Number sentences & properties for Grade 3

1 · The equals sign means "the same as"

A number sentence uses numbers and signs to say something true. 4 + 3 = 7 says "4 plus 3 is the same as 7."

The equals sign is a balance, not a "the answer goes here" sign. Both sides must have the same value. So 7 = 4 + 3 is true too, and so is 4 + 3 = 5 + 2.

2 · Turn-around rule

You can add in any order: 6 + 9 = 9 + 6. You can multiply in any order: 3 × 8 = 8 × 3. Grown-ups call this the commutative property.

It does not work for subtracting or dividing: 9 − 6 is 3, but 6 − 9 is not 3. 12 ÷ 4 is 3, but 4 ÷ 12 is much less than 1.

3 · Grouping rule

When you add three numbers, you can choose which two to add first: (7 + 3) + 8 = 7 + (3 + 8). Both are 18. The same is true for multiplying: (2 × 5) × 4 = 2 × (5 × 4) = 40.

Use it to make friendly numbers. 6 + 9 + 4: add 6 + 4 = 10 first, then 10 + 9 = 19.

4 · Zero and one

Adding 0 changes nothing: 37 + 0 = 37. Multiplying by 1 changes nothing: 37 × 1 = 37.

Multiplying by 0 always gives 0: 37 × 0 = 0. Any number divided by 1 is itself: 37 ÷ 1 = 37.

Watch the trap: 37 + 0 and 37 × 0 look alike, but one is 37 and the other is 0.

5 · Break a fact apart

A hard fact can be split into two easy ones. 6 × 7 is the same as 6 × 5 plus 6 × 2: 30 + 12 = 42. Grown-ups call this the distributive property.

The array shows why: 6 rows of 7 squares is 6 rows of 5 next to 6 rows of 2.

6 · Balance both sides

Sometimes the box is in the middle: 8 + 5 = □ + 6. First find the side you can finish: 8 + 5 = 13. Then ask, 13 is the same as what plus 6? □ = 7.

A common mistake is to write 13 in the box. Check it: 13 + 6 is 19, not 13. Always check both sides.

7 · Letters can stand for numbers

A letter can hold the place of a missing number, just like a box. n + 7 = 15 means "what number plus 7 is 15?" n = 8.

A letter means the same number everywhere in one sentence. In n + n = 10, n is 5.

8 · Match the story

Some questions give a story and ask which number sentence fits. Decide what happens first and which operation each step uses.

"Ana had 20 stickers. She gave 6 to Ben and got 4 from Mia." She loses 6, then gains 4: 20 − 6 + 4. A sentence like 20 + 6 − 4 uses the right numbers in the wrong way.

9 · Compare with <, >, =

The symbols point to the smaller number: 5 < 9 and 9 > 5. You can compare whole expressions: 4 × 6 ○ 30 − 5. Work each side: 24 and 25. So 4 × 6 < 30 − 5.

Sometimes you can compare without working it out. 46 + 29 ○ 46 + 31: both start with 46, and 29 is less than 31, so the left side is less.

10 · Undo to check

Adding and subtracting undo each other. So do multiplying and dividing. If 56 ÷ 7 = 8, then 8 × 7 = 56. If 41 − 17 = 24, then 24 + 17 = 41.

Use the undo to find a missing number: □ × 4 = 36, so □ = 36 ÷ 4 = 9.

11 · True or false?

To test a number sentence, work out each side and compare. 3 × 4 = 2 × 6 is true: 12 and 12. 10 − 4 = 4 − 10 is false.

On the test, read the question word: "Which is true?" and "Which is NOT true?" need opposite answers.