Anchor paper 482

Overall Achievement Level:

expert

Student Number:

Anchor Papers:

Problem Solving

expert

Problem Solving Rationale

The student's strategy of making a table of the days, puzzle pieces and total puzzle pieces works to solve part of the task. The student applies subtraction and states a correct answer, "5 pieces." The student shows evidence of analyzing the situation in mathematical terms. The student explores the numbers in the ones place and determines that a total of 150 pieces is not possible. The student also applies the Even + Odd + Even = Odd rule to support their analysis. The student also verifies that their solution is correct by using number lines as a new strategy.

Reasoning and Proof

expert

Reasoning Proof Rationale

The student uses correct reasoning of the underlying concepts of the task. The student organizes and determines a total of 145 puzzle pieces are used in three days. The student finds the number of remaining puzzle pieces needed to finish the puzzle by applying subtraction. The student explains the phenomenon that when adding, some sets of numbers can not have a total with a zero in the ones place. The student uses this thinking to explain how they realized that some puzzle pieces must be missing. The student uses number lines to verify that the data in their table is correct.

Communication Level

expert

Communication Rationale

The student correctly uses the mathematical term day from the task. The student also correctly uses the mathematical terms table, 1st, 2nd, 3rd, total, dozen, most, sum, number line, odd, even, sets, rule. The student correctly uses the symbolic notation E + O + E = O and defines E and O under the numbers.

Connections Level

expert

Connections RationaleAnchor paper 482

The student makes the mathematically relevant Practitioner observation, "36 is 3 dozen pieces" and "He puts the most pieces in on the 3rd day." The student makes the Expert connection, "36 41 68, 6 + 1 + 8 = 15. The sum does not end in 0 so they can not add up to 150." The student also states E + O + E = O, 36 + 41 + 68 = 145, even + odd + even = odd." The student applies this rule by using the equations, 6 + 1 + 8 = 15, 8 + 5 + 2 = 15, 4 + 9 + 10 + 23, and states, "it is a true rule." The student also verifies their answer by using two number lines to arrive at 150 pieces. The first number line considers addition and the second number line considers subtraction. The student states, "I am correct. I found 5 pieces 3 ways. I thinked of all I know."

Representation

expert

Representation Rationale

The student's table is appropriate to the task and accurate. All labels are included and the data is correct. The student attempts a number line and discards it as they realized the paper is too short to have a number line using increments of five. The student makes two correct number lines with increments of ten. The student indicates that the numbers represent pieces. The student compares these two number lines with their table to verify that their answer is correct.