Standards-based assessment and Instruction

## Crab Walk Relay Race

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

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

### Possible Problem-Solving Strategies

• Chart
• Guess and check
• Number line

### Formal Mathematical Language and Symbolic Notation

• 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.
• 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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## 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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