The 60-second card
The finding
Students who struggle with math learn fractions better when they first learn fractions as sizes, placed on a number line, rather than only as parts of a pizza.
Do this
Teach comparing, ordering, and placing fractions on a 0-to-1 number line before and alongside fraction procedures. Give students who are behind extra small-group time on it.
Best evidence
Five randomized trials of a 12-week small-group program for 4th graders with weak whole-number skills improved fraction understanding and calculation compared with the schools' regular fraction teaching (Fuchs et al. 2017(opens in a new tab)).
5 randomized trials
of a 12-week program for 4th graders at risk in math
The 5-minute brief
Why it works
Pizza-slice models teach fractions as "parts out of a whole," which leads to errors like thinking 1/8 is bigger than 1/6 because 8 is bigger than 6. Placing fractions on a number line shows each fraction is a number with a size. In a follow-up trial, the gains even carried over to decimals without decimals being taught (Malone et al. 2019(opens in a new tab)).
Why it matters. In a large study of U.S. and U.K. students, fraction and division knowledge in 5th grade predicted algebra and overall math in high school, even after accounting for IQ, reading, and family income (Siegler et al. 2012(opens in a new tab)). That study shows a link, not cause, but it is why this sits on the critical path to algebra.
What it looks like
| Grade band | In practice |
|---|---|
| K–2 | Whole numbers on number lines, so the tool is familiar before fractions arrive. |
| 3–5 | Students place 1/2, 1/4, 3/4, then 2/3 and 5/6 on a 0-to-1 line and explain which is larger and why. |
| 6–8 | Number lines carry over to negative numbers, decimals, and percents; quick checks of fraction size before any calculation. |
| 9–12 | Algebra students with fraction gaps get short daily number-line and equivalence practice. |
Common mistakes
- Teaching fractions only with area models, so students never see fractions as numbers.
- Moving to fraction procedures (common denominators, invert and multiply) before students can tell which fraction is larger.
- Waiting until middle school to fix fraction gaps.
What a leader looks for in 5 minutes
- In 3–5 fraction lessons, are number lines in use, not just shaded shapes?
- Can a student in the room tell you whether 3/8 is more or less than 1/2, and why?
What we don't know yet
The trials were with 4th graders at risk in math, taught in small groups by trained tutors. Whether the same approach delivered whole-class works as well is less tested.
Go deeper
- Researcher
- Lynn Fuchs; Robert Siegler
- Translator
- Anna Stokke (Chalk & Talk); Sarah Powell
Also called: number line, fraction sense
Grades and subjects
Sources
- Malone et al. 2019 (opens in a new tab)
edknowledge.stanford.edu
- Siegler et al. 2012, early predictors of high school math (opens in a new tab)
ncbi.nlm.nih.gov
- Fuchs et al. 2017, five fraction trials (opens in a new tab)
files.eric.ed.gov