Montana Math MT.3.NF.3

Math3rd GradeNumber and Operations – Fractions

The Standard

Understand the equivalence of fractions in special cases and compare fractions by reasoning about their size by: Understanding two fractions as equivalent if they are the same size or the same point on a number line, Recognizing and generating simple equivalent fractions and by demonstrating or justifying why the fractions are equivalent, Writing whole numbers as fractions, recognizing fractions that are equivalent to whole numbers, and locating them on a number line, Comparing two fractions with the same numerator or the same denominator by reasoning about their size and recognizing that comparisons are valid only when the two fractions refer to the same whole, and Recording the results of fraction comparisons with the symbols >, =, or < and justifying the conclusions.

2026 Montana Mathematics Content Standards

Teacher's field guide

What This Standard Means

What Students Need to Do: Students use fraction strips and number lines to show when fractions name the same amount. They write whole numbers as fractions. They compare fractions with matching numerators or denominators, use >, <, or =, and explain why the wholes must be the same size.
What Mastery Looks Like: A student places 1/2 and 2/4 at the same point on a number line and explains why they are equal. They write 2 as 8/4 and place it at 2. They explain why 3/4 > 2/4 and 1/3 > 1/4 when the wholes are the same size.
Common Misconceptions: Students may think 1/4 is bigger than 1/3 because 4 is bigger than 3. They may compare pieces from different-sized circles as if the wholes were the same size. Some think a fraction cannot equal 1 or 2.
How to Assess It: Exit ticket: On one number line from 0 to 1, mark 1/2, 2/4, and 4/4, then write which pair is equal. Compare 1/3 and 1/4 using a symbol and explain why the wholes must be the same size.

Lesson moves

Ways to Teach It

Fold two equal paper strips into halves and fourths, then line up 1/2 and 2/4 and mark both on a number line.
Show a half of a small paper circle and a third of a large circle; ask why these pieces cannot prove 1/2 > 1/3.
Deal pairs of fraction cards with matching numerators or denominators; partners place >, <, or = between them and explain with sketches.
For a recipe, pour two 1/4-cup scoops of water into a 1/2-cup measure and write the matching fractions.

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