Generate a Pattern and Explain a Feature

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: Start at two and add three: 2,5,8,11,14.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A rule generates a sequence by applying the same change repeatedly. A feature such as alternating odd and even terms can be explained from the rule, not merely noticed in three examples. Adding an odd number switches parity; adding an even number preserves it for whole numbers.

Apply the supplied rule for every step and record the terms. Check neighboring differences and explain a feature using the added amount. A finite list shows examples; the rule gives the reason the feature continues.

Check every neighboring difference against the rule. Do not invent a new rule after seeing only a few terms. Make a two-column table of step number and generated value.

1. Make a two-column table of step number and generated value.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Apply the supplied rule for every step and record the terms.
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

Start at five and add six four times. Expected: 11,17,23,29, all odd.

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