Virginia SOL 3.NS.3.c
The Standard
Use a model of a fraction greater than one to count the fractional parts to name and write it as an improper fraction and as a mixed number (e.g., 1 4 , 2 4 , 3 4 , 4 4 , 5 4 = 1 1 4 ).
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 count equal fraction pieces across one or more wholes and record the total as an improper fraction. They regroup complete wholes and leftover pieces to write the matching mixed number.
What Mastery Looks Like
- A student can identify how many equal pieces make one whole, then count all the pieces shown. The student writes equivalent improper fractions and mixed numbers and checks both names against the model.
Common Misconceptions
- Students may change the denominator when regrouping pieces into wholes. They may count only the leftover pieces or write the whole number as the numerator. Some treat the numerator and denominator as separate whole numbers.
How to Assess It
- Draw two rectangles divided into fourths, with all four parts of the first and three parts of the second shaded. Ask students to write the amount as an improper fraction and a mixed number, then explain their answer.
Lesson moves
Ways to Teach It
Give students fraction strips and whole outlines to build amounts greater than one, then label each model in both forms.
Ask, "How do 11 sixths become 1 5/6?" and have students explain what each number represents.
Play a matching game with model cards, improper fraction cards, and mixed number cards using halves, thirds, fourths, fifths, sixths, eighths, and tenths.
Show trays of brownies cut into equal pieces, then have students name the amount left across multiple trays in both forms.
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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 =...
- 3.NS.3.f
Compare two fractions (proper or improper) and/or mixed numbers with like numerators of 2, 3, 4, 5, 6, 8, and 10 (e.g., 2 3 > 2 8 ) using words (greater than, l...
- 4.NS.5.c
Write the decimal and fraction equivalent for a given model (e.g., 1 4 = 0.25 or 0.25 = 1 4 ; 1.25 = 5 4 or 11 4 ; 1.02 = 102 100 or 1 2 100 ).*
- 4.NS.3.f
Compose and decompose fractions (proper and improper) and/or mixed numbers with denominators of 12 or less, in multiple ways, with and without models.*
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