Understanding fractions
Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2
Lesson
Set out your lesson
“Understanding fractions here means writing simple fraction-of-a-set statements such as 1/2 of 6 = 3, and seeing that 2/4 and 1/2 name the same share of a whole. Equal parts of a set or a folded shape make the writing meaningful. We will share a set, fold equivalent shares, then check a fresh fraction.”
Bring to the table
- About 12 large counters, crackers, or paper squares (parent keeps tiny pieces away from mouths)
- Paper rectangles for folding halves and fourths
- Pencil
Extra for the adult
Worked example. 1/2 of 6 = 3 because six split into two equal groups leaves three in each. 2/4 = 1/2 on the same-size whole because two fourths cover the same amount as one half.
Optional challenge. For Understanding fractions, write 1/2 of 12 and show another equivalent pair such as 2/4 and 1/2 on a circle. Optional: invent a “half the crackers” kitchen story and write the fraction equation.
What to notice. Keep one parent note: fraction equations written; equivalence shown; support used. A photo of folds alone cannot record the written fraction. This session samples a few items, not mastery of all simple fractions.
Share and support
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Teaching approaches
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1 approach
Understanding fractions here means writing simple fraction-of-a-set statements such as 1/2 of 6 = 3, and seeing that 2/4 and 1/2 name the same share of a whole. Equal parts of a set or a folded shape make the writing meaningful. We will share a set, fold equivalent shares, then check a fresh fraction.
Spend about 12 minutes writing simple fractions of a set and showing that 2/4 equals 1/2 with folds or drawings, then checking one new fraction statement.
Family records and proof options
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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
Geometric pictures of one half
Before you open · source notes
Shapes are shaded to show one half as equal parts of a whole. Supports early fraction meaning, not every number-line fraction.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to point to a picture that shows one half and explain why the parts are equal.
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. “Geometric pictures of one half.” 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
- Write 1/2 of 10 = 5
- Explain that 2/4 is the same as 1/2 using a diagram
- Calculate simple unit fractions of quantities and write the result
“If your child has 6 strawberries and eats half of them, can they write that as "1/2 of 6 = 3" — and explain why 2/4 and 1/2 are the same amount?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Fractions
- Age range
- Ages 6–7
Standards