Maryland Math 4.NOS.D.9.b

Math4th GradeNumber and Operation Sense

The Standard

Explain why fractions are equivalent (c/d = (n × c)/(n × d)).

Maryland College and Career Ready Standards for Mathematics (2025) · EXTEND UNDERSTANDING OF FRACTION EQUIVALENCE AND ORDERING.

Teacher's field guide

What Students Need to Do: Students split each part of a fraction into the same number of smaller, equal parts. They explain why the number of shaded parts changes but the amount shaded stays the same.
What Mastery Looks Like: A student can draw 2/3 and 6/9 using bars of the same size. They show that splitting each third into three pieces gives six shaded ninths, with no change in the shaded amount.
Common Misconceptions: Students may multiply only the numerator or add the same number to the numerator and denominator. Some think a fraction with a larger denominator must be smaller, even when the numerator changes too.
How to Assess It: Exit ticket: Draw a bar to show why 2/5 = 6/15. Write one sentence explaining what happened to each fifth.

Lesson moves

Fold a paper strip into four equal parts, shade three, then split each part in half and label 3/4 and 6/8.
Ask: Why does splitting every third into two pieces change 2/3 to 4/6 without changing the shaded amount?
Play a card match with fraction bars and labels such as 1/2, 2/4, and 3/6; require an explanation for each match.
Draw a measuring cup marked in eighths and show why 3/4 cup of oats reaches the 6/8 mark.

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