Mental Math Strategies for Addition & Subtraction — 25 Practice Questions with Theory & Hidden Answers (Grades 2–4)

Two ways to solve 98 + 47

Column method (slow): Line them up, add 8 + 7 = 15, write 5 carry 1, add 9 + 4 + 1 = 14, write 14. Answer: 145. Requires paper, alignment, and remembering to carry.

Mental math (fast): 98 is 2 away from 100. So 98 + 47 = 100 + 47 − 2 = 147 − 2 = 145. Done in your head in 3 seconds.

Both give 145. But the mental math version is faster, more accurate on quizzes, and — most importantly — it teaches the student to see that numbers are flexible, not stuck in columns. That flexibility is what algebra will demand later.

The rule at SOMATH: if a problem can be solved mentally in under 10 seconds, it should be. Reach for pencil and paper only when the numbers are too messy for the head.

Turn any single-digit addition into “10 plus something”

Ten is the friendliest number in the base-10 system. Every mental math strategy leans on it. To use making 10, borrow from one addend to make the other equal to 10, then add what’s left.

Example: 8 + 6

8 needs 2 more to be 10. Take 2 from the 6, giving 8 the 2 it needs:

Ten-frame picture:

Slide 2 of the 6 over to fill up the 8’s frame. Now you have a full 10 and 4 leftover → 14.

When to use it: any time you’re adding two single digits and one is 7, 8, or 9.

Change one number to make it round; fix it at the end

Numbers ending in 8 or 9 are ugly to add. Numbers ending in 0 are beautiful. Compensation means: turn the ugly number into a nearby round number, do the easy addition, then adjust.

Example 1: 39 + 25

Example 2: 98 + 47 (from the intro)

The two-word rule: whatever you add to make it round, you must subtract at the end. Whatever you subtract, you must add at the end.

When to use it: when one number ends in 8 or 9 (or 98, 99, etc.).

If you know the doubles, you know almost everything

Doubles (1+1, 2+2, 3+3, …, 9+9) are the easiest facts to memorize. Most students know them cold by end of 1st grade. Near-doubles means: if the two numbers are 1 apart, use the double you already know and add or subtract 1.

Example 1: 7 + 8

Example 2: 6 + 7

Doubles-plus-2: same idea when the numbers are 2 apart. 6 + 8 = 6 + 6 + 2 = 14.

When to use it: when the two numbers are 1 or 2 apart.

Add the tens; then add the ones

For two-digit and larger numbers, break each number into tens and ones, add the tens, add the ones, and put them back together. This is the grade 3–4 backbone strategy.

Example: 34 + 52

What if the ones make more than 10? Break the extra ten out and hand it to the tens column. 37 + 28: tens 30+20=50, ones 7+8=15, total 50+15=65.

Subtraction version: 76 − 23: tens 70−20=50, ones 6−3=3, total 53. (Only clean when the top ones are bigger than the bottom ones; otherwise use equal-add or add-up, below.)

When to use it: two-digit or three-digit numbers with no nasty carrying.

For adding or subtracting 1, 2, or 3

The smallest strategy and the first one every student learns. If you’re adding 1, 2, or 3, just count on from the bigger number. If you’re subtracting 1, 2, or 3, count back.

Rule 1 — always start with the bigger number: 2 + 47 is the same as 47 + 2. Start at 47 and count on: 48, 49. Answer: 49. Don’t start at 2 and try to count on 47 times.

Rule 2 — keep it to 3 or fewer counts. If you’re adding or subtracting 4 or more, switch to a different strategy. Counting 5, 6, 7 in your head is where errors sneak in.

Example: 86 − 3 = ? Start at 86, count back three: 85, 84, 83. Answer: 83.

When to use it: +1, +2, +3, −1, −2, −3. Nothing else.

Shift both numbers to make the smaller one round

Here’s a subtraction trick almost no adult remembers, and it’s magical. The distance between two numbers doesn’t change if you slide both of them by the same amount. So make the number you’re subtracting into a nice round number, and shift the other one to match.

Example 1: 83 − 29 is hard. But 84 − 30 is easy.

Example 2: 63 − 38

Why does it work? If two people are 30 feet apart and both walk forward 5 feet, they are still 30 feet apart. Subtraction is a distance; sliding both numbers by the same amount doesn’t change the distance.

When to use it: when the number being subtracted ends in 7, 8, or 9. Round it up to the next 10 and shift the top by the same amount.

Round to the nearest 10 or 100, then fix

This is the older sibling of compensation. Round a hard number to the nearest 10 (or 100), do the easy problem, then adjust by the same amount you rounded.

Addition example: 237 + 199

Subtraction example: 452 − 198

The rule of thumb: Rounded UP for addition → adjust DOWN. Rounded DOWN for addition → adjust UP. For subtraction, it’s the opposite: rounded UP the subtracted number → adjust UP; rounded DOWN → adjust DOWN.

Kid-friendly test: after you finish, ask “Is my answer bigger or smaller than it should be?” and fix in that direction.

Turn subtraction into addition

Subtraction is just the distance between two numbers. Instead of “take away,” ask “how far is it from the smaller number to the bigger one?” Then hop up in easy chunks.

Example 1: 62 − 47

Example 2: 205 − 168

Why it’s great: no borrowing, no negatives, no aligning columns. This is the strategy every cashier used before calculators and it’s still the fastest for making change.

When to use it: subtracting two 2- or 3-digit numbers that are not far apart.

A cheat sheet for picking the right tool

The 5-second rule: if you can’t pick a strategy in 5 seconds, just use place-value split. It always works for two-digit and three-digit problems.