Amy, Clara, Joel, Eric, Ryan, and Brody are students attending a summer math camp together. Each student comes from a different town in Texas. The students work in teams of two to determine which team comes from towns with the greatest combined population. The teams also decide to use the greater than and less than symbols to compare their home town populations. The students look online to find the population of each of their home towns. Here is what the students find out.

Team 1 Amy lives in Odessa which has a population of 99,940. Clara lives in Denton which has a population of 113,383.

Team 2 Joel lives in Richardson which has a population of 99,203. Eric lives in College Station which has a population of 93,857.

Team 3 Ryan lives in Amarillo which has a population of 190,695. Brody lives in Grapevine which has a population of 46,334.

The students decide to round each population number to the nearest hundreds place to make calculating easier. Which team lives in towns with the greatest combined rounded population?

Team 1 uses the greater than or less than symbol to compare the exact populations of their two towns. What statement does Team 1 write?

Team 2 uses the greater than or less than symbol to compare the rounded populations of their two towns. What statement does Team 2 write?

Team 3 uses the greater than or less than symbol to compare the exact and rounded populations of their two towns. What statements does Team 3 write? Show all your mathematical thinking.

Place Value Unit

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

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

How can you use the multiplicative property of place value to describe the meaning of each digit in the number 654,321?

How can you use the base ten property of place value to explain the
relationship between each of the digits in the number 555,555?

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

TEKS covered in this Unit include: 3.2A, 3.2B, 3.2C, 3.2D

Exemplars Task-Specific Evidence

This task requires students to use place value to round whole numbers to the nearest 100. Students are also expected to add rounded numbers to find a total and then use comparative symbols to compare totals.

TEKS Mathematical Process Standards

3.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

3.1B 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.

3.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

3.1G Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.

Underlying Mathematical Concepts

Rounding whole numbers to the nearest 100

Adding or combining whole numbers

Comparing whole numbers

Possible Problem-Solving Strategies

Model (manipulatives)

Diagram/Key

Table

Chart

Number line

Formal Mathematical Language and Symbolic Notation

Model

Diagram/Key

Table

Chart

Number line

Greather than (>)/Less than (<)

Estimate/Estimation

Odd/Even

Round

Place value

Possible Solutions

Team 3 lives in towns with the greatest rounded population. Comparison statements each team could write are as follows:

Possible Connections

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

The total rounded population of all 6 towns is 643,400.

The total exact population of all 6 towns is 643,412.

643,412 > 643,400

The difference between the exact population of all six towns and the rounded

population of all six towns is only 12 people.

Relate to a similar task and state a math link.

Solve more than one way to verify the solution.

Scoring Rationales and Corresponding Anchor Papers

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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.