Equivalent Fractions
Same amount, different name. 2/4 is 1/2.
New to fractions? Start here.
A short lesson where one bar gets cut up while you watch, so you can see for yourself that one half and two quarters are the same amount. About about 5 minutes.
Show me how fractions work →
Why are one half and two quarters the same?
For grown-ups
- How long: 10 to 15 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
- When they get one wrong: the page shows the working. Read it together rather than moving straight on. Feedback that explains is worth several times more than feedback that only marks right or wrong, and that gap is wider in maths than in any other subject.
- Not timed: thinking time is the point of a book. Let silences run.
- Print it too: doing the same problems on paper a few days later is worth more than doing twice as many today.
What this practises
Recognising and generating equal fractions, and simplifying to lowest terms.
Equivalence is the hinge between placing a fraction on a line and doing arithmetic with unlike denominators. Without it, finding a common denominator is a memorised ritual with no meaning attached, and it collapses under any variation.
- The underlying idea
- Equivalence: different names for the same position on the line.
- Where this sits in Illustrative Mathematics
- 4th grade Unit 2: Fraction Equivalence and Comparison
- Sources
- Fuchs et al. (2013) · What Works Clearinghouse (2020) · Institute of Education Sciences / What Works Clearinghouse (2021) all references →
Related measured skills: ALPACA · Elementary operations, MagPI · Number line estimation. What this means