Lesson 8: Area of a Rectangle without a Grid

Area of a Rectangle without a Grid

The purpose of this How Many Do You See? is for students to subitize or use grouping strategies to describe the images they see.

When students use equal groups and a known quantity to find an unknown quantity, they are looking for and making use of structure (MP7).

Teacher Instructions

How many do you see? How do you see them?

Sample responses:

20: I counted by 5 four times. I know that 4 times 5 is 20.
24: It was like the first problem, but there was 1 dot more in each group. So I added 20 to 4 to get 24.
16: It was like the first problem, but each group was missing 1 dot so I subtracted 4 from 20 to get 16.

“What numbers were easy to see in the images?” (4, 5, 6)
“How did the first image help you find the number of dots in the next 2 images?” (I know each group in the second image has 1 dot more than each group in the first image, so I figured out 4 groups of 5, then added 4 dots more. For the last image, I subtracted 4 from 20, since 1 dot was missing from each group.)

Standards

Addressing

3.OA.5·Apply properties of operations as strategies to multiply and divide.
3.OA.B.5·Apply properties of operations as strategies to multiply and divide.Students need not use formal terms for these properties. Examples: If \(6 \times 4 = 24\) is known, then \(4 \times 6 = 24\) is also known. (Commutative property of multiplication.) \(3 \times 5 \times 2\) can be found by \(3 \times 5 = 15\), then \(15 \times 2 = 30\), or by \(5 \times 2 = 10\), then \(3 \times 10 = 30\). (Associative property of multiplication.) Knowing that \(8 \times 5 = 40\) and \(8 \times 2 = 16\), one can find \(8 \times 7\) as \(8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56\). (Distributive property.)