Browse topics

Curriculum

Explore all 1,590 open curriculum concepts.

Advanced filters
MathematicsAlgebraAges 10–11

Equations with Two Unknowns

Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)

Entire curriculum

1858 concepts · 9 subjects

Loading map…
Continue learning
Share and support
Compare teaching approaches

Teaching approaches

Gakuva’s recommended starting approach is selected. You can still compare every option.

1 approach

Selected Default Gakuva

List ordered pairs that satisfy a two-variable equation and justify that a bounded list is complete.

List ordered pairs that satisfy a two-variable equation and justify that a bounded list is complete.

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

Using lengths to represent equality

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

Using lengths to represent equality supports equations with two unknowns. Not every worksheet pack.

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 explain one step of “Using lengths to represent equality” in their own words.

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. “Using lengths to represent equality.” 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

  • List all whole-number pairs (a, b) where a + b = 12 with a, b > 0
  • Find three pairs that satisfy 2x + y = 20
  • Explain systematically how to generate all integer solutions to a two-variable equation within a given range
“Can your child find different pairs of numbers that both satisfy a rule — for example, all the pairs of whole numbers that add up to 10?”

Curriculum record

Type
Procedural
Subject
Mathematics
Domain
Algebra
Age range
Ages 10–11

Standards

uk-nc-2013:Ma6/2.5d