Students were asked to read Counting on Frank by Rod Clement and to write a letter to the author commenting on at least one example of the mathematical claims made.

 Circumstances of performance This sample of student work was produced under the following conditions: - alone - in a group - in class - as homework - with teacher feedback with peer feedback timed - opportunity for revision

Four students discussed the mathematics in depth in Counting on Frank before they wrote their analyses. The students spent class time as well as many recesses figuring out how to test the claims in the book. For example, the students discussed how to use the classroom sink to test the claim in the book about the bathroom filling up with water. The students worked together to develop strategies for testing the claims about the peas and the ball-point pen. The teacher encouraged the students’ discussions, and provided time and materials in school for them to work out their reasoning. The students met outside of class to work together on the writing. Students completed the writing individually, at home.

The students completed this activity near the end of the school year. Earlier in the year, the students had studied area and perimeter concepts in depth, as well as applications of multiplication and division in problem solving activities.

This work sample illustrates a standard-setting performance
for the following parts of the standards:

 a Arithmetic and Number Concepts: Add, subtract, multiply, and divide whole numbers. b Arithmetic and Number Concepts: Demonstrate understanding of the base ten place value system and use this knowledge to solve arithmetic tasks. c Arithmetic and Number Concepts: Estimate, approximate, round off, use landmark numbers, or use exact numbers, as appropriate, in calculations. d Arithmetic and Number Concepts: Describe and compare quantities by using concrete and real world models of simple fractions. e Arithmetic and Number Concepts: Describe and compare quantities by using simple decimals. f Arithmetic and Number Concepts: Describe and compare quantities by using whole numbers up to 10,000. g Geometry and Measurement Concepts: Use basic ways of estimating and measuring the size of figures and objects in the real world. i Geometry and Measurement Concepts: Select and use units for estimating and measuring quantities. j Geometry and Measurement Concepts: Carry out simple unit conversions. a Problem Solving and Reasoning: Formulation. b Problem Solving and Reasoning: Implementation.
 c Problem Solving and Reasoning: Conclusion. a Mathematical Skills and Tools: Add, subtract, multiply, and divide whole numbers correctly. b Mathematical Skills and Tools: Estimate numerically and spatially. c Mathematical Skills and Tools: Measure accurately. d Mathematical Skills and Tools: Compute time. f Mathematical Skills and Tools: Use +, -, x, ÷, /,…and . (decimal point) correctly in number sentences and expressions. h Mathematical Skills and Tools: Use recall, mental computations, pencil and paper, measuring devices, manipulatives, calculators and advice from peers, as appropriate, to achieve solutions. a Mathematical Communication: Use appropriate mathematical terms, vocabulary, and language. b Mathematical Communication: Show mathematical ideas in a variety of ways. c Mathematical Communication: Explain solutions to problems clearly and logically. d Mathematical Communication: Consider purpose and audience when communicating about mathematics. e Mathematical Communication: Comprehend mathematics from reading assignments and from other sources.