Maryland Math 4.NOS.E.11
The Standard
Apply understanding of a fraction c/d with d > 1 as a sum of unit fractions (1/d) to decompose a fraction (including fractions greater than 1) into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation. Justify decompositions using visual fraction models and equations (e.g., 3/8 = 1/8 + 1/8 + 1/8 or 3/8 = 1/8 + 2/8 or 2 1/8 = 1 + 1 + 1/8 or 2 1/8 = 8/8 + 8/8 + 1/8).
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 split a fraction into sums of fractions with the same denominator, even when the amount is greater than one whole. They use equal-size pieces to find more than one split, then show each with an equation and a drawing.
What Mastery Looks Like
- Given 11/8, a student writes 11/8 = 8/8 + 3/8 and 11/8 = 6/8 + 5/8. They shade two bars divided into eighths to show that both groupings cover 11 pieces.
Common Misconceptions
- Students may add denominators, writing 3/8 + 2/8 = 5/16. Some think 11/8 cannot be split because it is greater than one whole. Others count unequal pieces as if they were all eighths.
How to Assess It
- On an exit ticket, ask students to write two different sums for 11/8 using only eighths. Have them draw fraction bars to show why both equations work.
Lesson moves
Ways to Teach It
Give pairs two paper bars marked in eighths; have them shade 11 sections, regroup the sections twice, and write both equations.
Ask, 'Why do 8/8 + 3/8 and 6/8 + 5/8 both make 11/8?' Have students explain with a drawing.
Play Fraction Split: flip a card showing 9/6, then race to write three different sums of sixths that equal it.
A pizzeria sells slices that are one eighth of a pizza; ask how 11 slices could be split between two boxes and write two equations.
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Printable 4.NOS.E.11 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).
- 3.NOS.F.10.b
Explain that a fraction 1/d represents one part of a whole that is divided into d equal parts, and that a fraction c/d represents c parts of size 1/d.
- 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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