MathematicsMathematical ThinkingAges 5–13

Hands-On Problem Solving

Select and use familiar tools (concrete objects, fingers, ten frames) to help solve a mathematical problem

Lesson

Set out your lesson

Choose and explain a tool for solving a small number problem.

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 ten large paper squares or draw ten empty boxes in two rows of five. Small objects are unsuitable for children who mouth them. 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.

Next: Show

Adult extras

What this lesson covers and its limits

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

partial: Select and use familiar tools (concrete objects, fingers, ten frames) to help solve a mathematical problem
One choice among familiar tools; regular self-selection in new contexts is not observed.
partial: Choose cubes, counters, or fingers to help solve an addition or subtraction problem
One choice among familiar tools; regular self-selection in new contexts is not observed.
partial: Use a ten frame to organise objects for counting or comparing
One choice among familiar tools; regular self-selection in new contexts is not observed.
partial: Explain why a particular tool (e.g. cubes rather than fingers) was chosen for a given problem
One choice among familiar tools; regular self-selection in new contexts is not observed.
partial: When {{name}} is working out a maths problem, do they reach for helpful tools — like using their fingers, counters, or a number line — to support their thinking?
One choice among familiar tools; regular self-selection in new contexts is not observed.

One choice among familiar tools; regular self-selection in new contexts is not observed.

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Teaching approaches

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1 approach

Selected Default Gakuva

Choose and explain a tool for solving a small number problem.

Family records and proof options

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Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

View learner plans ($12/mo per learner) See sample family archive

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

NRICH · Practice link — not the full lesson

Primary

Open practice(new tab)

Before you open · source notes

Primary supports Hands-On Problem Solving. An adult previews and guides; this is a learning page, not a scored quiz.

Free educational page, no sign-in required for the tested path.

Before you open

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

Opening this link does not save learning or assess mastery.

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.

NRICH. “Primary.” External page; Gakuva does not copy, host, embed, or redistribute materials.

Unknown — link only

Check understanding

Choose cubes, counters, or fingers to help solve an addition or subtraction problem
Use a ten frame to organise objects for counting or comparing
Explain why a particular tool (e.g. cubes rather than fingers) was chosen for a given problem

“When your child is working out a maths problem, do they reach for helpful tools — like using their fingers, counters, or a number line — to support their thinking?”

Curriculum record

Type: Meta
Subject: Mathematics
Domain: Mathematical Thinking
Age range: Ages 5–13

Standards

ccss-math:MP.5the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G1-A1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G2-A1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G3-A1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G4-A1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-A1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-A1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-A1

Curriculum