Break Apart Multiplication with Arrays (3rd Grade)

What is it?

Big times facts like 7 × 6 are easier in pieces. An array shows the fact as rows and columns: 7 rows with 6 dots in each row. Your child splits the rows into two parts they already know, multiplies each part, then adds the two answers. Splitting off 5 rows is handy because fives are easy. Math books call this the break apart strategy or the distributive property.

Step by step: 7 × 6

1. 7 × 6 is 7 rows of 6.
2. Break the array into 5 rows and 2 rows.
3. 5 rows of 6 is 30.
4. 2 rows of 6 is 12.
5. Add the parts: 30 + 12 = 42. So 7 × 6 = 42.

Common mistakes

• Breaking the rows apart but then multiplying only one part (giving 30).
• Splitting both numbers at once, like 5 × 5 and 2 × 1. Split only the rows; each part keeps all 6 columns.
• Forgetting to add the two parts at the end.

Your turn

The lesson ends with a problem to try. Pause and let your child work it out before you check.

What is 8 × 6?

Answer: 48. Break 8 rows into 5 rows and 3 rows. 5 rows of 6 is 30, 3 rows of 6 is 18, and 30 + 18 = 48.

Practice at home

Draw dot arrays on graph paper or line up coins in rows. Cover part of the array with a sheet of paper to split it, find each part, and add. Start with facts where 5 rows is the easy part, like 6 × 4, 7 × 8 and 8 × 3.