Skill: multiplication
Multiplication Facts & Arrays
Master facts to 12 × 12 with arrays, skip-counting, and turn-around facts.
1 Multiplication is equal groups
3 × 4 means three groups of four. The numbers being multiplied are factors; the result is the product.
3 × 4 = 12: three groups of four make twelve. The × sign means “groups of”.
3 bags with 4 apples each: 3 × 4 = 12 apples.
2 Arrays: rows times columns
An array arranges dots in neat rows and columns. Count one row, count the rows, multiply.
4 rows of 6 dots: 4 × 6 = 24 dots.
3 Turn-around facts: order does not matter
The commutative property says 7 × 8 = 8 × 7. Learn one fact, get its turn-around free — half the memorizing!
7 × 8 = 56, so 8 × 7 = 56 as well.
4 Special facts: ×0, ×1, ×10
Times 0 is always 0 (zero groups of anything). Times 1 keeps the number. Times 10 just adds a zero.
12 × 0 = 0 — twelve groups of nothing.
9 × 10 = 90.
5 Break apart big facts
The distributive property splits a hard fact into easy ones: 7 × 8 = 7 × 5 + 7 × 3 = 35 + 21.
7 × 8 = 7 × 5 + 7 × 3 = 35 + 21 = 56.
6 Common mistakes
Two multiplication traps.
Wrong: 3 × 4 = 7.
Right: × means equal groups: three groups of four. Draw it: 4 + 4 + 4 = 12.
Wrong: drilling both separately.
Right: the commutative property: the order never changes the product. One fact covers both.
7 Quick checks
Try these yourself, then reveal the answer.
8 Key points and vocabulary
| Word | What it means |
|---|---|
| Factor | A number being multiplied. |
| Product | The result of multiplying. |
| Array | Dots arranged in equal rows and columns. |
| Equal groups | Groups with the same number in each. |
| Commutative | Order does not change the product: a × b = b × a. |
| Distributive | Breaking a fact apart: a × (b + c) = a × b + a × c. |
Remember
- × means equal groups — draw them when stuck.
- Arrays show rows × columns.
- Turn-around facts halve the memorizing.
- Break apart hard facts with the distributive property.
- ×0 = 0, ×1 keeps the number, ×10 adds a zero.