes 1 000.
Show answer
Compatible numbers: 125 + 875 = 1 000, so 1 368.
Quiz
Lesson quiz: 10 questions
Answer every question, then press Check my answers. Score 8 or more to earn the Mental Maths Master badge.
Mental maths strategies: worksheet
Name: ____________________ Date: ______________
Part A: Let’s practise
1. Work out 27 + 45 + 73.
2. What is 6 × 30?
3. What is 800 ÷ 4?
4. Work out 6 × 14 using tens then units.
5. Work out 4 × 45 by doubling.
6. What is 15 + 15 + 15 + 15?
7. Work out 499 + 238.
8. Which strategy would you use for 125 + 368 + 875? Why?
Part B: Quiz
1. What is 64 + 19 + 36?
2. 4 × 20 is the same as …
(a) 8 tens
(b) 8 ones
(c) 6 tens
(d) 80 tens
3. What is 5 × 300?
4. What is 8 × 12? Use tens then units.
5. Which is a good way to do 5 × 16?
(a) 5 × 2 × 8 = 10 × 8
(b) 5 + 16
(c) 16 − 5
(d) 5 × 1 + 6
6. 25 + 25 + 25 = 3 × 25.
True or False? Circle one: True / False
7. Which two numbers are compatible to make 1 000?
(a) 350 and 650
(b) 350 and 750
(c) 400 and 500
(d) 999 and 10
8. What is 4 × 25? Double, then double again.
9. Which strategy fits 199 + 56 best?
(a) Think 200 + 56, then take 1
(b) Count on in ones
(c) Factoring
(d) Equal addends
10. Mental maths means you must count on your fingers.
True or False? Circle one: True / False
Answers (for the adult)
Part A
1. 27 + 73 = 100, so 145.
2. 18 tens = 180
3. 2 hundreds = 200
4. 60 + 24 = 84
5. 90, then 180
6. 4 × 15 = 60
7. 500 + 238 = 738, take 1: 737
8. Compatible numbers: 125 + 875 = 1 000, so 1 368.
Part B
1. 119
2. (a) 8 tens
3. 1 500
4. 96
5. (a) 5 × 2 × 8 = 10 × 8
6. True
7. (a) 350 and 650
8. 100
9. (a) Think 200 + 56, then take 1
10. False
Recap
- Compatible numbers: look for pairs that make 10, 100 or 1 000.
- Place value: 4 × 20 = 8 tens = 80.
- Tens then units: 7 × 23 = 140 + 21.
- Factoring and doubling: 5 × 18 = 10 × 9.
- Equal addends: 25 + 25 + 25 + 25 = 4 × 25.
- Look at the numbers first, then choose a strategy.
Words to know
- mental maths
- Working out answers in your head.
Example: I did 50 × 3 by mental maths. - compatible numbers
- Numbers that are easy to put together.
Example: 70 and 30 are compatible numbers. - factor
- A number that multiplies to make another.
Example: 2 and 9 are factors of 18. - addend
- A number being added.
Example: In 5 + 4, the addends are 5 and 4. - strategy
- A plan or a clever way to solve a problem.
Example: My strategy was tens then units.
Try it at home
- At the market, add the prices of two or three items in your head before the vendor tells you the total.
- Mini project: make a poster of your three favourite mental maths strategies, with one example of each.
Test tips
Tips for class tests
- Look at the numbers before you start. Is there a pair that makes 100?
- Check a mental answer with a different strategy.
- Keep your times tables sharp. They make every strategy faster.
For parents and teachers
After this lesson, your child should be able to:
- use compatible numbers within 1 000;
- use place value, factoring, tens then units and equal addends to calculate mentally;
- recall facts to 10 × 10 and choose and explain a strategy.
These are the mental strategies named in the guide. Ask your child to say how they did a sum. There is often more than one good way, and explaining it builds number sense.
Quiz scores and badges are saved only in this browser on this device. Nothing is sent anywhere. If the browser data is cleared, or another device is used, the badges will be lost.
Previous: Multiplication and Division Word Problems – Standard 3 Maths
Next: Equivalent Fractions and Lowest Terms (coming soon)
Course: Standard 3 Maths
Updates
2026/11/04
– First version of this lesson.
Attributions to media used in this post:
Abacus actually in use at kimono shop in Otaru.jpg – Syced – CC0 1.0 (via Wikimedia Commons)
© 2026 Vedesh Kungebeharry. All rights reserved.


