Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 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 is built from a single equal piece. When a whole is cut into b equal parts, one of those parts is the unit fraction 1/b: cut a granola bar into 4 equal pieces and one piece is 1/4. A fraction like 3/4 is then three of those quarter pieces put together. The denominator tells the size of the piece by saying how many make the whole, and the numerator counts how many pieces you have.
The word equal carries the meaning. A shape cut into 4 pieces of different sizes does not show fourths. Students also discover a surprising fact: the more pieces a whole is cut into, the smaller each piece becomes, so 1/8 is less than 1/3. Third grade work uses denominators of 2, 3, 4, 6 and 8, with area models like rectangles and circles and with length models like fraction strips. Thinking of 5/6 as five copies of 1/6 is the foundation for everything that follows, from number lines to adding fractions in fourth grade.
A circle cut into 3 uneven slices is often labeled thirds. Ask students to check that every part is the same size before writing a fraction.
Because 8 is bigger than 4, children may think 1/8 is bigger than 1/4. Fold strips into 4 and 8 parts and compare a single piece of each.
A shape with 2 shaded and 3 unshaded parts is sometimes called 2/3. The denominator counts all the equal parts in the whole, so the fraction is 2/5.
Students may read 3/4 as "3 and 4" rather than one number. Use language like "three one-fourths" to keep it a single quantity.
A rectangle is split into 6 equal parts and 5 parts are shaded. Name the unit fraction and the shaded fraction.
Answer: The unit fraction is 1/6; the shaded part is 5/6 (five sixths).
Folding paper strips and cutting play dough or paper "pizzas" helps students feel what equal parts mean. Use precise language like "one fourth" and "three one-fourths" before writing symbols. Always show non-examples, such as shapes with unequal parts, and ask students to argue why they are not fourths.
Assessment items show shaded shapes and ask for the fraction, ask students to shade a given fraction, or ask which picture shows a given fraction. Some include unequal partitions as distractors, so practice judging equal parts.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: D) 1/8
One part out of 8 equal parts is the unit fraction 1/8.
Answer: 3/4
There are 4 equal parts, each 1/4, and 3 are shaded: three fourths, or 3/4.
Answer: B) 5
5/6 is 5 copies of the unit fraction 1/6.
Answer: C) 1/3
The fewer equal parts a whole is cut into, the bigger each part. Thirds are bigger than fourths, sixths or eighths.
Answer: D) No, because the pieces are not equal
Fourths must be 4 EQUAL parts. With unequal pieces we cannot name the shaded part as 1/4.
Answer: 2/8 (also accepted: 1/4)
There are 2 + 6 = 8 equal parts in the whole, and 2 are shaded, so 2/8 is shaded (the same amount as 1/4).
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
A full lesson with slides, activities and an exit ticket on understanding unit fractions, pitched to grade 3 and editable in PowerPoint or Google Slides.
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Build a test βGrade 3 fraction standards limit denominators to 2, 3, 4, 6 and 8, so models stay simple to draw and compare.
A fraction with a numerator of 1, such as 1/3 or 1/8. It is one of the equal parts that a whole is divided into, and every other fraction is built from unit fractions.