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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)

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Teaching Table

Set out your lesson

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

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.

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.

Record the actual response and assistance. These tasks do not establish mastery.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.

Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

  • Only bounded integer ranges and linear rules are used. Simultaneous equations and unbounded solution sets are not covered. Signed subtraction is local support, not a full negative-number lesson.

Record the actual response and assistance. These tasks do not establish mastery.

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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

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

Learning resources

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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