Problem of the Week Teacher Packet
Pocket Money
John, Tina, and Erin each have 10 cents in their pockets. However, they each do not
have the same number of coins.
What coins could each person have?
Extra: Erin has the fewest possible coins. What does she have in her pocket?
Answer Check
After students submit their solution, they can choose to “check” their work by looking at the answer that we
provide. Along with the answer itself (which never explains how to actually get the answer) we provide hints
and tips for those whose answer doesn’t agree with ours, as well as for those whose answer does. You might
use these as prompts in the classroom to help students who are stuck and also to encourage those who are
correct to improve their explanation.
One could have a dime. Another could have two nickels. Another could have ten pennies.
If your answer does not match our answer, did you
•
•
•
act it out?
draw a picture?
talk in your group?
If your answer does match ours,
•
•
•
explain?
describe your picture?
help anyone in your group
Our Solutions
Method 1: Notice and Wonder®
We made a list of everything we noticed and wondered.
We noticed:
John has 10 cents in his pocket.
Tina has 10 cents in her pocket.
Erin has 10 cents in her pocket.
they each have a different number of coins.
We wondered:
how many ways can you make 10 cents.
how did they get their money.
why did they have money in their pockets.
© 2016 The Math Forum at NCTM
Problem 3563
http://mathforum.org/pows/
We talked about what we had noticed. We decided to list the different ways you could have 10 cents.
• 10 pennies
• 1 nickel and 5 pennies
• 2 nickels
• 1 dime
We decided John had 10 pennies, Tina had 2 nickels, and Erin had 1 dime.
Extra: There was only one possibility in our list that gave Erin the fewest possible coins. Erin had 1 dime in her
pocket.
Method 2: Draw a Picture
Our group drew a picture. We drew all the coins we could think of that you might have.
We remembered that they only had 10 cents in their pockets and so we crossed out the coins that were too
much money. We only had three coins left to think about.
We talked about the ways that we could make 10 cents with those coins.
We thought of four different ways. We decided that
• Erin had 5 one cent coins and 1 five cent coin.
• Tina had 2 five cent coins.
• John had 1 ten cent coin.
Method 3: Make a Table
We made a table using the information in the problem.
coins
value
penny
1¢
nickel
5¢
dime
10¢
Next we talked about how we could combine the coins so that the total value would be 10¢.
© 2016 The Math Forum at NCTM
Problem 3563
http://mathforum.org/pows/
coins
value
total value is 10¢
penny
1¢
1¢+1¢+1¢+1¢+1¢+1¢+1¢+1¢+1¢+1¢
nickel
5¢
5¢+5¢
penny and nickel
1¢ and 5¢
1¢+1¢+1¢+1¢+1¢+5¢
dime
10¢
10¢
Those were the four ways we thought about the coins John, Tina, and Erin had in their pockets.
Extra: If Erin had the fewest possible coins, she would just have 1 dime in her pocket.
Standards
If your state has adopted the Common Core State Standards, you might find the following alignments helpful.
Grade 2: Measurement & Data
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols
appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?
Mathematical Practices
1. Make sense of problems and persevere in solving them.
3. Construct viable arguments and critique the reasoning of others.
Additional alignment information can be found through the Write Math with the Math Forum service, where
teachers can browse by CCSS, NCTM, and individual state standards to find related problems.
Teaching Suggestions
This problem has not yet been discussed during any of our online courses. If you try it with your students and
have a short story to tell about
• how you prepared/planned to present the problem to your students
• what happened when you used it with students
• what classroom environment did you use? individual, pairs, groups, whole class?
• something you noticed about your students’ approaches to the problem
• something you wondered about your students’ understandings or misunderstandings
we’d love to hear from you.
—Suzanne, @SuMACzanne
© 2016 The Math Forum at NCTM
Problem 3563
http://mathforum.org/pows/