**Middle School Number Sense Lesson 92: Converting Distance Units with Area--2 Dimensions**

This concept is an extension of

**ConvDistance**, but with more complexity. These problems can involve either English units of measure (inches, feet, yards, etc.) or metric units. This concept has appeared

**3 times**so far this year, with a median placement at

**question # 33**.

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Like its easier counterpart, this concept has real-life application. We recently decided we wanted to replace the worn-out carpet in our home, so we measured each of the carpeted rooms to see how many square feet of carpet we needed to buy. When we got to the carpet store, we realized their carpet is priced by the square yard. Let’s look at our calculation.

One of our living areas measures 15 feet by 18 feet, which is

**270 square ft**. How many

*square*

*yards*of carpet do we need?

- Convert each distance from feet to yards by dividing by 3 (twice). 15 ÷ 3 =
**5**, and 18 ÷3 =**6**. - Multiply these distances to find the area in square yards. 5 x 6 =
**30**square yards.

Notice that we need to use our conversion factor (1/3) once for each dimension of distance. This understanding is key to having success with these number sense problems.

**Example 1: 24 inches x 72 inches = ___ square ft**

- Going from inches to feet requires dividing by 12 in both directions. 24 ÷ 12 =
**2**, and 72 ÷ 12 =**6**. - Now multiply to find the area. 2 x 6 =
**12**.

**Example 2: 3 square yards = ___ square feet**

- Going from yards to feet requires multiplying by 3 in both directions.
- 3 x 3 =
**9**; 9 x 3 =**27**.

**Example 3: 48 square inches = ___ square feet**

- Going from inches to feet requires dividing by 12 in both directions.
- 48 ÷ 12 =
**4**; 4 ÷ 12 =**1/3**.

**Example 4: 2.43 sq cm = ___ sq mm**

- There are 10 mm in each cm, so we’ll multiply by our conversion factor of 10,
*twice***.** - 2.43 x 10 x 10 =
**243**.

**Example 5: 5 sq ft = ___ sq in**

- Going from feet to inches requires multiplying by 12 in both directions.
- 5 x 12 =
**60**. 60 x 12 =**720**.

**Example 6: 1 square meter = ___ square cm**

- There are 100 centimeters in a meter, so multiply by 100 twice.
- 1 x 100 x 100 =
**10000**.

**Up Next for Middle School: PolygonSides**