Fraction Foundry
Common denominators, then the four operations.
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
Adding, subtracting, multiplying and dividing fractions with unlike denominators.
The four operations on fractions with unlike denominators. Answers are compared as exact fractions rather than decimals, so 19/12 and 1 7/12 are both accepted and nothing is ever wrong by a rounding error.
- The underlying idea
- Operating on fractions requires a common unit — the reason common denominators exist.
- Where this sits in Illustrative Mathematics
- 5th grade Unit 2: Fractions as Quotients and Fraction Multiplication · 5th grade Unit 3: Multiplying and Dividing Fractions · 5th grade Unit 6: More Decimal and Fraction Operations
- Sources
- Fuchs et al. (2013) · What Works Clearinghouse (2020) · Institute of Education Sciences / What Works Clearinghouse (2021) all references →
Related measured skill: ALPACA · Elementary operations. What this means