MathematicsNumber Representation & Place ValueAges 10–11

Place Value × 10 and ÷ 10

Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left

Lesson

Set out your lesson

Explain how a digit’s value changes between neighbouring places and across several places.

Before teaching

Use this short check, then start teaching.

Activity

Learner readiness not observed. Ask for the values of the digit 3 in 30 and 3. If the values are not distinguished from the digit name, revisit the ×10 relationship first.

Policy

Check learner readiness separately; the existence of a prerequisite lesson is not evidence of attainment.

Printer, credit, and teaching notes

Check learner readiness separately; the existence of a prerequisite lesson is not evidence of attainment.

Estimated Minutes

20–30; split if useful

Sequence

Use S for the model, G for supported practice and T for a fresh attempt.
Optional pencil and scrap paper only. All scenarios, charts and blanks are supplied.
Put S, G and all adult keys away before T. Open only the T learner sheet.
Discuss the reasoning; use the adult key afterward and record only actual support and responses.

No Printer

No printer, purchases, cutting, login or installation required. Use one sheet on screen at a time; answer aloud or write only responses on scrap paper.

Safety

Pause if tired or frustrated. Fictional contexts need no personal information, travel, measuring equipment or real purchases. Participation is optional.

Access

Read prompts aloud without explaining answers; allow pointing, speech, zoom or adult scribing. Record adaptations separately from independent written evidence.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

Adult extras

Teaching limits and safe use

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

No learner results or lesson efficacy have been established.
Canonical assessment contains an arithmetic error: 50 is 100 times 0.5, not 10 times. Canonical text is preserved as provenance but that clause is blocked as written; corrected reasoning is taught separately.

Record actual responses, assistance and access mode; never invent observations or infer mastery.

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Entire curriculum

1858 concepts · 9 subjects

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Teaching approaches

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1 approach

Selected Default Gakuva

Explain how a digit’s value changes between neighbouring places and across several places.

Family records and proof options

Keep a record of your learning

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.

Illustrative Mathematics · Practice link — not the full lesson

Party Favors

Open practice(new tab)

Before you open · source notes

Party Favors supports place-value grouping that prepares ×10 and ÷10 thinking. Not every fraction multiplication rule.

Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.

Before you open

Ask the learner how a group of ten changes the value of a digit.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.

Illustrative Mathematics. “Party Favors.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.

CC BY-NC-SA 4.0 — link only

Check understanding

Explain that the 4 in 0.04 is 1/10 of the 4 in 0.4
State that a digit moving one place left is ×10 and one place right is ÷10
Compare the value of the 6 in 6,000 and in 0.006

“Can your child explain that in 4.56, the digit 5 is worth 5 tenths — ten times less than the 5 in 54, and ten times more than the 5 in 0.056?”

Curriculum record

Type: Conceptual
Subject: Mathematics
Domain: Number Representation & Place Value
Age range: Ages 10–11

Standards

ccss-math:5.NBT.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-B2.3