Standards-based assessment and Instruction

## A New Video Game

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.

#### 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

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
• 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.
• 40 quarters is 10 dollars.
• Solve more than one way to verify the answer.
• Austin starts with more pennies (80 more).
• 25 pennies is a quarter.
• 50 pennies is a half-dollar.

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## Here's What People Are Saying

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.

S. Dement
Teacher

Converse, TX

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