The student’s strategy of making a table to show the large and small stones found on the 10th day and then totaling the large and small stones needed to make the stone wall works to solve this task. The student’s answers, “on the 10th day she got 40 small and 32 large stones,” and, “In all she got 220 small stones in all and 185 large stones in all,” is correct. The student uses alternate strategies of rules and graphs.
The student justifies and supports her/his correct reasoning by using a table to generate two numerical patterns and computation to find the total number of small and large stones Sarah collects for her wall. The student verifies her/his decisions by generalizing two rules and making a graph.
The student correctly uses the mathematical terms tenth, day, pattern from the task. The student also correctly uses the terms table, key, rules. The student correctly uses the symbolic notation (3 x D) + 2 = LG, and 4 x D = SM.
The student makes mathematically relevant Practitioner observations, “Patterns, D = +1, LG = +3, SM = +4. (The student provides a key to define D, LG, and, SM). The student uses an alternate strategy of a graph to show the large and small stones collected each day for 10 days. The student makes Expert connections. The student generalizes two rules, (3 x D) + 2 = LG, and 4 x D = SM, with the variables defined in a key. The student uses (3 x D) + 2 = LG to find the number of large stones for days 1, 5, 50, and 10. The student uses 4 x D = SM to find the number of small stones for days 3, 8, 100, and 10. The student’s rules verify that the totals for day 10 are correct. The student states, “my table is correct.”
The student’s table is appropriate and accurate. All labels are provided and the data is correct. The student uses the table to note two numerical patterns and then to generalize two rules used to extend the task to other days. The student’s graph is also appropriate and accurate. The X and Y axis is labeled correctly and a key is provided to define large and small stones.