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Overall Achievement Level:

expert

Student Number:

Anchor Papers:

Problem Solving

expert

Problem Solving Rationale

The student’s strategy to use a table and multiplication to find the total number of tiles Mrs. Garcia needs for her border works to solve the task. The student’s answer, “3 x 63 = 189 tiles,” is correct. The student uses division to find the total number of boxes of tiles Mrs. Garcia needs. The student’s answer, “So buy 24 boxes” is correct. The student uses alternate strategies of a table and generalized rule.

Reasoning and Proof

expert

Reasoning Proof Rationale

The student demonstrates correct reasoning of multiplication and division as well as generalizing and applying a rule, 8 · b = t, to justify the second part of the task.

Communication Level

expert

Communication Rationale

The student correctly uses the mathematical term row from the task. The student also correctly uses the terms total, table, dozen, second, pattern, key, rule. The student correctly uses the mathematical symbolic notation 8 · b = t.

Connections Level

expert

Connections RationaleTile Border

The student makes the mathematically relevant Practitioner observations, “two dozen is 24 boxes,” and, “3 left over.” The student makes an Expert connection. The student generalizes a rule, 8 · b = t, and applies the rule for 4, 8, 10, 23, and 24 boxes. The student defines the variables b and t in a key.

Representation

expert

Representation Rationale

The student’s tables are appropriate to the task and are accurate. All columns are labeled correctly and the entered data is correct. The student creates the second table to justify their division equation and to extend their thinking to a generalized rule.