Foundations to Algebra
In Class: Proportional Relationships with Tables & Graphs
Name ________________
Date _________________
How can I see a proportion?
In the previous lesson, you learned that you could identify proportional relationships by
looking for a constant multiplier. In fact, you have already seen a relationship with a
constant multiplier in this course. Today you will revisit the earlier situation that
contains a proportional relationship.
1. Graphing the Penny-Tower Data
Earlier you found a multiplicative (or proportional)
relationship between the height of a stack of pennies and
the number of pennies in the stack. That is, you could
always find one piece of information by multiplying the
other by a constant number.
Height of
Tower (cm)
1
15
4
a. Fill in the missing values on the table to the right.
What strategies did you use to determine the missing
numbers?
# of Pennies
28
63
3
12
b. How many pennies are in a tower with a height of 0 cm? Add a row to your
table with this value.
c. Graph this data. Be sure to scale the axes so that all of the points in
your table are visible on your graph.
105
98
91
84
77
70
63
# of Pennies
56
49
42
35
28
21
14
7
0
5
10
Height of Tower (cm)
15
d. What do you notice about the graph of height and the number of pennies?
How does this graph compare to Sonja’s graph of birdseed weight and cost
that you made in yesterday’s lesson? What do the graphs have in common?
How are they different?
2. Kaci loves cheese and buys it whenever she can. Recently, she bought 5 pounds of
mozzarella cheese for $15.00 and 3 pounds of havarti for $7.50.
a. Obtain a copy of the Lesson 4.2.2 Resource Page for each member of your
team. Then work together to record, plot, and label Kaci’s two cheese
purchases.
b. Find another combination of the number of pounds of cheese and the
associated cost for the mozzarella by locating another point on this line.
Then, find another combination of pounds of cheese and cost for the havarti.
Mozzarella - # of pounds _______, cost _______
Havarti - # of pounds _______, cost ________
c. Find any other points that should appear on the mozzarella graph and add
them to its table. Then do the same for the havarti graph and its table.
d. Should the points for these tables be connected to form lines on the graph?
Discuss this with your group whether or not it would make sense to connect
the points to form lines for each.
e. Which cheese is more expensive (costs more per pound)?
How can you tell by looking at the graph?
How can you tell by looking at the table?
3. Look back at the tables and graphs you created for proportional relationships in the
previous problems.
a. How can you use a table to decide if a relationship is proportional?
b. How can you use a graph to decide if a relationship is proportional?
4. Which of the tables below shows a proportional relationship between x and y? How
can you tell?
a.
x y
1
2
3
4
b.
2
4
6
8
x y
1
2
3
4
2
3
4
5
5. Use your understanding of proportions to help Kaci find each of the missing
quantities below, using the information given in Problem 2. Be prepared to explain
your strategies.
a. How much do 7.5 pounds of mozzarella cheese cost?
b. How much do 1.5 pounds of havarti cheese cost?
c. How much mozzarella cheese can Kaci buy for $12?
d. How much havarti cheese can Kaci buy for $10?
e. Challenge: Write an equation relating the amount of cheese to the cost of the
cheese.
Mozzarella
Havarti