Mental Math Strategies

For Elementary Students

What is Mental Math?

Mental math means solving math problems in your head without writing anything down or using a calculator.

Think about it like this: Your brain is powerful! With some smart tricks, you can solve problems faster than reaching for paper.

Strategy 1: Making Ten

Find ways to make 10 first, because 10 is easy to work with.

Example: 8 + 7 = ?

Think: 8 needs 2 to make 10. Break 7 into 2 + 5. So: 8 + 2 = 10, then 10 + 5 = 15.

Answer: 15

Another example: 6 + 9 = ?

Think: 9 needs 1 to make 10. Break 6 into 5 + 1. So: 9 + 1 = 10, then 10 + 5 = 15.

Answer: 15

Strategy 2: Doubling

If you know your doubles (1+1, 2+2, 3+3...), you can use them to solve nearby problems.

Example: 6 + 7 = ?

Think: 6 + 6 = 12 (double 6). Then add 1 more: 12 + 1 = 13.

Answer: 13

Example: 8 + 9 = ?

Think: 8 + 8 = 16 (double 8). Then add 1 more: 16 + 1 = 17.

Answer: 17

Strategy 3: Adding from Left to Right

Instead of lining up numbers, add the big parts first.

Example: 34 + 52 = ?

Think: First add tens: 30 + 50 = 80 Then add ones: 4 + 2 = 6 Combine: 80 + 6 = 86

Answer: 86

This is the opposite of how we write it on paper, but it's faster in your head!

Strategy 4: Using Friendly Numbers

Friendly numbers are easy numbers like 10, 20, 50, 100.

Example: 29 + 17 = ?

Think: 29 is close to 30 (a friendly number). Add: 30 + 17 = 47 Adjust: We added 1 extra, so subtract 1: 47 - 1 = 46

Answer: 46

Example: 48 + 25 = ?

Think: 48 is close to 50. Add: 50 + 25 = 75 Adjust: We added 2 extra, so subtract 2: 75 - 2 = 73

Answer: 73

For Junior High Students

Strategy 5: Compensation

Compensation means adjusting one number to make it easier, then fixing your answer.

Example: 67 + 38 = ?

Step 1: Round 38 up to 40 (easier to add) 67 + 40 = 107

Step 2: Compensate by subtracting 2 (because we added 2 extra) 107 - 2 = 105

Answer: 105

Example: 85 - 29 = ?

Step 1: Round 29 up to 30 85 - 30 = 55

Step 2: Compensate by adding 1 (because we subtracted 1 too much) 55 + 1 = 56

Answer: 56

Strategy 6: Breaking Apart Numbers

Split numbers into tens and ones (or hundreds, tens, ones for bigger numbers).

Example: 56 + 37 = ?

Break it apart: 56 = 50 + 6 37 = 30 + 7

Add tens: 50 + 30 = 80 Add ones: 6 + 7 = 13 Combine: 80 + 13 = 93

Answer: 93

Strategy 7: Multiplying by 5

Trick: Multiply by 10, then divide by 2.

Example: 14 × 5 = ?

Think: 14 × 10 = 140 140 ÷ 2 = 70

Answer: 70

Why it works: 5 is half of 10, so multiplying by 5 is the same as multiplying by 10 and halving.

Strategy 8: Multiplying by 9

Trick: Multiply by 10, then subtract the number once.

Example: 7 × 9 = ?

Think: 7 × 10 = 70 70 - 7 = 63

Answer: 63

Example: 15 × 9 = ?

Think: 15 × 10 = 150 150 - 15 = 135

Answer: 135

Strategy 9: Adding by Jumping on a Number Line (Mentally)

Imagine a number line in your head and "jump" forward or backward.

Example: 43 + 28 = ?

Start at 43:

• Jump to 50 (add 7): 43 + 7 = 50
• Jump 20 more: 50 + 20 = 70
• Jump 1 more (to complete the 28): 70 + 1 = 71

Answer: 71

Strategy 10: Dividing by 5

Trick: Multiply by 2, then divide by 10.

Example: 75 ÷ 5 = ?

Think: 75 × 2 = 150 150 ÷ 10 = 15

Answer: 15

Why it works: Dividing by 5 is the same as dividing by 10 then doubling, or doubling then dividing by 10.

Practice Makes Perfect

The more you use these strategies, the faster you'll get!

Start small: Use them on easy problems first. Build up: Try them on harder problems as you get comfortable. Mix and match: Sometimes you'll use two or three strategies on the same problem!

Practice