Austin and Eli have been saving pennies to buy a video game. Austin and
Eli know the video game will cost 1,000 pennies. Austin has five hundred
fifteen pennies. Eli has 400 + 30 + 5 pennies. Austin and Eli have some
bags. Austin and Eli begin putting ten pennies in each bag. Austin
thinks they each need to save twenty-five more pennies to have enough
pennies to buy the video game. Is Austin correct? Show all your
mathematical thinking.

Alternative Versions of Task

More Accessible Version

Austin and Eli have been saving pennies to buy a video game. Austin and
Eli know the video game will cost 700 pennies. Austin has three hundred
fifteen pennies. Eli has 300 + 30 + 5 pennies. Austin and Eli have some
bags. Austin and Eli begin putting ten pennies in each bag. Austin
thinks they each need to save twenty-five more pennies to have enough
pennies to buy the video game. Is Austin correct? Show all your
mathematical thinking.

More Challenging Version

Austin and Eli have been saving pennies to buy a video game. Austin and
Eli know the video game will cost 1,000 pennies. Austin has five hundred
fifteen pennies. Eli has 400 + 30 + 5 pennies. Austin and Eli have some
bags. Austin and Eli begin putting twenty-five pennies in each bag.
Austin thinks they each need to save twenty-five more pennies to have
enough pennies to buy the video game. Is Austin correct? Show all your
mathematical thinking.

Place Value Unit

The Place Value Unit involves understanding
the relative position, magnitude and relationships within the numeration
system in order to answer questions such as:

How could you use base-10 blocks to show what the numerals in this number mean?

How can you use the additive property of place value to decompose this number?

What other way(s) can you use thousands, hundreds, tens, and ones to show this number without changing its value?

Standards covered in this Unit include: 2.2B, 2.2C, 2.3A, 2.7B

Exemplars Task-Specific Evidence

Students are expected to use different representations of whole numbers to find sums and differences.

TEKS Mathematical Process Standards

2.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

2.1B Use a problem-solving model that incorporates analyzing given
information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and
the reasonableness of the solution.

2.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

2.1G Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.

Underlying Mathematical Concepts

Additive Property of the Base-10 Number System

Finding sums when the parts are known and differences when the whole and one part is known.

Number sense to 1,000

Addition/Subtraction

Comparison

Possible Problem-Solving Strategies

Model (manipulatives)

Table

Diagram/Key

Number line

Formal Mathematical Language and Symbolic Notation

Model

Table/Key

Number line

Total/Sum

Part/Whole

Odd/Even

Subtrahend

Minuend

Difference

Amount

Coin

Money: penny, nickel, dime, quarter, half-dollar, dollar

Money notation: $, ¢

Per

Tens, hundreds, thousands

Expanded notation/Standard notation

Equal share

Equivalent/Equal to

Possible Solutions

Yes, Austin is correct.

More Accessible Version Solution

Yes, Austin is correct.

More Challenging Version Solution

Yes, Austin is correct.

Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

Austin and Eli have a total of 950 pennies.

25 pennies is a quarter.

10 pennies is a dime.

Each bag holds a dime’s worth of pennies, 10¢, or 2 nickels.

100 pennies is a dollar, $1.00.

1,000 pennies is 10 dollars, $10.00.

It takes 100 bags to hold enough pennies to buy the video game.

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The Exemplars program is designed to assess students' problem-solving and mathematical-communication skills. It also supports higher-level thinking and extension of mathematical reasoning.