Collecting Like Terms
Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence
Share and support
Teaching Table
Set out your lesson
Combine only terms with the same variable part and power, keep their signs and explain why the new expression is equivalent.
Ask for the coefficient in −x and the signed terms in 3x − 2. Expect −1, and 3x with −2. Check 2 − 5: expect −3. If signed addition is unfamiliar, use a number line drawn from −6 to 6: start at 2 and move five unit steps left to −3. Practise signed whole-number sums before the full lesson; mark that support.
Check readiness directly. Prerequisite availability is not attainment.
Use the supplied sheets in order: Show, Guided, then Try. Start with the readiness check. This chain may need several short sessions. Do not set a speed target. Read the active sheet on screen and use plain paper or a keyboard. No printer, cutting, purchase or internet is needed. The adult may read the exact prompt, but must record any hints, scribing or calculation help. Oral reasoning is allowed; it does not show independent reading or handwriting. Pause or split the lesson if needed. Keep the adult guide and keys private. Share the Show model during teaching. Before Try, put Show, Guided work and notes aside. Leave 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. Discuss the keys after the attempt; do not invent a learner result. These are paper or oral mathematics tasks. No personal data, public sharing, purchase, real-world measurement or experiment 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.
No bracket expansion or factorisation is taught. Signed-number readiness is required. A single numerical check is not a proof of an identity.
Record the actual response and assistance. These tasks do not establish mastery.
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Teaching approaches
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1 approach
Combine only terms with the same variable part and power, keep their signs and explain why the new expression is equivalent.
Combine only terms with the same variable part and power, keep their signs and explain why the new expression is equivalent.
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
- Identify like terms in an algebraic expression
- Combine like terms involving positive and negative coefficients
- Simplify expressions involving multiple variables and constant terms
“If your child sees an expression like "5a + 3b + 2a," can they simplify it by collecting the like terms to get "7a + 3b"?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 11–12
Standards