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)
Lesson
Set out your lesson
List ordered pairs that satisfy a two-variable equation and justify that a bounded list is complete.
Before teaching
Use this short check, then start teaching.
Ask what the equal sign in x + y = 6 states. Expect both sides have the same value. Ask the learner to check x = 2, y = 4 in it. Expect 2 + 4 = 6. Revisit Writing Algebraic Equations if a letter is treated as a label rather than a number. Use Substituting into Formulae for extra support.
Check readiness directly. Prerequisite availability is not attainment.
Share and support
Family records and proof options
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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
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 openAsk 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