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Beginner math lesson

Multiplication as repeated addition and arrays

Multiplication is a faster way to add equal groups. Before memorizing facts, it helps to see what the facts mean with groups, skip counting, and arrays.

Who this helps

This lesson is for grade-school learners beginning multiplication, parents and teachers introducing facts, and adults who want multiplication to feel less like memorized symbols and more like a model they can picture.

Step-by-step explanation

  1. Start with equal groups. Three bags with 4 apples each means 3 equal groups of 4.
  2. Write repeated addition. 4 + 4 + 4 shows the same amount.
  3. Write multiplication. 3 groups of 4 can be written as 3 x 4.
  4. Use skip counting. Count by 4s three times: 4, 8, 12.
  5. Use arrays for a picture. An array has rows and columns. 3 rows of 4 dots shows 3 x 4.
  6. Notice the turn-around fact. 3 x 4 and 4 x 3 both equal 12, even though the picture is turned.

Worked examples

Example 1: Equal groups

A teacher has 5 boxes. Each box has 6 pencils. How many pencils are there?

5 groups of 6
6 + 6 + 6 + 6 + 6 = 30
5 x 6 = 30

Answer: 30 pencils.

Example 2: Array model

Find 4 x 3 by drawing 4 rows of 3.

* * *
* * *
* * *
* * *

4 rows x 3 in each row = 12

Answer: 4 x 3 = 12.

Example 3: Skip counting

Find 7 x 5.

Count by 5s seven times:
5, 10, 15, 20, 25, 30, 35

Answer: 7 x 5 = 35.

Common mistakes

  • Using multiplication for unequal groups. 3, 4, and 6 cannot be written as 3 x 4 because the groups are not equal.
  • Confusing groups and items in each group. In 5 x 6, think 5 groups of 6 or 5 rows of 6.
  • Counting the starting number as a step. For 4 x 3, count 3, 6, 9, 12. That is four counts, not five.
  • Forgetting the turn-around fact. If you know 6 x 4 = 24, then 4 x 6 = 24 too.
  • Memorizing without meaning. Facts are easier to remember when you can rebuild them with groups or arrays.

Practice questions

  1. Write 3 + 3 + 3 + 3 as a multiplication fact.
  2. Write 6 x 2 as repeated addition.
  3. Find 4 x 5.
  4. Find 8 x 3.
  5. A table has 2 rows of 7 chairs. How many chairs are there?
  6. Draw or imagine an array for 3 x 6. How many dots are in it?
  7. Use the turn-around fact: if 9 x 4 = 36, what is 4 x 9?
  8. Which expression matches 5 equal groups of 8: 5 + 8, 5 x 8, or 8 - 5?

Answer key

  1. 4 x 3 = 12
  2. 2 + 2 + 2 + 2 + 2 + 2
  3. 20
  4. 24
  5. 14 chairs
  6. 18 dots
  7. 36
  8. 5 x 8

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