Maryland Math 5.NOS.D.13.b
The Standard
- 5.NOS.D.13
- Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factors greater than 1.
Apply and extend whole number multiplication strategies (e.g. area model, partial products).
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 split a factor into parts, then multiply each part by the other factor. They use partial products or a labeled area model to find the total.
What Mastery Looks Like
- For 1 1/2 × 3/4, a student finds 3/4 + 3/8 = 1 1/8. Their rectangle shows both sections, and they can explain why the areas add.
Common Misconceptions
- Some students split 1 1/2 into 1 and 1/2 but multiply only one part by 3/4. Others add the original factors instead of adding the partial products.
How to Assess It
- Exit ticket: Draw and label an area model for 1 1/2 × 2/3. Write the two partial products and the total. Look for 2/3 + 1/3 = 1.
Lesson moves
Ways to Teach It
On grid paper, use four squares per unit side to draw a 1 1/2 by 3/4 rectangle, then label its two sections.
Ask, "Why does (1 + 1/2) × 3/4 equal 3/4 + 3/8?" Have partners explain using a labeled rectangle.
Prepare product, area model, and partial-product cards for 1 1/2 × 2/3 and 1 1/4 × 2/5; pairs race to match triples.
A garden bed is 1 1/2 meters long and 3/4 meter wide; students sketch sections and find its area.
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Printable 5.NOS.D.13.b Worksheet
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Related Standards
- 4.NOS.B.5.b
Use strategies based on place value (e.g., partial products) to multiply.
- 4.NOS.E.12.c
Apply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compensation, properties of operations, the i...
- 5.NOS.B.7.c
Use strategies based on place value (e.g., partial products, partial quotients) to multiply and divide.
- 5.NOS.D.12.b
Apply and extend whole number multiplication strategies (e.g. area models).
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