The Book Shelf

Overall Achievement Level:

expert

Student Number:

Anchor Papers:

Problem Solving

expert

Problem Solving Rationale

The student's strategy of diagraming the books Ryan and Zak put on the shelf and comparing each boy's total books to determine that Ryan is correct, works to solve the task. The student's answer, "yes," is correct. The student brings prior knowledge of greater than and less than notation and fair share/equal to the task.

Reasoning and Proof

expert

Reasoning Proof Rationale

The student shows understanding of the mathematical concepts of the task. The student shows correct totals of books for each boy and compares the two totals to conclude that Ryan is correct as he has a greater number of books. The student also uses conceptual thinking of the notation for greater than and less than. The student discovers that a total of 14 books can be a fair share if seven books are put on each shelf. The student also justifies that their answer is correct.

Communication Level

expert

Communication Rationale

The student correctly uses the mathematical terms diagram, key, more, pair, greater than, total, fair share, equal, number lines, ten frames, more than. The student correctly uses the mathematical symbolic notation 8 > 6, 6 < 8.

Connections Level

expert

Connections RationaleThe Book Shelf

The student makes mathematically relevant Practitioner observations about their solution. "I see Ryan has two more books than Zak. That is a pair," "This is 14. They have 14 books in all. That is total books," "Ryan needs two more for ten," and "Zak needs four more for ten." The student makes Expert connections. The student states, "8 > 6, This means eight is greater than six. My brother taught me." The student also states, "If they each put seven on it is a fair share of books. It is equal books." The student verifies their solution by using number lines and ten frames. The student states, "I did two number lines and two ten frames and Ryan always has more books than Zak."

Representation

expert

Representation Rationale

The student's diagram is appropriate and accurate. A key defines the books and each boy's name is clearly labeled. The student's number lines are appropriate and accurate. The numbers are labeled "books," each boy's name is assigned to the correct number line, and the "jumps" are correct. The student's ten frames are appropriate and accurate. A label for books is used and each boy's name is clearly labeled. The student uses the number lines and ten frames to clarify that their answer is correct.