NY Next Generation Math NY-3.NF.3.a

Math3rd GradeExplain equivalence of fractions and compare fractions by reasoning about their size.

The Standard

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students recognize two fractions as equivalent when they name the same amount or the same point on a number line. They use fractions with denominators 2, 3, 4, 6, and 8.
What Mastery Looks Like: The student shows that one half and two fourths cover the same amount and land at the same point. The student explains equality using a shared whole.
Common Misconceptions: Students may compare numerators and denominators separately or ignore whether the wholes match. They may think different fraction names must represent different amounts.
How to Assess It: Show one half and two fourths on equal fraction strips and a number line. Ask whether they are equivalent and why.

Lesson moves

Fold equal paper strips into halves, fourths, and eighths, then align pieces that cover the same length.
Ask students why fractions at the same number-line point must be equal even when their names differ.
Play equivalent-or-not sort using area models and number-line points with permitted denominators.
Compare equal portions of same-size recipe bars cut into different numbers of pieces.

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