Virginia SOL 3.NS.3.b
The Standard
Identify a fraction represented by a model as the sum of unit fractions.
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 determine the size of one equal part in a fraction model. They count the represented parts and write the total as repeated copies of the same unit fraction.
What Mastery Looks Like
- Students identify the size of one equal part, then repeat that unit fraction for every shaded part. They can write a model such as seven fourth-size pieces as 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 and 7/4.
Common Misconceptions
- Students may count shaded parts for the numerator but use the number of unshaded parts as the denominator. They may also write different denominators for equal-sized pieces or combine unit fractions by adding both numerators and denominators.
How to Assess It
- Show two rectangles divided into fourths, with seven parts shaded in all. Ask students to write the shaded amount as a repeated sum of unit fractions and as one fraction.
Lesson moves
Ways to Teach It
Give students fraction strips, have them cover three fifth-size pieces, label each piece 1/5, and write the repeated sum.
Ask students to explain why three fourth-size pieces equal 3/4 but three third-size pieces do not.
Play a matching game using cards with shaded models, repeated unit-fraction sums, and single fractions.
Sketch two pizzas cut into eighths, shade ten slices, then write the amount as repeated eighths and as an improper fraction.
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Printable 3.NS.3.b Worksheet
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Related Standards
- 2.NS.3.d
Using same-size fraction pieces, from a region/area model, count by unit fractions up to two wholes (e.g., zero one-fourths, one one-fourth, two one-fourths, th...
- 4.NS.5.b
Identify and model equivalent relationships between fractions (proper or improper) and/or mixed numbers and decimals, using halves, fourths, fifths, tenths, and...
- 2.NS.3.a
Model and describe fractions as representing equal-size parts of a whole.
- 3.NS.3.c
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...
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