Whole-class sequence, grades 3–5
- Whole numbers first. Students place whole numbers on a 0-to-10 line until it's routine.
- Unit fractions on 0-to-1. Partition the line into equal parts; place 1/2, 1/4, 1/3. "The fraction is a point on the line, a distance from zero."
- Compare by position. Which is closer to 1? Which is more than 1/2? Use the benchmark 1/2 constantly.
- Equivalence on the line. 2/4 and 1/2 land on the same point.
- Past 1. Extend to 0-to-2 and 0-to-5 lines; improper fractions and mixed numbers have places too.
- Then procedures, with estimation first: "Will 1/2 + 1/3 be more or less than 1?"
The federal fractions practice guide rates number-line instruction as having moderate evidence, and recommends starting with fully labeled lines and gradually removing labels (Marzano summary of IES Rec. 2(opens in a new tab)).
Misconceptions and the fix
| What students say | What it shows | Fix |
|---|---|---|
| "1/8 is bigger than 1/6 because 8 is bigger" | Treating top and bottom as separate whole numbers | Place both on the same line; same-size whole cut into more parts |
| "1/2 + 1/3 = 2/5" | Adding parts like whole numbers | Estimate first: 2/5 is less than 1/2, so it can't be right |
| "Fractions are always less than 1" | Only seen part-of-a-pizza models | Number lines running to 2 and beyond |
Intervention version (the tested program)
The trials used Fraction Face-Off!: 12 weeks, three 35-minute sessions a week, groups of two or three, led by trained tutors (Stanford NSSA(opens in a new tab); Blueprints(opens in a new tab)). Students are chosen from 4th graders with weak whole-number skills.
Four-week try-it plan (grade 4 team)
| Week | Do | Check |
|---|---|---|
| 1 | Daily 5-minute number-line warm-up: place three fractions | Can students place 1/2, 1/4, 3/4 accurately? |
| 2 | Comparing with benchmark 1/2 | Exit ticket: "Is 3/8 more or less than 1/2? Show it." |
| 3 | Equivalence on the line | Can students show 2/4 = 1/2 on a line? |
| 4 | Screen for students still struggling; start small-group intervention | Number of students needing the intervention version |
Sources
- Marzano summary of IES Rec. 2 (opens in a new tab)
marzanoresearch.com
- Fraction Face-Off! program profile (Stanford NSSA) (opens in a new tab)
nssa.stanford.edu
- Blueprints for Healthy Youth Development: Fraction Face-Off! rating (opens in a new tab)
blueprintsprograms.org