Fraction Notation
Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole
Lesson
Set out your lesson
“A fraction is a number that names equal parts of one or more wholes. The denominator tells the size of each equal part, and the numerator tells how many of those parts we have; when the numerator is larger, a fraction can be greater than one whole.”
Bring to the table
- Paper
- Pencil
- 8 small objects such as buttons or blocks
Extra for the adult
Worked example. Six counters split into 3 equal groups have 2 counters in each group. One group is 1/3 of the whole set; two groups are 2/3.
Optional challenge. Use two groups of 4 objects as two wholes. Represent 5/4 and connect it to the mixed number 1 1/4.
What to notice. Save a photo of one correctly grouped set beside its written fraction, or a short note recording how your child explained the numerator and denominator.
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
A fraction is a number that names equal parts of one or more wholes. The denominator tells the size of each equal part, and the numerator tells how many of those parts we have; when the numerator is larger, a fraction can be greater than one whole.
Spend 10 minutes building and labeling halves, thirds, and fourths with small objects. Divide each set into equal groups, then write the matching fraction.
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
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Find 1
Before you open · source notes
Locating 1 on a fraction number line supports fraction notation. Not every mixed-number conversion.
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 1 and name one unit fraction mark on the line.
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. “Find 1.” 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
- Point to and name the numerator and denominator in any given fraction and explain what each tells you
- Correctly classify fractions as unit, proper, improper, or mixed number with an example of each
- Explain in own words why 2/4 and 1/2 are equivalent fractions
“If your child saw the fraction 3/4 written down, could they point to the numerator and the denominator — and explain what each number actually means?”
Curriculum record
- Type
- Language
- Subject
- Mathematics
- Domain
- Fractions
- Age range
- Ages 6–9
Standards