MathematicsMathematical ThinkingAges 5–9

Finding efficient methods

Notice when a calculation or pattern repeats and use this to count more efficiently or predict results

Lesson

Set out your lesson

Use repeated number changes to predict rather than recount.

Before teaching

Activity

Can discuss the supplied example in an accessible mode; adapt directions without supplying the target answer.

Policy

Check the learner can follow the model with support before moving on. Source prerequisite ordering is not learner mastery; return to prerequisite work when needed.

Printer, credit, and teaching notes

Use the small structured chart; its rows are a 1–100 chart convention, not a zero-start chart. Open S first, G together, then T alone; put S and G away before T. Keys stay adult-only. No purchase or printing is required; an unavailable physical observation remains pending, not passed.

Materials are ready in each step. Use them on screen or print just the current step. Put teaching examples aside before the learner tries.

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Adult extras

What this lesson covers and its limits

These are bounded opportunities, not learner attainment. Partial and blocked source requirements remain so.

partial: Notice when a calculation or pattern repeats and use this to count more efficiently or predict results
Canonical odd/even pattern clause is clarified: twos preserve parity, not alternate it. Efficiency on these examples is not general fluency.
partial: Notice that skip counting by 2s follows a repeating odd/even pattern
Canonical odd/even pattern clause is clarified: twos preserve parity, not alternate it. Efficiency on these examples is not general fluency.
partial: Recognise that adding 1 to any number always gives the next counting number
Canonical odd/even pattern clause is clarified: twos preserve parity, not alternate it. Efficiency on these examples is not general fluency.
partial: Use a repeated pattern (e.g. +10 on a hundred chart always moves down one row) to predict answers
Canonical odd/even pattern clause is clarified: twos preserve parity, not alternate it. Efficiency on these examples is not general fluency.
partial: When {{name}} is counting or doing repeated additions, have they started to notice the pattern — like "5, 10, 15, 20…" — and used it to predict the next number without counting one by one?
Canonical odd/even pattern clause is clarified: twos preserve parity, not alternate it. Efficiency on these examples is not general fluency.

Canonical odd/even pattern clause is clarified: twos preserve parity, not alternate it. Efficiency on these examples is not general fluency.

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Use repeated number changes to predict rather than recount.

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Learning resources

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NRICH · Practice link — not the full lesson

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Before you open · source notes

Primary supports Finding efficient methods. An adult previews and guides; this is a learning page, not a scored quiz.

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Ask the learner one fact they learned and one question they still have.

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Source, access and review notes

Public NRICH page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.

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Check understanding

Notice that skip counting by 2s follows a repeating odd/even pattern
Recognise that adding 1 to any number always gives the next counting number
Use a repeated pattern (e.g. +10 on a hundred chart always moves down one row) to predict answers

“When your child is counting or doing repeated additions, have they started to notice the pattern — like "5, 10, 15, 20…" — and used it to predict the next number without counting one by one?”

Curriculum record

Type: Meta
Subject: Mathematics
Domain: Mathematical Thinking
Age range: Ages 5–9

Standards

ccss-math:MP.8the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G1-B1.5the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G1-C1.4the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G2-C1.4the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G3-C1.4

Curriculum