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Let’s Practice!

Can you find the area using the distributive property?

Goal:

Goal:

multiplication monkey

You Can Do It!

Goal: Relate the area of a rectangle to multiplication and addition.

Remember, when you are solving an area problem, you can use the distributive property to multiply by the sum or the addends to get the same product.

An array of 5 columns and 7 rows of circles. \({7 \times 5}\) We can use the distributive property to make 5 \({(3 + 2)}\). Now we can mulitply using the distributive property \({(7 \times 3) + (7 \times 2) = 35}\) 35 is the answer, 35 is circled in red. There is a large yellow arrow pointing to how the distributive property is show in arrays. The first array is 3 collums and 7 rows. \({(7 \times 3)}\) plus an array of 2 columns and 7 rows \({(7 \times 2)}\) \({7 \times 3 = 21}\) and \({7 \times 2 = 14}\). Next we add \({21 + 14 = 35}\) The answer is 35. 35 is circled in red.

For each problem below, find the total area using the distributive property. Think of the addends that are used when we use the distributive property. Then, click on the sentence to check your work.

a grid of 5 columns and 2 rows. 3 columns of 2 rows is pink and 2 columns of 2 rows is orange.

\({2 \times (3 + 2) = (2 \times 3) + (2 \times 2) = 6 + 4 = 10}\) square units

a grid of 15 columns and 3 rows. 9 columns of 3 rows are blue and 6 columns of 3 rows is red.

\({3 \times (9 + 6) = (3 \times 9) + (3 \times 6) = 27 + 18 = 45}\) square units

A grid. The left side of the grid is labelled 6 for length and 8 for width. The right side is labelled 2 for width and is not lablled for width.

\({8 \times (6 + 2) = (8 \times 6) + (8 \times 2) = 48 + 16 = 64}\) square units

You know your multiplication facts of 1 through 10. Let’s use them to practice using the distributive property. Select the correct multiplication sentence for the area images.

Which multiplication sentences match the image?

A grid. The left side of the grid is labelled 5 for length and 3 for width. The right side is labelled 2 for width and is not labelled for width.

  1. \({5 \times 3 + 2 = 17}\) square units
  2. \({5 \times (3 + 2) = 25}\) square units
  3. \({5 \times 3 = 15 + 5 = 20 + 2 = 22}\) square units
  4. \({5 \times 2 = 10 + 5 = 15 \times 3 = 45}\) square units

Which multiplication sentences match the image?

A grid. The left side of the grid is labelled 4 for length and 4 for width. The right side is labelled 3 for width and is not lablled for width.

  1. \({(4 \times 4) + 3 = 19}\) square units
  2. \({4 + (3 \times 4) = 16}\) square units
  3. \({(4 \times 3) \times (4 \times 4) = 192}\) square units
  4. \({(4 \times 3) + (4 \times 4) = 28}\) square units

Which multiplication sentences match the image?

A grid. The left side of the grid is labelled 3 for length and 2 for width. The right side is labelled 1 for width and is not lablled for width.

  1. \({3 \times (2 + 1) = 9}\) square units
  2. \({3 \times 2 \times 1 = 6}\) square units
  3. \({2 \times (3 + 1) = 8}\) square units
  4. \({1 \times (3 + 2) = 5}\) square units

Summary

Questions answered correctly:

Questions answered incorrectly: