Maryland Math 5.NOS.D.11.b
The Standard
- 5.NOS.D.11
- Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × 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).
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 whole number into equal parts, then take the number of parts named by the fraction. They use a drawing or equation to find the product and tell whether it is less or greater than the starting number.
What Mastery Looks Like
- A student finds 3/4 of 12 by making four groups of 3, then taking three groups to get 9. They find 5/4 of 12 by taking five groups of 3 to get 15, and explain why that answer is greater than 12.
Common Misconceptions
- Students may divide by the numerator instead of the denominator, or stop after finding one fourth. They may think five fourths of 12 is impossible because the fraction is greater than one.
How to Assess It
- Exit ticket: Find 3/4 of 12 and 5/4 of 12. Draw equal groups to show both answers.
Lesson moves
Ways to Teach It
Give pairs 24 counters; have them make four groups of 3, then use the groups to show 3/4 and 5/4 of 12.
Ask: Why is 3/4 of 12 less than 12, while 5/4 of 12 is greater?
Give pairs whole-number cards labeled 8, 12, and 16 and fraction cards labeled 1/4, 3/4, and 5/4; partners draw and check each product.
Give students a recipe using 8 cups of broth; have them write the amounts needed for 3/4 and 5/4 of the recipe.
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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
Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × b).
- 4.NOS.E.13.c
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 ...
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