1 · Equal groups
Here are 3 bags with 4 apples in each bag. To count them all you could add: 4 + 4 + 4 = 12.
Multiplication is a faster way to say the same thing: 3 groups of 4 = 3 × 4 = 12. The × sign means "groups of."
2 · Arrays: rows and columns
Line the dots up in rows and you get an array. This one has 3 rows with 4 dots in each row: 3 × 4 = 12.
Turn it on its side and it has 4 rows of 3. Same dots, same answer: 4 × 3 = 12. You can multiply in either order.
3 · Skip counting on a number line
Multiplying is also skip counting. 4 × 3 means 4 jumps of 3: land on 3, 6, 9, 12.
Skip counting by 2s, 5s, and 10s is the fastest way to learn those tables.
4 · Tricks for the times tables
× 2 is doubling. × 5 always ends in 0 or 5. × 10 puts a 0 on the end. × 1 keeps the number, and × 0 is always 0.
A times table shows every fact at once. Slide across row 3 and down column 4 to find 3 × 4 = 12.
5 · Division: sharing equally
Division is the opposite of multiplication. 12 cookies shared equally by 3 kids: each kid gets 12 ÷ 3 = 4.
The ÷ sign means "split into equal parts."
6 · Division: making groups
Division also answers "how many groups?" 12 cookies, 4 in each bag: 12 ÷ 4 = 3 bags.
Same drawing, different question. Sharing asks "how many in each?" Grouping asks "how many groups?"
7 · Fact families
The numbers 3, 4, and 12 make a fact family: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, 12 ÷ 4 = 3.
Know one fact and you know all four. The big number always sits on top of the triangle.
8 · Missing numbers
5 × □ = 30. Ask "5 times what is 30?" or use the family: 30 ÷ 5 = 6.
□ ÷ 4 = 7. The missing number is the big one, so multiply: 7 × 4 = 28.
9 · Bigger numbers: break them apart
3 × 20: think 3 × 2 tens = 6 tens = 60.
4 × 12: split 12 into 10 and 2. 4 × 10 = 40 and 4 × 2 = 8, so 40 + 8 = 48. The dotted line shows the split.
10 · Leftovers: remainders
Sometimes the groups do not come out even. 13 cookies in bags of 4: 3 full bags and 1 left over.
We write 13 ÷ 4 = 3 R1. The R means remainder.
11 · Which operation?
Read for the clues. "Each box has 6, there are 5 boxes, how many in all?" You know the groups and the size: multiply, 5 × 6 = 30.
"28 stickers shared by 4 friends, how many each?" You know the total: divide, 28 ÷ 4 = 7.
12 · Two steps and checking
Some problems take two steps. "3 packs of 8 pencils, then 5 are given away." First 3 × 8 = 24, then 24 − 5 = 19.
Check a division by multiplying back: 42 ÷ 6 = 7 because 7 × 6 = 42. You are ready for the test! 🎉
Ready to check what stuck?
Take the free 24-question test. It starts easy and builds to harder, ISEE-style reasoning. It's auto-scored, and you can review every answer afterward.