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MathematicsAddition & SubtractionAges 8–10

Adding and subtracting (age 8+)

Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction

Lesson

Set out your lesson

Set out four-digit addition and subtraction in place-value columns. Explain each exchange and check with the inverse operation.

Before teaching

Use this short check, then start teaching.

Activity

Ask for the value of 6 in 2,643 (600), and for 10 tens in hundreds (1 hundred). Ask for 352 + 126 (478). If place alignment or exchanging is unclear, revisit the two named hard prerequisites. These checks are local readiness, not mastery.

Policy

Check readiness directly. Prerequisite availability is not attainment.

Printer, credit, and teaching notes

Check readiness directly. Prerequisite availability is not attainment.

Start with the readiness check. Use Show, then Guided, then a fresh Try. These linked lessons may need several short sessions; do not impose a speed target. Read the active sheet on screen and answer on plain paper or by typing. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt. Record any hints, scribing or calculation help. Oral explanations are allowed but do not show independent reading or handwriting. Use as much space and time as needed; pause or split the lesson. Keep this adult guide and all keys private. Share only the active learner sheet. Before Try, put Show, Guided work and notes aside. Keep the fresh Try givens available. Give no answer or target method during the first attempt. If help is needed, give it and mark the attempt supported. Review the key after the attempt. Record the actual response and help; do not invent success or infer mastery from one attempt. These are fictional paper or oral mathematics tasks. No personal information, public sharing, purchase, physical experiment or real measurement is required.

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

Next: Show

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Teaching approaches

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1 approach

Selected Default Gakuva

Set out four-digit addition and subtraction in place-value columns. Explain each exchange and check with the inverse operation.

Set out four-digit addition and subtraction in place-value columns. Explain each exchange and check with the inverse operation.

Family records and proof options

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Learning resources

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

Illustrative Mathematics · Practice link — not the full lesson

Valid Equalities?

Open practice (new tab)
Before you open · source notes

True/false equalities support adding and subtracting with the equal sign. Not every algebra equation.

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 to mark one equality true or false and explain both sides.

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. “Valid Equalities?.” 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

  • Set out and solve a columnar addition with up to four-digit numbers
  • Set out and solve a columnar subtraction with exchange across multiple columns
  • Check the answer using estimation or inverse operations
“Can your child line up a sum like '3,842 + 1,765' or '4,301 − 2,658' in columns and work through it correctly — carrying and borrowing across multiple columns?”

Curriculum record

Type
Procedural
Subject
Mathematics
Domain
Addition & Subtraction
Age range
Ages 8–10

Standards

acara-v9:AC9M4N06ccss-math:4.NBT.4the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G4-B2.4uk-nc-2013:Ma/KS2/Y4/AS/1