MathematicsAlgebraAges 11–12

Substituting into Formulae

Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations

Lesson

Set out your lesson

Replace each variable with its given value, keep grouping and powers, and calculate with units where needed.

Before teaching

Use this short check, then start teaching.

Activity

Ask what 3p and p² mean. Expect 3 × p and p × p. Ask which operation comes first in 2 + 3 × 4. Expect multiplication, with a result of 14. If needed, revisit Algebraic Notation and Order of operations before starting. Signed products are explained again below.

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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Entire curriculum

1858 concepts · 9 subjects

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Teaching approaches

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Selected Default Gakuva

Replace each variable with its given value, keep grouping and powers, and calculate with units where needed.

Family records and proof options

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

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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

Comparing Fractions with the Same Numerators, Assessment Variation

Open practice(new tab)

Before you open · source notes

Comparing Fractions with the Same Numerators, Assessment Variation supports substituting into formulae. 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 “Comparing Fractions with the Same Numerators, Assessment Variation” 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. “Comparing Fractions with the Same Numerators, Assessment Variation.” 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

Substitute positive and negative values into algebraic expressions and evaluate
Substitute values into formulae involving multiple operations and powers
Use correct order of operations when evaluating expressions after substitution

“If a formula says that the area of a triangle is ½ × base × height, can your child substitute in the measurements and calculate the answer correctly?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Algebra
Age range: Ages 11–12

Standards

ccss-math:6.EE.2cuk-nc-2013:KS3.Maths.Alg.2