DMS · School Lab · Teacher card
Fraction Workshop
The big question: If you split a whole into more equal parts, does each part get bigger or smaller?
Goal: Children split a whole into equal parts and use a model to show that the more equal parts there are, the smaller each part is.
In the lesson
Lesson flow
| Step | What children do | min |
|---|---|---|
| 1 · Ready? | Meets the paper strips, the cake model, the cutting ruler and the number line. | ≤ 1 |
| 2 · What do I know? | Shows what they think about “How do two siblings share one apple? Is it fair?” | 1 |
| 3 · In everyday life | Thinks about flatbread, a chocolate bar and half a loaf of bread. | 1 |
| 4 · Predict | Predicts at their grade: 2 or 4 equal parts (grade 2), is an unequal piece a quarter (grade 3), is 1/3 or 1/8 bigger (grade 4)? | 1–2 |
| 5 · Try and observe | The strips are split and the pieces stacked; the piece they expected to be bigger turns out smaller. | 2–5 |
| 6 · Why? | Sees “more equal parts, smaller parts” with strips and, in grades 3–4, with symbols. | 2–4 |
| 7 · Try something new | Hunts for equal parts, changes the numerator and denominator, or places fractions on the number line. | 2–6 |
| 8 · My explorer notebook | Picks which of three models shows “a quarter”; the one with four unequal pieces is the trap. | 1–3 |
| Off-screen activity, discussion and wrap-up | ≈ 15 | |
Class prediction vote
If we split one strip into 3 equal parts and another into 8, which part is bigger?
Discussion questions
- Why did the parts get smaller when there were more of them?
- What if we split the strip into 100 equal parts?
- How can we tell the parts are equal?
Avoid saying: “8 is bigger than 3, so an eighth is bigger too.”
Say instead: “The whole stays the same: the more equal parts we cut, the smaller each part.”
Off-screen activity for the teacher's desk: Folding strips
Fold same-length paper strips into 2, 4 and 8 and cut along the folds. Stack the pieces on the teacher's desk to compare them, and show one unequal cut too.
You need: Paper strips of the same length · Scissors · Colored pencils
Details
Grades and learning outcomes
- Grade 2: MAT.2.1.7 (Maarif Model 2026)
- Grade 3: MAT.3.1.9 (Maarif Model 2026), MAT.3.1.10 (Maarif Model 2026), MAT.3.1.11 (Maarif Model 2026)
- Grade 4: M.4.1.6.1 (2018 curriculum), M.4.1.6.2 (2018 curriculum), M.4.1.6.4 (2018 curriculum), M.4.1.7.1 (2018 curriculum) · Equivalent from 2027–28: MAT.4.1.6, MAT.4.1.7, MAT.4.1.8, MAT.4.1.9, MAT.4.1.11
Scope
Grade 2 uses no fraction symbols and grade 3 does not compare fractions. No realistic food textures while the idea is being built.
Misconceptions
- “A unit fraction with a bigger denominator is bigger (1/8 > 1/3).” (grade 4) → Two equal strips are split into 3 and 8 equal parts; stacked, 1/3 sticks out past 1/8.
- Calling unequal pieces “a half”, “a quarter” or “one fourth”. → Stacked, the pieces are clearly not equal; only equal parts get these names.
Getting ready
- Open the lab on the board and pick the grade.
- For the screen-free activity: two or three paper strips of the same length per pupil.
- In grade 2, don't write symbols like ½ on the board; say “half” and “quarter”.
This lab is mapped to learning outcomes M.4.1.6.1, M.4.1.6.2, M.4.1.6.4 and M.4.1.7.1 of the Turkish Ministry of National Education's 2018 Mathematics curriculum. It has not been reviewed or approved by the Ministry of National Education (MEB) or its Board of Education (TTKB).
This lab is mapped to learning outcomes MAT.2.1.7, MAT.3.1.9, MAT.3.1.10 and MAT.3.1.11 of the Turkish Ministry of National Education's Türkiye Century Maarif Model Mathematics curriculum (2026 version). It has not been reviewed or approved by the Ministry of National Education (MEB) or its Board of Education (TTKB).
From the 2027–28 school year, the grade 4 equivalent in the Türkiye Century Maarif Model is MAT.4.1.6, MAT.4.1.7, MAT.4.1.8, MAT.4.1.9 and MAT.4.1.11.