Explain Zero, One, and Even-Product Patterns

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: There are zero packets of nine cards: 0×9=0 cards.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Multiplying by one gives one copy of an amount, so it preserves the amount. Multiplying by zero gives no copies, so the product is zero. Multiplying by two creates two equal copies; every such whole-number product can be paired into an even number.

Use the stated factor pattern to explain the product before calculating. Distinguish zero groups from one group. For a factor of two, draw two matching rows and pair the objects to demonstrate why the product is even.

Explain zero groups and one group with a model. A zero factor gives zero, not the other factor. Draw zero, one, and two group boxes with the same possible group size.

1. Draw zero, one, and two group boxes with the same possible group size.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Use the stated factor pattern to explain the product before calculating.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Explain 2×7 without only naming fourteen. Expected: two copies of seven form seven pairs.

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