Fractions as sums of unit fractions
Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)
Lesson
Set out your lesson
“Fractions as sums of unit fractions 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 Fractions as sums of unit fractions, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Fractions as sums of unit fractions, 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 practiceFractions as sums of unit fractions practice
Practice key ideas from Fractions as sums of unit fractions.
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
Making 22 Seventeenths in Different Ways
Before you open · source notes
22/17 is written as sums of unit fractions and other fraction addends. Supports unit-fraction sums, not every mixed-number shortcut.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk for two different sums of fractions that make 22/17, including unit fractions.
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. “Making 22 Seventeenths in Different Ways.” 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
- Express 5/8 as a sum of five copies of 1/8
- Show on a number line how 4/3 is built by iterating 1/3 four times
- Explain why 7/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4
“If you ask your child to show 4/5 as a sum of smaller equal fractions, can they write it out as 1/5 + 1/5 + 1/5 + 1/5?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Fractions
- Age range
- Ages 8–10
Standards