3.3.D
The Standard
compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students break a fraction into equal unit fractions and join unit fractions to make a given fraction. They use models and equations to show, for example, that 3/4 is three copies of 1/4.
What Mastery Looks Like
- A student can show a fraction with strips, drawings, or a number line and name each equal part. The student can write 3/4 = 1/4 + 1/4 + 1/4 and explain why the denominator stays the same.
Common Misconceptions
- Students may split 3/4 into 1/2 + 1/2 + 1/2, matching the number of parts but not the denominator. They may also think 4/4 is four wholes instead of one whole made from four fourths.
How to Assess It
- Give students a blank fraction strip and ask them to show 4/5, then write it as an addition equation using unit fractions.
Lesson moves
Ways to Teach It
Give pairs fraction strips to build 2/3, 3/5, and 4/4 from separate unit-fraction pieces, then record each addition equation.
Ask students to explain in writing why 3/5 uses three copies of 1/5 rather than five copies of 1/3.
Play Fraction Build: draw a fraction card, collect the matching unit-fraction cards, and earn a point for a correct equation.
Cut a paper sandwich into eight equal pieces, choose a fraction to serve, and write the unit-fraction addition that matches the serving.
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Printable 3.3.D Worksheet
A ready-to-print activity worksheet aligned to 3.3.D, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 4.3.A
represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b
- 4.3.B
decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbo...
- 3.3.C
explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whol...
- 6.2.E
extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0
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