**I. A 4th grade (TERC) Investigations homework assignment, assigned in late November:**

**II. From a similar point in the 4th grade Singapore Math Curriculum (Primary Mathematics 4A):**

**III. Extra Credit:**

Neither traditional math, nor Singapore Math, spell out shortcuts as explicitly Investigations does ("Can you use the first problem to help you solve the second problem?"). Instead, students of traditional math and Singapore Math discover these tricks on their own. Which is better, child-centered discovery of ad hoc shortcuts, or more explicit hints via teachers, worksheets, and other authoritative entities?

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