Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A fraction such as 5/6 can be seen as five copies of the unit fraction 1/6 joined together: 1/6 + 1/6 + 1/6 + 1/6 + 1/6. That simple view drives everything in this standard. Adding fractions with the same denominator means joining parts of the same size, so 2/6 + 3/6 = 5/6. Subtracting means separating parts. The denominator names the size of the pieces and stays the same; only the count of pieces changes.
The standard has four parts. Students understand addition and subtraction as joining and separating parts of the same whole; they decompose a fraction into a sum of fractions in more than one way (3/8 = 1/8 + 2/8 = 1/8 + 1/8 + 1/8); they add and subtract mixed numbers with like denominators, often by renaming them as fractions greater than one; and they solve word problems that involve these operations. Visual fraction models and equations are used throughout to show the thinking.
Writing 2/6 + 3/6 = 5/12 is the classic error. Ask what size the pieces are after joining them: still sixths, so the answer is 5/6.
For 3 1/4 - 1 3/4, students may subtract 3/4 - 1/4 instead. Renaming 3 1/4 as 2 5/4 makes the subtraction possible.
Students may believe 5/8 can only be 1/8 + 4/8. Showing several ways to split a fraction strip builds flexibility needed for mixed numbers.
A board is 3 1/4 feet long. Jamal cuts off 1 3/4 feet. How long is the piece that is left?
Answer: The piece left is 1 2/4 feet, which is 1 1/2 feet.
Fraction strips and number lines make the unit fraction idea concrete: hop 1/5 at a time and count the hops. When students add, ask them to say the unit out loud ("two sixths plus three sixths is five sixths") so the denominator is treated as a label for piece size.
Common test formats include decomposition items ("select all equations equal to 5/8") and two-step word problems with mixed numbers. Practice regrouping a whole into fourths, sixths or eighths until it feels natural.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 5/6
Two sixths plus three sixths is five sixths. The pieces stay sixths, so the answer is 5/6.
Answer: A) 5/8 = 2/8 + 3/8
2/8 + 3/8 = 5/8. The other equations either use a different piece size or add up to a different amount.
Answer: 3/10
Seven tenths take away four tenths leaves three tenths, 3/10.
Answer: 4 2/5
Add the wholes: 2 + 1 = 3. Add the fractions: 3/5 + 4/5 = 7/5 = 1 2/5. Total: 3 + 1 2/5 = 4 2/5.
Answer: D) 1 2/4
Regroup 3 1/4 as 2 5/4. Then 2 5/4 - 1 3/4 = 1 2/4 miles.
Answer: A) The denominators were added, but the piece size does not change
Adding fourths to fourths still gives fourths. The correct sum is 3/4.
A full lesson with slides, activities and an exit ticket on adding and subtracting fractions with like denominators, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 4.NF.B.3 with an answer key, ready in about a minute.
Make a worksheet βTurn adding and subtracting fractions with like denominators into a quiz students answer online that marks itself, with a class summary for you.
Build a test βThe denominator tells the size of the pieces. Joining 2 sixths and 3 sixths gives 5 pieces that are still sixths, so only the numerator changes.
Not under this standard. Adding fractions with unlike denominators is a fifth grade expectation in 5.NF.A.1. Fourth graders do add tenths and hundredths under 4.NF.C.5.