Multiplication as scaling
Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1
Lesson
Set out your lesson
“Multiplication as scaling means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper strips or a folded circle
- Pencil and labels (1/2, 1/4)
Extra for the adult
Worked example. Fold a strip in half: each piece is 1/2 of the whole.
Optional challenge. For Multiplication as scaling, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Multiplication as scaling, not mastery.
Share and support
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.
Practice this concept
Start practiceMultiplication as scaling practice
Practice key ideas from Multiplication as scaling.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Running a Mile
Before you open · source notes
Comparing run times as scaling supports multiplication as scaling. Not every area model.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk which runner is faster using a scale-factor comparison.
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. “Running a Mile.” 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
- Predict without calculating whether 3/4 × 7 is greater or less than 7
- Explain why multiplying by 5/3 makes a number larger and multiplying by 2/5 makes it smaller
- Relate multiplying a/b by n/n = 1 to the principle of fraction equivalence
“If your child multiplies 20 by 1/4, can they predict whether the answer will be bigger or smaller than 20 — and explain why, before doing the calculation?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Fractions
- Age range
- Ages 10–11
Standards