Multiplication and Arrays: Grade 3 Study Guide
Multiplication is a faster way of adding the same number again and again. Pictures of rows and columns make it easy to see why it works.
Multiplication tells us how many there are altogether when we have equal groups. If there are 4 plates with 3 cookies on each plate, we write 4 × 3 = 12. The first number is how many groups, the second is how many in each group, and the answer is called the product.
In Grade 3 you learn to picture multiplication in several ways: equal groups, repeated addition (3 + 3 + 3 + 3), jumps on a number line, and arrays. By the end of the year the goal is to know all the facts from 0 × 0 to 10 × 10 from memory, and to understand why they work so you can work out the ones you forget.
Arrays: rows and columns
An array arranges objects in equal rows and equal columns. The array below has 3 rows with 6 dots in each row, so 3 × 6 = 18. Count the dots row by row and you are really skip counting: 6, 12, 18.
Turn-around facts (the commutative property)
Turn the array on its side and you get 6 rows of 3. The number of dots does not change, so 3 × 6 = 6 × 3. This turn-around rule halves the number of facts you have to learn: if you know 7 × 4 you also know 4 × 7.
| Fact | Turn-around | Product |
|---|---|---|
| 2 × 9 | 9 × 2 | 18 |
| 3 × 7 | 7 × 3 | 21 |
| 4 × 8 | 8 × 4 | 32 |
| 5 × 6 | 6 × 5 | 30 |
Strategies for the harder facts
Use facts you already know to build new ones.
Know 2s? Then 4s are double the 2s (4 × 7 is double 2 × 7 = 14, so 28).
5s end in 0 or 5. 10s are the number with a zero on the end. 9s are 10s minus one group: 9 × 6 = 60 − 6 = 54.
6 × 7 = (5 × 7) + (1 × 7) = 35 + 7 = 42. This is called the distributive property.
Any number times 0 is 0. Any number times 1 stays the same.
Worked examples
Example 1. A tray holds 6 rows of muffins with 5 muffins in each row. How many muffins? Multiply rows by amount in each row: 6 × 5 = 30. You can check by skip counting: 5, 10, 15, 20, 25, 30.
Example 2. Find 7 × 8. If you do not remember it, use 5 × 8 = 40 and 2 × 8 = 16. Add: 40 + 16 = 56. This breaks the fact into two easier ones.
Example 3. Is 4 × 9 the same as 9 × 4? Yes. Draw 4 rows of 9 or 9 rows of 4 and the total is 36 each time.
Common mistakes
Many students add instead of multiply when they see 'altogether'. Look for equal groups: if every group has the same amount, multiply. Another mistake is mixing up the zero rules: 6 × 0 is 0 (no groups of anything), but 6 + 0 is 6. Finally, do not memorize facts without understanding them. If you know why 6 × 4 = 24 (6 groups of 4), you can rebuild it when memory fails.
Check your understanding: model answers
1. 8 × 4 = 32 seats (8 rows of 4). 2. 5 × 7 means 5 rows of 7, which is 35 dots. Turned on its side it is 7 rows of 5. The total, 35, stays the same because the same dots are only arranged differently. 3. 5 × 8 = 40. One more group of 8 gives 6 × 8 = 40 + 8 = 48.
✨ Key Takeaways
- Multiplication finds the total of equal groups: groups × amount in each group.
- An array uses equal rows and columns to show a multiplication fact.
- The order does not matter: 3 × 6 = 6 × 3.
- Use known facts (doubles, fives, tens) to work out harder facts.
💬 Questions for Discussion & Reflection
- A bus has 8 rows with 4 seats in each row. Write a multiplication sentence and find how many seats there are.
- Draw an array for 5 × 7. Then turn it to show 7 × 5. What stays the same?
- Use 5 × 8 to work out 6 × 8. Explain your steps.