View examples of student solutions by clicking on a level below:

Piggy Bank

Justin and Sarah shook all the money out of the piggy bank they shared. They put the coins in these two groups:

Justin's Group of Coins	Sarah's Group of Coins

Justin and Sarah's mom looked at the groups of coins. She told Justin and Sarah that if they could make each group total the same amount, she would match them that amount of money. Show Justin and Sarah how to arrange their coins in 2 equal groups. Explain your math thinking.

Suggested Grade Span

Grades Pre-K-2

Grade(s) in Which Task Was Piloted

Grade 2

Task

Justin and Sarah shook all the money out of the piggy bank they shared. They put the coins in these two groups: (see image above). Justin and Sarah's mom looked at the groups of coins. She told Justin and Sarah that if they could make each group total the same amount, she would match them that amount of money. Show Justin and Sarah how to arrange their coins in 2 equal groups. Explain your math thinking.

Alternative Versions of Task

More Accessible Version:

Justin and Sarah shook all the money out of the piggy bank they shared. They put the coins in these two groups:

Justin's Group of Coins	Sarah's Group of Coins

More Challenging Version:

Justin and Sarah shook all the money out of the piggy bank they shared. They put the money in these two groups:

Justin's Group of Coins	Sarah's Group of Coins

Justin and Sarah's mom looked at the groups of money. She told Justin and Sarah that if they could make each group total the same amount, she would match them that amount of money. Show Justin and Sarah how to arrange their money in 2 equal groups. Explain your math thinking.

NCTM Content Standards and Evidence

Number and Operation Standard for Grades Pre-K-2

Instructional programs from Pre-Kindergarten through grade 12 should enable students to...

Understand meanings of operations and how they relate to one another.

NCTM Evidence A: Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations
Exemplars Task Specific Evidence A: This task requires students to "even out" coin values that results in subtracting an amount from one value and adding it to another, the result being equal values. The degree to which this will occur will depend on the student's problem solving strategy.
NCTM Evidence B: Understand situations that entail multiplication and division, such as equal grouping of objects and sharing equally.
Exemplars Task Specific Evidence B: This task requires students to understand a situation involving division where objects (coin values) need to be shared fairly. The degree to which this will occur will depend on the student's problem solving strategy.

Time/Context/Qualifiers/Tip(s) From Piloting Teacher

This task is a medium length task. It can be used to assess number and operation concepts, as well as identification of coin values and manipulation of money. It is helpful to have actual coins available in the class for students to manipulate.

Links

Other Exemplar Tasks that involve the manipulation of money include Holiday Fair, Salad Bar, and Nine Cents featured in Volume 7 of Exemplars.

Common Strategies Used to Solve This Task

Most students will arrive at a strategy for first counting the coins in each group. Then most seem to "guess and check" to find new groupings that are equal.

Possible Solutions

Original Version:

The total amount of money Justin has is 83 cents. Sarah has 63 cents. If Justin gives a dime to Sarah, they will each have 73 cents from the bank, and 73 cents each from their mother, resulting in a total of $1.46 each.

More Accessible Version:

The total amount of money Justin has is 10 cents. Sarah has 6 cents. If Justin gives 2 pennies to Sarah, they will each have 8 cents from the bank, and 8 cents each from their mother, resulting in a total of $0.16 each.

More Challenging Version:

The total amount of money Justin has is $5.57 cents. Sarah has $6.29. If Sarah gives a quarter, a dime, and a penny to Justin, they will each have $5.93 from the bank, and $5.93 each from their mother, resulting in a total of $11.86 each.

Task Specific Assessment Notes

General Notes: This task will allow the teacher to assess students' knowledge of addition and coin identification. The task does not lend itself to making mathematical representations to solve or portray solutions.

Task Specific Rubric/Benchmark Descriptors Click on a level for student example.
Novice	The novice will show little or no engagement with the task. An attempt may be made to find the sum of the money, but it will be incomplete or incorrect.
Apprentice	The apprentice will have an incorrect solution due to a computation or reasoning error.
Practitioner	The practitioner will have an adequate argument with correct reasoning present. Work will be shown and organized.
Expert	The expert will analyze the situation in mathematical terms, achieving a correct solution that is well communicated.

Author

This task was written by Deb Armitage, K-8 Mathematics Assessment Consultant at the Vermont Department of Education. The task was piloted by teachers and students in Vermont.