Virginia SOL 4.NS.3.f
The Standard
Compose and decompose fractions (proper and improper) and/or mixed numbers with denominators of 12 or less, in multiple ways, with and without models.*
Virginia Standards of Learning for Mathematics · The student will use mathematical reasoning and justification to represent, compare, and order fractions (proper, improper, and mixed numbers with denominators 12 or less), with and without models.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students break fractions and mixed numbers into equal-value sums in more than one way. They also combine fractional parts into one fraction or mixed number, using pictures and equations.
What Mastery Looks Like
- A student can show that 7/4 equals 4/4 + 3/4, 1 + 3/4, and 1 3/4. They can use a model or an equation to explain why each form names the same amount.
Common Misconceptions
- Students may treat the numerator and denominator as separate whole numbers or think a fraction has only one decomposition. They may read 1 3/4 as 4/7 or forget that 4/4 makes one whole.
How to Assess It
- Give an exit ticket: “Write 11/6 in three different ways, including a mixed number, and draw a model for one way.”
Lesson moves
Ways to Teach It
Give pairs fraction strips and ask them to build 9/4, then record three ways to regroup the pieces.
Ask students to explain whether 8/6 and 1 + 2/6 name the same amount, using words, numbers, or a sketch.
Play a matching game with cards showing fractions, mixed numbers, sums, and area models that represent equal amounts.
Use measuring cups to show three ways to make 1 1/2 cups, then write an equation for each combination.
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Printable 4.NS.3.f Worksheet
A ready-to-print activity worksheet aligned to 4.NS.3.f, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 3.NS.3.d
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 =...
- 6.NS.1.c
Represent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and pe...
- 6.NS.1.d
Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or ...
- 4.NS.3.e
Represent equivalent fractions with denominators of 12 or less, with and without models.*
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