Grade: 4, Topic(s): multiplication/division

## Purpose

To practice math facts by connecting fact families to arrays.

None

Draw an array of dots on the board, such as a 3-by-5 array. Ask students for the fact family that describes the array. For this example, the fact family would be 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5, and 15 ÷ 5 = 3. Draw other arrays, with small enough dimensions to keep this activity fast-paced, and continue asking students for the fact family that describes the array. As students become more comfortable, you might give a member of a fact family, such as 4 × 3 = 12, and ask students to describe a matching array and then give the other members of the fact family. In this example, an array with 4 rows and 3 columns or an array with 3 rows and 4 columns would be appropriate. The other members of the fact family are 3 × 4 = 12, 12 ÷ 3 = 4, and 12 ÷ 4 = 3.

Part 1 asks students to visualize arrays with smaller dimensions and name the fact family describing each array. Part 2 and the extension progresses to *either* naming the fact family from visualizing the array *or* describing the array from knowing a fact from the fact family.

Let’s picture some arrays and name the fact family that describes each one. For example, I’m thinking of an array that has 3 rows and 5 columns. What fact family describes this array?

(5 × 3 = 15, 3 × 5 =15, 15 ÷ 5 = 3 and 15 ÷ 3 = 5)

Examples:

- 2 rows and 4 columns (2 × 4 = 8, 4 × 2 = 8, 8 ÷ 4 = 2, 8 ÷ 2 = 4)
- 2 rows and 2 columns (2 × 2 = 4, 4 ÷ 2 = 2)
- 3 rows and 2 columns (3 × 2 = 6, 2 × 3 = 6, 6 ÷ 3 = 2, 6 ÷ 2 = 3)
- 3 rows and 3 columns (3 × 3 = 9, 9 ÷ 3 = 3)
- 3 rows and 4 columns (3 × 4 = 12, 4 × 3 = 12, 12 ÷ 4 = 3 and 12 ÷ 3 = 4)

*While children are enjoying their building of mastery, feel free to repeat. When children are eager for more, try Part 2.*

Let’s explore some bigger arrays and their fact families. This time, you will be given an array to picture or a member of a fact family. If given an array to picture, you will name the members of its fact family. If given a fact, you will describe the array associated with this fact and name the other members of the fact family. Here we go!

Examples:

- 6 rows and 5 columns (6 × 5 = 30, 5 × 6 = 30, 30 ÷ 5 = 6, 30 ÷ 6 = 5)
- 6 rows and 3 columns (6 × 3 = 18, 3 × 6 = 18, 18 ÷ 3 = 6, 18 ÷ 6 = 3)
- 6 x 6 = 36 (describe array with 6 rows and 6 columns, 36 ÷ 6 = 6)
- 7 rows and 6 columns (7 × 6 = 42, 6 × 7 = 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6)
- 7 x 4 = 28 (describe array with 7 rows and 4 columns, 4 × 7 = 28, 28 ÷ 4 = 7, 28 ÷ 7 = 4)
- 7 rows and 7 columns (7 × 7 = 49, 49 ÷ 7 = 7)

*As always, when children seem excited for a new challenge, move on.*

Now we’ll picture some even bigger arrays and their fact families.

Examples:

- 10 rows and 8 columns (10 × 8 = 80, 8 × 10 = 80, 80 ÷ 8 = 10, 80 ÷ 10 = 8)
- 11 × 10 (describe array with 11 rows and 10 columns, 10 × 11 = 110, 110 ÷ 10 = 11, 110 ÷ 11 = 10)
- 11 rows and 11 columns (11 × 11 = 121, 121 ÷ 11 = 11)
- 12 × 10 (describe array with 12 rows and 10 columns, 10 × 12 = 120, 120 ÷ 10 = 12, 120 ÷ 12 = 10)
- 12 rows and 12 columns (12 × 12 = 144, 144 ÷ 12 = 12)

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