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MathematicsAlgebraAges 11–13

Expanding Single Brackets

Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers

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Teaching Table

Set out your lesson

Multiply every term in one bracket. Keep each sign, then collect like terms.

Activity

Ask the learner to simplify 2x + 3x and to explain why x + 3 cannot be collected. Expect 5x; x and a constant are different kinds of term. Revisit Collecting Like Terms if needed. Ask what 2x means. Expect 2 times x, not a two-digit number. Do not use speed as a readiness test.

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.

  • Signed multiplication is taught here as local support. This is not a full lesson or assessment of the separate Sign Rules for Multiplication topic.

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

Multiply every term in one bracket. Keep each sign, then collect like terms.

Multiply every term in one bracket. Keep each sign, then collect like terms.

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

External links for extra practice. They do not replace Gakuva’s teaching approach.

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Check understanding

  • Multiply a single positive term over a bracket to expand the expression
  • Multiply a negative term over a bracket, correctly handling signs
  • Combine expanding brackets with collecting like terms to simplify fully
“Can your child expand a bracket like 3(2x + 5) by multiplying everything inside, to get 6x + 15?”

Curriculum record

Type
Procedural
Subject
Mathematics
Domain
Algebra
Age range
Ages 11–13

Standards

ccss-math:6.EE.3ccss-math:7.EE.1uk-nc-2013:KS3.Maths.Alg.4b