Standards-based assessment and Instruction

## How Much Is a Name Worth?

Whitney and Scotty are playing a math game. Whitney uses the skip counting by five number pattern to name the letters of the alphabet: A = 5 points, B = 10 points, C = 15 points, D = 20 points, and so forth. Whitney adds together the letter points of her name and gets 520 points. Scotty adds together the letter points of his name. Scotty says his name has more points than Whitney's name. Scotty writes this on his paper: Scotty's points > Whitney's points. Is Scotty correct? Show all your mathematical thinking.

### Alternative Versions of Task

#### More Accessible Version

Whitney and Scotty are playing a math game. Whitney uses the skip counting by two numbers to name the letters of the alphabet: A = 2 points, B = 4 points, C = 6 points, and so forth. Whitney adds together the letters of her name and gets 208 points. Scotty adds together the letters in his name and says his name has more points than Whitney's. Scotty writes this on his paper: Scotty's points > Whitney's points. Is Scotty correct? Show all your mathematical thinking.

#### More Challenging Version

Whitney and Scotty are playing a math game. Whitney uses the skip counting by three numbers to name the letters of the alphabet: A = 3 points, B = 6 points, C = 9 points, and so forth. Whitney adds together the letters of her name and gets 312 points. Scotty adds together the letters in his name and says his name has more points than Whitney's. Scotty writes this on his paper: Scotty's points > Whitney's points. Is Scotty correct? Show all your mathematical thinking.

### Comparing Numbers Unit

The Comparing Numbers Unit involves understanding the relative position and magnitude of whole numbers, and their relationships within the numeration system. Students will answer questions such as–

• Which number is greatest? Least? How do you know? How can you use symbols to show these relationships?
• How can you order these numbers from least to greatest? How can you prove you are correct?
• How can you use a number line to show the relationships between these numbers?

### Math Concepts and Skills Covered

The student compares whole numbers and understands place value relationships. The student:

• Uses place value to compare and order numbers up to 1,200 and describes the comparison using words, numbers, and symbols (>, <, or =).
• Assigns the position of a specific whole number on a number line and identifies the number that corresponds to a given point on a number line.

### Exemplars Task-Specific Evidence

Students are expected to use the symbols >, =, and < to record comparisons between two three-digit numbers. They are also asked to find the sum of up to seven addends.

### Underlying Mathematical Concepts

• Positional Property of Base-10 Number System
• +5 pattern starting at letter A
• Number sense to 520
• Order of alphabet letters
• Comparison

### Possible Problem-Solving Strategies

• Model (manipulatives)
• Diagram/Key
• Table
• Number line

### Formal Mathematical Language and Symbolic Notation

• Model
• Diagram/Key
• Table
• Number line
• Total/Sum
• Amount
• Odd/Even
• More than (>)/Greater than (>)/Less than (<)
• Equivalent/Equal to
• Difference
• Part/Whole
• Pattern
• Digit
• Numeral

### Possible Solutions

Scotty is not correct. The sentence should read Scotty < Whitney (510 < 520).

#### More Accessible Version Solution

Scotty is not correct.

#### More Challenging Version Solution

Scotty is not correct.

### Possible Connections

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

• Scotty should write: Scotty < Whitney.
• Both names have a total of even number of points.
• Together their names are a total of 1,030 points.
• The difference between their names is 10 points.
• Solve more than one way to verify the answer.
• Relate to a similar task and state a math link.
• All letter numbers end in 0 or 5 because of the +5 pattern.
• Scotty has 1 less letter than Whitney, so she has a higher chance of having more total points.

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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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