MULTIPLICATION 6.NS.1
Missing Dimensions of Rectangles with Fractional Lengths
Purpose:
To compute the missing dimension of a rectangle given its area and one dimension.
Materials:
Copies of activity sheet " Grid Paper" (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Finding the area of a rectangle given its dimensions
1. Distribute a sheet of grid paper to each student and pose the following problem.
Grid Paper
 If a logging company purchases a rectangular piece of woodland having
dimensions of 2/3 mile by 1/2 mile, what is the area of the land in square miles?
a. Using one of the unit squares on the grid sheet, divide the left
edge into 3 equal parts, label the length of two of the parts as 2/3,
and extend lines to divide the square into 3 equal parts. Then
divide the top length into 2 equal parts, label the length of 1 part
as ½, and extend one line vertically to divide the square in half.
b. If the area of the unit square is one square mile, what is the area
of one of the small rectangles? (1/6 square mile.)
c. What is the area of the 2/3 mile by 1/2 mile rectangular piece of woodland? (2/6 or 1/3
square mile.) Discuss two methods of finding this area: (1) Using the grid sketch or (2)
multiplying the two dimensions.
d. What is the profit from logging this land, if the profit from logging one square mile is
$18,000,000? ($6,000,000)
2. A restaurant counter-top has dimensions of 2½ yards by 3¼ yards. Use your grid paper
to outline the rectangular region and label its sides.
a. What is the area of the
counter in square yards?
(8 1/8 square yards)
b. Can this area be found by
multiplying the lengths of
the two sides? (Yes)
Compute their product. (2½
× 3¼ = 5/2 × 13/4 = 65/8
= 8 1/8 sq. yards)
d. If each square yard of
granite countertop costs $48,
what is the cost of the granite
for the countertop? ($390)
Activity 2 Finding the missing dimension of a rectangle when the
area and one dimension are given
1. Determine the missing factor in each product.
a. 8 × K = 32
b. 6 × M = 27
c.
3
× N = 27
4
d.
2
2
×R=
3
5
(K = 4; M = 4 ½; N = 36; and R = 3/5)
e. State a general rule for finding the missing factor in a product of two numbers when the
product and one of the numbers is known. (The missing factor equals the product divided by
the given number.) Discuss the close relationship between multiplication and division.
2. For each of the following rectangles, the area is given and one of the dimensions. What is
the missing dimension? Point out that these rectangles are not to scale.
a.
b.
1½
1/3
c.
area12
12sq.
sq. units
units
1
5
3
4
sq. unit
1 1 sq unit
8
(Missing dimensions: a. 8 units; b. 3/5 unit; and c. 3/2 or 1½ units)
Grid Paper
Activity 3 Solving word problems involving areas of rectangles
1. An airport is being constructed on a rectangular strip of land with length 2/3 mile and area
1/2 square mile.
a. Use one of the squares on your grid paper to outline a rectangular region representing
1/2 square mile and label one of the sides with the dimension 2/3 mile.
1
2
b. What is the missing dimension of the strip of land? ( ÷
2
1
3
3
= × = mile.)
3
2
2
4
2. A rectangular section of lawn with an area of 21 square yards and one dimension of
3½ yards is being planted with grass.
a. What is the missing dimension of the lawn? (21 ÷ 3½ = 21 ÷
7
2
42
= 21 × =
= 6 yards)
2
7
7
b. If a fence is to be built along one of the longer sides of the lawn, and each yard of fence
costs $18, what is the total cost of the fence? (6 × 18 = $108)
3. At a certain print shop that does oversize printing, it costs $23 for each square yard of
copying. At this rate, what is the expense of copying a map that has length 2/3 yard and
width 9/10 yard? ($13 4/5 or $13.80)
INDEPENDENT PRACTICE and ASSESSMENT
Worksheet 6.NS.1 #7