Pattern-Block Fish. Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins.

Transcription

1 Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins. If this pattern continued... How many fins did 7 fish have? 1 of 13

2 How many fins did 10 fish have? How many fins did 20 fish have? 2 of 13

3 Suggested Grade Span 3 5 Grade(s) in Which Task Was Piloted 3 Task Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins. If this pattern continued... How many fins did 7 fish have? How many fins did 10 fish have? How many fins did 20 fish have? 3 of 13

4 Alternative Versions of Task More Accessible Version: (Use the same fish pattern that appears in the original version of the task.) Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins. If this pattern continued... How many fins did 4 fish have? How many fins did 5 fish have? How many fins did 6 fish have? Teacher Note: See page 8 of the PDF to print a complete worksheet with graphics. More Challenging Version: (Use the same fish pattern that appears in the original version of the task.) Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins. If this pattern continued... How many fins did 10 fish have? How many fins did 100 fish have? How many fins did n fish have? Teacher Note: See page 9 of the PDF to print a complete worksheet with graphics. NCTM Content Standards and Evidence Algebra Standard for Grades 3 5: Instructional programs from pre-kindergarten through grade 12 should enable students to... 4 of 13

5 Understand patterns, relations and functions. NCTM Evidence: Describe, extend and make generalizations about geometric and numeric patterns. Exemplars Task-Specific Evidence: This task requires students to identify and extend a geometric pattern. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a short-length task. To print a copy of the more accessible version of the task with the graphic image, refer to page 8. To print a copy of the more challenging version of the task with the graphic image, refer to page 9. Links This task could link to units on fish, water or oceans. "Pattern-Block Walls," another Exemplars task, requires the same strategy. It could be given to students along with "" as part of a choice menu. Common Strategies Used to Solve This Task Most students create a chart to record data given in the task and then extend the chart to achieve a solution. Possible Solutions Fish Fins of 13

6 More Accessible Version Solution: Fish Fins More Challenging Version Solution: Task-Specific Assessment Notes Fish Fins n General Notes Most students will create a representation to organize the information presented in the task. Look for all three parts to be correct in a practitioner's solution. Novice The Novice will present no strategy for solving the problem. The student will merely interact with the drawings of the fish, adding eyes and mouths. Apprentice The Apprentice will be able to organize the information presented in the task in a representation but will then either proceed incorrectly or will be unable to proceed at all. Practitioner The Practitioner will achieve a correct answer and show supporting work. The student will also note patterns seen in solving the task. 2n 6 of 13

7 Expert The Expert will not only identify and extend the pattern, but will also be able to generalize her/his solution so that the total number of fins for any number of fish can be found. 7 of 13

8 More Accessible Version Worksheet Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins. If this pattern continued... How many fins did 4 fish have? How many fins did 5 fish have? How many fins did 6 fish have? 8 of 13

9 More Challenging Version Worksheet Pat and Sam were having fun building fish with pattern blocks. 1 fish had 2 fins. 2 fish had 4 fins. 3 fish had 6 fins. If this pattern continued... How many fins did 10 fish have? How many fins did 100 fish have? How many fins did n fish have? 9 of 13

10 Novice 10 of 13

11 Apprentice 11 of 13

12 Practitioner 12 of 13

13 Expert 13 of 13