2.3.3
When you solve a puzzle, is there always one answer? To a crossword puzzle with
words, this is typically true. There is only one way that the letters can be entered so
that everything will work and match the clues. But in a number puzzle there may be
more than one answer that fits the clues. As you work today, think about and discuss
with your team whether there is more than one way to solve a problem and how you
know this to be true
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
2-70. There are several ways to write the dimensions of the rectangle at right.
a. How many ways can you write the dimensions of the generic rectangle at
right? Draw a new rectangle for each way.
b. The factor on the short side of each of the rectangles you drew in part (a) had to
be a factor of both 120 and 18. When two products share the same factor, that
factor is called a common factor. What do you think is meant by the greatest
common factor of 120 and 18? What is the GCF for 120 and 18? If you need
to review the meaning of a factor, see the Math Notes box in Lesson 1.2.3.

2-71. In problem 2-70, the greatest common factor and its generic rectangle could be
used to write a multiplication sentence with parentheses:
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

120 + 18 = 6(20 + 3)
For each generic rectangle below, draw as many rectangles with different dimensions
as you can. Then use the greatest common factor for the numbers in each rectangle to
write a multiplication sentence with parentheses.
.
a.
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
2-72. Ethan thinks that 5(13) can be found by adding 50 + 15.
. Is Ethan correct? Draw a diagram to demonstrate Ethan's idea or show where
he went wrong.
a. Write a multiplication sentence with parentheses to represent Ethan’s generic
rectangle.

2-73. Use Ethan’s idea to draw a generic rectangle to find each product below. Then
write a multiplication sentence with parentheses for each one.
. 7(1 + 11)
a. 5(500 + 4)
b. 3 · 206
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2-74. LEARNING LOG

Discuss the idea of a greatest common factor with your team. Then write a definition
for greatest common factor in your Learning Log. Create your own example to help
explain your definition. Title this entry “Greatest Common Factor” and include
today’s date.

Greatest Common Factor

The greatest common factor of two or more integers is the greatest positive integer
that is a factor of both (or all) of the integers.
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For example, the factors of 18 are 1, 2, 3, 6, and 18 and the factors of 12 are 1, 2, 3, 4,
6, and 12, so the greatest common factor of 12 and 18 is 6.

2-75. Solve each generic-rectangle puzzle. For each part, write a multiplication
sentence, as you did in problem 2-72. Homework Help ✎
a.
b.

2-76. James is painting his 10-by-8-foot bedroom wall that contains a 2-by-3-foot
window. Homework Help ✎
. Draw a diagram of his wall and the window.
a. How many square feet of wall does he need to paint?

.
2-77. Figure out whether each of the following pairs of fractions is a pair of equivalent
fractions. Be sure to show all of your work or explain your thinking
clearly. Homework Help ✎
and
a.
and
b.
and

2-78. Misty and Yesenia have a group of Base Ten Blocks. Misty has six more blocks
than Yesenia. Yesenia’s blocks represent 17. Together they have 22 blocks, and the
total numbers of blocks represent 85. What blocks could each girl have? What is the
value? Homework Help ✎

2-79. COMPARING WAYS TO REPRESENT DATA.

Use the golf-tournament data below to complete parts (a) through (e). Homework
Help ✎
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
Ages of golfers participating in a golf tournament:
44, 48, 40, 25, 28, 37, 29, 34, 45, 51, 43, 35, 38, 57, 50, 35, 47, 30, 63, 43, 44, 60, 46,
43, 33, 45, 42, 34, 32
. Use the data to create a dot plot.
a. Why is a dot plot not the best choice for graphing this data?
b. Create a stem-and-leaf plot for the data.
c. Use the stem-and-leaf plot to create a histogram for the data.
d. What range of ages do most golfers fall between? Do you see any ages that are
much larger or smaller than other ages?