+ — =¢
x —
MATH THAT MAKES
¢ ENTS
GRADE
6
worksheet 9 - PICKING PRETZELS
Nate is buying some pretzels before his friends come over. He can go
to the vending machine and get 1.5 ounce bags for 75 cents, he can
go to the corner store and get 8 ounce bags for $2, or he can go to the
grocery store and buy 16 ounce bags for $3.49.
He has $10 to spend.
At which place can he buy the most pretzels for his money? Which
pretzels are the best buy?
Extra: Can you think of any other factors that might affect his decision?
MATH STANDARDS ALIGNMENT
Grade 6: Ratios & Proportional Relationships
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the
context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is
3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
Mathematical Practices
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
Personal Finance Big Ideas:
Cost/Benefit Analysis
Jump$tart Standard:
Planning and Money Management
Standard 4: Apply consumer skills to purchase decisions
METHOD 1: I NOTICE, I WONDER™
After reading the problem, our group decided to write down everything we noticed and wondered:
We noticed:
• Nate is buying pretzels
• He can buy them in three different places
• The sizes are 1.5 ounces, 8 ounces, or 16 ounces
• The costs are 75 cents, $2, and $3.49
• He wants to buy as many pretzels as possible
• One price is in cents and the other ones are in dollars
• He could buy 5 of the 8 ounce bags and spend exactly $10
• He will have money leftover if he buys the 1.5 ounce or 16 ounce bags
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MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
worksheet 9 - PICKING PRETZELS
GRADE
6
We wondered:
• Are all the pretzels the same kind or are some better?
• Can he only go to one store?
• Are the stores all about the same distance away?
• Do all his friends like pretzels or is someone bringing something else?
• Will he also have something to drink? Does he have to buy it with his $10?
• Are the big bags the best deal?
We decided to start by figuring out how many bags of each size he could buy with his $10. We divided $10 by the cost
of each bag.
10/0.75 = 13.33
10/2 = 5
10/3.49 = 2.87
Since we can only buy whole bags of pretzels, we ignored the decimals and decided that he could buy 13, 5, and 2
bags. Then we figured out how many ounces that would be for each type by multiplying the number of bags of each
size times the weight.
13 • 1.5 = 19.5
5 • 8 = 40
2 • 16 = 32
If he buys the 8 ounce bags at the corner store, he could get 40 ounces for his $10. That is more than the other two
choices.
Then we tried to figure out which size was the best deal. We saw that the 8 ounce bags weighs more than 4 times the
1.5 ounce bag, but it doesn’t cost more than 4 times as much (in fact, it doesn’t even cost 3 times as much, since 0.75
times 3 = $2.25). So the 8 ounce bag is the better buy of those two.
But then we noticed that the 16 ounce bag weighs exactly twice as much, but costs less than twice as much. So that
must be the best deal.
Extra: S
ometimes it might be good to buy a smaller size if you think you won’t eat all of the larger size, and they
might go stale. Or if it’s soda, it will go flat if you don’t drink it soon. But 8 ounces doesn’t seem like too much,
especially if he has friends coming.
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MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
GRADE
6
worksheet 9 - PICKING PRETZELS
METHOD 2: COUNTING BAGS
I noticed that the 8 ounce bag costs $2 and so he could buy 5 bags exactly with his $10. But it was harder to see how
many of the other sizes he could buy. I decided to make a table and keep adding bags until I got to $10.
For the 1.5 ounce bag, which costs $0.75:
Bags
1
2
4
12
13
14
Cost$0.75$1.50$3.00$9.00$9.75$10.50
This means that 14 bags will be too much, so he could buy 13 bags from the vending machine.
For the 16 ounce bag, which costs $3.49:
Bags
1
2
3
Cost$3.49$6.98$10.47
That means 3 bags will be too much, so he can only buy 2 of the big bags.
Then I figured out how many ounces he could buy of each kind:
Ounces Per Bag
Number of Bags
Total Ounces
1.5
13
19.5
8
5
40
16
2
32
He can get the most pretzels if he buys 5 of the 8 ounce bags at the corner store.
Then we wondered if that size bag was the best deal. We decided to divide the cost of each bag by the number of
ounces to figure out how much one ounce would cost.
0.75/1.5 = 0.50
2/8 = 0.25
3.49/16 = 0.22
The small bag has the highest cost per ounce, at 50 cents. The middle bag costs 25 cents an ounce, which is a lot
better deal. But the big bag is the best deal, at 22 cents an ounce.
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MATH THAT MAKES CENTS