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
Share and support
Teaching Table
Set out your lesson
Replace each variable with its given value, keep grouping and powers, and calculate with units where needed.
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.
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.
The triangle and constant-speed formulae are supplied, not derived. Only small values and a square power are used. These fictional calculations are not experimental or measurement evidence.
Record the actual response and assistance. These tasks do not establish mastery.
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Replace each variable with its given value, keep grouping and powers, and calculate with units where needed.
Replace each variable with its given value, keep grouping and powers, and calculate with units where needed.
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.
No additional resources are listed for this topic.
The teaching approach appears above.
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