Mr. Fair, the physical education teacher, is forming three crab walk
relay teams. There must be four students on each relay team. To
determine the teams, Mr. Fair uses the students' crab walk times from
the last physical education class. The students are timed to the nearest
tenth of a second.

Student

Time in seconds

Harry

12.2

Sally

10.3

Joseph

8.9

Amy

8.7

Ryan

9.9

Josh

11.4

Meredith

10.5

Anna

9.1

Brooke

10.9

Travis

11.1

Greg

11.9

Emily

11

Mr. Fair wants each of the three relay teams to be as equally matched in
total time as possible. Mr. Fair writes the three teams on a piece of
paper. What four students could Mr. Fair put on each team? Mr. Fair
decides to write the less than, greater than, or equal symbols on his
paper to compare the three teams. What could be on Mr. Fair's paper?
Show all your mathematical thinking.

Decimal Place Value Unit

The Decimal 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 decimal number?

How can you use the multiplicative property of place value to describe the meaning of each digit in the number 0.123?

How can you use the base ten property of place value to explain the relationship between each of the digits in the number 5.555?

Standards covered in this Unit include: 5.2A, 5.2B, 5.2C

Exemplars Task-Specific Evidence

This task requires students to order and compare decimals. It also
requires students to add and subtract decimal values to tenths place.

TEKS Mathematical Process Standards

5.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

5.1B 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.

5.1C Select tools, including real objects, manipulatives, paper and pencil,
and technology as appropriate, and techniques, including mental math,
estimation, and number sense as appropriate, to solve problems.

5.1D Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.

5.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

5.1G Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.

Underlying Mathematical Concepts

Compare decimals

Decimal notation

Inequality/Equality symbols

Addition/Subtraction of decimals

Possible Problem-Solving Strategies

Chart

Guess and check

Number line

Possible Mathematical Vocabulary/Symbolic Representation

Chart

Number line

Time (second, minute)

Decimals (8.7, 12.2 ...)

Place value (ones, tenths)

Equivalent/Equal to

Greater than (>)/Less than (<)

Combination

Total/Sum

Range

Possible Solutions

See the charts below for three suggested teams. Team 1's time > Team
2's time. Team 2's time = Team 3's time. Team 1's time > Team 3's
time.

Possible Connections

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

Find a new combination of 3 relay teams.

Harry is the slowest crab walker – 12.2 seconds.

Amy is the fastest crab walker – 8.7 seconds.

The range is 12.2 – 8.7 = 3.5 seconds.

Emily's time < Travis' time by 0.1 second.

Ryan's time is < Greg's time by 2.0 seconds.

All seconds are recorded to the tenths place.

42.1 seconds is 17.9 seconds from 1 minute.

41.9 seconds is 18.1 seconds from 1 minute.

The girls' combined total time is 60.5 seconds.

The boys' combined total time is 65.4 seconds.

60.5 < 65.4 so the girls' total time is faster than the boys' total time.

Relate to a similar task and state a math link.

The combined total time of all the students is 125.9 seconds, so there cannot be 3 exactly equal times.

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.