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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)

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.

Activity

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.

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

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

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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

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