Anchor paper 82

Overall Achievement Level:

expert

Student Number:

Anchor Papers:

Problem Solving

expert

Problem Solving Rationale

The student's strategy of using a diagram to determine the total number of fish caught by 12 people works to solve the task. The student's answer, "36 fish were caught," is correct. The student verifies their answer by making a table and equations. The student also verifies their answer by generalizing a rule for finding the total number of fish caught for any number of boats.

Reasoning and Proof

expert

Reasoning Proof Rationale

The student demonstrates correct reasoning of the underlying concepts in the problem. The student uses multiplication correctly. The student generalizes a rule, 6 · b = f, to verify that the data in their table is accurate, the answer is correct, and to find the number of fish for larger numbers of boats.

Communication Level

expert

Communication Rationale

The student correctly uses the mathematical terms diagram, key, table, total, more than, dozen, pattern and rule. The student correctly uses symbolic notation 6 · b = f with the variables "b" and "f" defined in a key.

Connections Level

expert

Connections RationaleAnchor paper 82

The student makes the Practitioner mathematically relevant observations, "The boat pattern is + 1," "The friends pattern is + 2," "The fish pattern is + 6," "There are more total fish than boats or friends," "36 fish is 3 dozen." The student makes the Expert connection of generalizing a rule, 6 · b = f. The student supplies a key to define the variables, b and f, and states, "Each boat will always have two people in it." The student uses the rule to verify that the data in their table is accurate and states, "I am right because I get 36 fish all the time." The student also uses the rule to find the number of fish for 10 and 50 boats.

Representation

expert

Representation Rationale

The student's diagram is appropriate to the problem and accurate. A key is provided to define boat, fish, and person. The student's table is appropriate and accurate with all necessary labels and correctly entered data. The student uses their table to analyze the relationship between the boats and fish to generalize a rule to find the total number of fish for any number of boats.