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MathematicsAlgebraAges 11–13

Expressions & Equations Vocabulary

Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)

Lesson

Set out your lesson

Distinguish expressions, equations and inequalities. Identify terms, coefficients and factors, and explain their different roles.

Before teaching

Use this short check, then start teaching.

Activity

Ask what 5x means and what x² means. Expect 5 × x and x × x. Ask whether 5 + 2 = 7 says the two sides have equal value. If the learner cannot read the notation, revisit Algebraic Notation before introducing more labels.

Policy

Check readiness directly. Prerequisite availability is not attainment.

Printer, credit, and teaching notes

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.

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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Distinguish expressions, equations and inequalities. Identify terms, coefficients and factors, and explain their different roles.

Distinguish expressions, equations and inequalities. Identify terms, coefficients and factors, and explain their different roles.

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

Halves, thirds, and sixths

Open practice (new tab)
Before you open · source notes

Halves, thirds, and sixths supports expressions & equations vocabulary. 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 “Halves, thirds, and sixths” 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. “Halves, thirds, and sixths.” 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

  • Define and distinguish between expression, equation, and inequality
  • Identify terms, coefficients, and factors in algebraic expressions
  • Use the vocabulary of algebra precisely in mathematical discussions
“Can your child explain the difference between an expression like "3x + 2," an equation like "3x + 2 = 11," and an inequality like "3x + 2 > 11"?”

Curriculum record

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

Standards

ccss-math:6.EE.2bccss-math:6.EE.6the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-C2.1uk-nc-2013:KS3.Maths.Alg.3