Fluent addition and subtraction (age 9+)
Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm
Lesson
Set out your lesson
Extend column addition and subtraction to five and six digits, including three addends and exchanges through zeros.
Before teaching
Use this short check, then start teaching.
Use the earlier four-digit lesson first. Ask the learner to align 23,406 and 7,582 with ones together, and identify 10 ten-thousands as 100,000. Stop for place-value support if this is unclear; no timed test is required.
Check readiness directly. Prerequisite availability is not attainment.
Share and support
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.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Making a ten
Before you open · source notes
Making a ten supports fluent addition and subtraction. Not every multi-digit long subtraction.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to remake an addition as a ten-plus fact and finish it.
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. “Making a ten.” 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
- Calculate 34,567 + 28,945 using columnar addition
- Calculate 500,000 − 234,178 using columnar subtraction with multiple exchanges
- Add three five-digit numbers in a single column layout
“Can your child accurately add or subtract large numbers — like '23,846 + 14,579' — using the column method, carrying and borrowing correctly however many columns it takes?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 9–12
Standards