Virginia SOL 3.NS.3.d
The Standard
Compose and decompose fractions (proper and improper) with denominators of 2, 3, 4, 5, 6, 8, and 10 in multiple ways (e.g., 7 4 = 4 4 + 3 4 or 4 6 = 3 6 + 1 6 = 2 6 + 2 6 ) with models.
Virginia Standards of Learning for Mathematics · The student will use mathematical reasoning and justification to represent and compare fractions (proper and improper) and mixed numbers with denominators of 2, 3, 4, 5, 6, 8, and 10), including those in context.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students join unit fractions and other fractional parts to make a given fraction. They split proper and improper fractions in several ways and show each equation with a model.
What Mastery Looks Like
- Students use fraction strips, number lines, or area models to show a fraction split into smaller fractions. They write several correct addition equations for the same fraction, including improper fractions.
Common Misconceptions
- Students may add denominators when combining parts, such as claiming 1/4 + 2/4 = 3/8. They may divide models into unequal parts or think an improper fraction cannot be split into a whole and a fraction.
How to Assess It
- Ask students to draw a model for 7/4 and write two different addition equations that match it. Have them label each part of the model.
Lesson moves
Ways to Teach It
Use fraction strips to build 7/4, then rearrange the pieces and record three matching addition equations.
Ask how 4/6 can be split in two different ways, then have students draw models and explain why both sums equal 4/6.
Play Fraction Match: students pair a fraction card with model cards showing two different decompositions, then justify each match.
Plan shared pizzas cut into halves, fourths, or eighths, and write two ways to combine servings for each total.
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Printable 3.NS.3.d Worksheet
A ready-to-print activity worksheet aligned to 3.NS.3.d, with an answer key for the teacher on its own page. No account needed.
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- 4.NS.3.f
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