Maryland Math 5.NOS.D.12.b
The Standard
- 5.NOS.D.12
- Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.
Apply and extend whole number multiplication strategies (e.g. area models).
Maryland College and Career Ready Standards for Mathematics (2025) · APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF MULTIPLICATION AND DIVISION TO MULTIPLY AND DIVIDE FRACTIONS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use area models to multiply fractions, building on how they used rectangles to multiply whole numbers. They divide a rectangle into equal parts, shade each factor, and count the overlap.
What Mastery Looks Like
- A student can show 2/3 × 3/4 on a rectangle with 12 equal cells. They count 6 overlapping cells and write 6/12 = 1/2.
Common Misconceptions
- Some students count every shaded cell instead of only the overlap. Others draw unequal cells or add the fractions rather than multiply them.
How to Assess It
- Give students a blank rectangle and ask: “Show 2/3 × 3/4 with an area model. Label the overlap and write the product in simplest form.”
Lesson moves
Ways to Teach It
Fold paper into thirds across and fourths down, color two thirds blue and three fourths yellow, then count cells with both colors.
Ask partners: “Why is 2/3 × 3/4 less than 2/3?” Have them point to cells on their grids.
Match cards showing 1/2 × 3/4, 2/3 × 3/4, and 1/3 × 1/2 to prepared overlap grids.
A recipe uses 3/4 cup of flour; draw a grid to find how much flour a 2/3 batch needs.
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Printable 5.NOS.D.12.b Worksheet
A ready-to-print activity worksheet aligned to 5.NOS.D.12.b, with an answer key for the teacher on its own page. No account needed.
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