Maryland Math 4.NOS.E.13.c
The Standard
- 4.NOS.E.13
- Apply and extend previous understandings of multiplication to multiply a fraction by a whole number (b × c/d).
Use understanding of multiplication as equal groups to multiply a fraction by whole number (e.g., interpret b × c/d as b groups of c/d when c/d is greater than or less than 1).
Maryland College and Career Ready Standards for Mathematics (2025) · BUILD FRACTIONS FROM UNIT FRACTIONS BY APPLYING AND EXTENDING PREVIOUS UNDERSTANDINGS OF OPERATIONS ON WHOLE NUMBERS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students make equal groups of a fraction, whether the fraction is less than or greater than 1. They find the total and show how their drawing matches a multiplication equation.
What Mastery Looks Like
- A student can draw 3 groups of 5/4 and find a total of 15/4, or 3 3/4. They can explain why 3 × 2/5 is 6/5, not 6/15.
Common Misconceptions
- Students may multiply the denominator by the whole number, giving 6/15 for 3 × 2/5. Some expect every answer involving a fraction to be less than 1, even when several groups add up to more.
How to Assess It
- Exit ticket: Draw 3 groups of 5/4, then write a multiplication equation and the total. Explain why the denominator stays 4.
Lesson moves
Ways to Teach It
Give students fraction strips and have them build 2 groups of 5/4, then count the fourths in all.
Ask students to draw 3 groups of 2/5 and explain in writing why the total is 6/5, not 6/15.
Have pairs draw a whole-number card and a fraction card, then sketch the groups and write the product.
Show a recipe needing 5/4 cups of oats per batch, and ask students to find the amount for 3 batches.
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Printable 4.NOS.E.13.c Worksheet
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Related Standards
- 4.NOS.E.13.b
Use understanding of multiplication as equal groups to multiply a unit fraction by whole number (e.g., interpret b × 1/d as b groups of 1/d).
- 5.NOS.D.11.b
Multiply a whole number by a fraction (e.g., interpret c/d × b as c/d of b when c/d is greater than or less than 1).
- 5.NOS.D.11
Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × b).
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