Shape patterns

MathematicsMultiplication & DivisionAges 9–10

Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

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Teaching Table

Set out your lesson

Generate number and shape patterns from stated rules. Explain odd/even and growth features using the rule, pairs, or a repeating unit.

Activity

Ask the learner to add three to four. Ask what two equal groups of three make. Draw seven dots and ask for pairs and any single dot. Teach pairing or equal groups first if needed. The adult names △, □, and ○ before pattern work. Shape naming and fluent reading are not scored. Availability of a prerequisite lesson does not show readiness.

Policy

Check readiness directly. Prerequisite availability is not attainment.

Use plain paper and a pencil. Keep the model and later practice on separate sheets. Use drawn dots rather than small counters. Keep the stated rule cards visible. Put earlier completed examples aside for Try.

Record the actual response and assistance. These tasks do not establish mastery.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.

Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

The tasks assess a bounded set of positive whole-number and repeating-shape patterns, not every possible pattern.
The number facts and rule types are rehearsed across the lesson. Changed inputs do not establish independent arithmetic fluency.
The start of each number pattern is supplied. Copying that first term is not independent generation.
T A and B supply their feature conclusions. C selects and explains a taught, cued feature. This is not independent feature discovery.
Equivalent repeating units can describe a strip, but the task requests the shortest unit under its stated complete-copy condition.
Spoken shape names and adult transcription are adapted modes. They do not establish unaided visual naming, reading, handwriting, or drawing.
Record the learner’s actual response and any help used. These activities do not establish mastery.
The active reflection model names the pair check. That cue supplies a planning example and can support method choice. It does not supply the mathematical explanation.

Record the actual response and assistance. These tasks do not establish mastery.

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Generate number and shape patterns from stated rules. Explain odd/even and growth features using the rule, pairs, or a repeating unit.

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Check understanding

Given 'start at 1, add 3', generate terms and notice they alternate odd/even
Given a shape pattern, predict the next three terms and describe the rule
Explain why starting at 2 and adding 4 always gives even numbers

“If your child is told 'start at 3 and multiply by 2 each time', can they write out the pattern — 3, 6, 12, 24, 48 — and spot any interesting features in how it grows?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Multiplication & Division
Age range: Ages 9–10