Adding and Subtracting in Your Head

Adding in Any Order #

Pick the order that makes a ten first.

Addition comes out the same in any order, so you may pick the friendly order

Start at 2 and add 9: 2 + 9 = 11.

Start at 9 and add 2: 9 + 2 = 11. This is the commutative property of addition.

So in 7 + 38 + 3, add the 7 and 3 first: 7 + 3 = 10, and 38 + 10 = 48.

Adding by Splitting #

Tens with tens, ones with ones, then together.

Split each number into tens and ones, add the parts, and put the total back together

34 is 3 tens and 4 ones. 25 is 2 tens and 5 ones.

Add the ones together. Also add the tens together. The answer is 59.

Bridging Through Ten #

Two easy hops, resting at the ten between.

Break a hard jump into two easy ones, resting at the ten in between

Add 47 + 8 quickly by splitting 8 = 3 + 5. Then 47 + 3 = 50.

Add the remaining 5 to get 55.

Doubles and Near Doubles #

Know the double and its neighbors come free.

Doubles are facts you own, and one more or one less sits right beside them

Two equal rows of 6. A double — and doubles stick in the mind.

6 + 7 is the double and one more: 12 + 1 = 13.

Bigger numbers too. 36 + 37 is double 36, then one more: 73.

Rounding and Adjusting #

Add the round number, then give back the change.

Add the round number nearby, then put right the little you changed

To add 45 + 29, notice 29 is 30 − 1. Add 45 + 30 to get 75, then hand the 1 back.

Add the 30, then give the extra one back: 74.

Subtraction works the same way. 62 − 19: take away 20, then hand one back: 43.

Counting Up to Subtract #

Measure the gap upwards, the shopkeeper’s way.

A subtraction is a gap between two numbers, and you can measure it by counting up

63 − 58 asks how far apart these two are. Count up from the small one.

2 to reach 60, then 3 more to reach 63. The gap is 5.

The Same Difference #

Slide both numbers and the gap stays put.

Slide both numbers by the same amount and the gap between them does not move

83 − 29 is the difference — the gap between these two marks.

Slide both up by 1, giving you 84 − 30. Both marks move but the gap between them does not.

84 − 30 = 54. The gap never moved, so 83 − 29 = 54 too.

Adding and Subtracting Tens and Hundreds #

One digit moves; the others stand still.

Adding tens or hundreds moves one digit and leaves the rest alone

Adding 20 touches only the tens: 345 + 20 = 365, the other digits stand still.

Adding hundreds is the same one-digit move: 345 + 200 = 545.

Subtracting moves the digit the same way: 345 − 200 = 145.