MACC.4.MD.3

Attend to Precision

MACC.4.MD.3

Example: A plan for a house includes a rectangular dining room with an area of 60 square meters and a perimeter of 32 meters. What is the length and the width of the dining room if the width is longer than the length?

What is being asked?

A plan for a house includes a rectangular dining room with an area of 60 square meters and a perimeter of 32 meters. What is the length and the width of the dining room if the width is longer than the length?

First we look to see what is being asked of us.

What is the length and the width of the dining room?

Solving the problem…

This problem seems easy at first but it is rather complex. The student needs to understand the difference between perimeter and area. They should begin by listing the factors of 60 knowing that they will have to multiply 2 sides of the rectangle together to get the area.

Step 1:

Find the factors of 60:

60:

1 x 60

2 x 30

3 x 20

4 x 15

5 x 12

6 x 10

Students can make a list or chart of the factors and check to see if each set works.

Guess and Check ✔Next the student may use the guess and check method.

Draw a rectangle and label each side with the factors

60m

1m   1m

60m

The factors 1 and 60 do not work because when you add the sides of the rectangle together to find the perimeter, you get 122. We are looking to find a perimeter of 32m. We move to the next set of factors.

Gu

ess &

Check

We try the next set of factors: 2, 30

30m

2m 2m

30m

The factors 2 and 30 do not work. When you add the sides of the rectangle together to find the perimeter, you get 64. Again, we are looking for 32m. We move to the next set of factors.

Check the next factors…The factors 3 and 20 do not work. When you add the 4 sides of the rectangle together to find the perimeter, you get 46. Again, we are looking for a perimeter of 32m so this is incorrect. We continue trying the other factors.

20m

3m 3m

20m

The factors 4 and 15 do not work. When you add the 4 sides of the rectangle together to find the perimeter, you get 38. Again, we are looking for a perimeter of 32m so this is incorrect.

15m

4m 4m

15m

More factors

The factors 5 and 12 do not work. When you add the 4 sides of the rectangle together to find the perimeter, you get 34. Again, we are looking for a perimeter of 32m so this is incorrect.

12m

5m 5m

12m

It works!! The final factors 6 and 10 do work. When you add the 4 sides of the rectangle together to find the perimeter, you get 32. Again we are looking for a perimeter of 32m so this is correct. They student should be able to identify that these 2 factors work!

10m

6m 6m

10m

Step 1:

Find the factors of 60:

60: Perimeter:

1 x 60 122m

2 x 30 64m

3 x 20 46m

4 x 15 38m

5 x 12 34m

6 x 10 32m

Students can make a list or chart of the factors and check to see if each set works.

Finding the solutionTo answer the original question, “ What is the length and the width of the dining room?”

Don’t forget…

The word problem states that the width is longer than the length, which indicates that the bigger number will represent the width.  

The width of the room is

10m.The length of the room is 6m.

The Answer:

Attend to Precision

This ties in with attending to precision because it forces the student to be precise. The students must understand the specific formulas to find the perimeter and area of a shape and be able to apply it. In this specific example, they have to know the exact factors of 60 and be able to list them out. They also have to be precise when calculating their measurements to find the length and width of the given shape.