Virginia SOL 5.NS.1.d
The Standard
Compare (using symbols <, >, =) and order (least to greatest and greatest to least) a set of no more than four decimals and fractions (proper, improper) and/or mixed numbers using multiple strategies (e.g., benchmarks, place value, number lines). Justify solutions orally, in writing, or with a model.*
Virginia Standards of Learning for Mathematics · The student will use reasoning and justification to identify and represent equivalency between fractions (with denominators that are thirds, eighths, and factors of 100) and decimals; and compare and order sets of fractions (proper, improper, and/or mixed numbers having denominators of 12 or less) and decimals (through thousandths).
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare fractions, mixed numbers, and decimals by using benchmarks, place value, equivalent forms, or number lines. They order up to four values and justify why each value belongs in its position.
What Mastery Looks Like
- Students accurately order up to four fractions, mixed numbers, and decimals, then use <, >, or = correctly. They explain their choices with benchmarks, place value, equivalent forms, or a number line.
Common Misconceptions
- Students may think more decimal digits means a greater value, so they place 0.805 above 0.82. They may compare only numerators or denominators, or treat every improper fraction as less than one. They may also overlook the whole-number part of a mixed number.
How to Assess It
- Order 1.18, 6/5, 1.205, and 1 1/4 from least to greatest. Justify two adjacent placements, using place value for one and a model or benchmark for the other.
Lesson moves
Ways to Teach It
Place fraction strips and decimal grid cards on a floor number line, then have students arrange four values and defend each placement.
Use the prompt, "Decide whether 7/8 or 0.84 is greater, then prove it with a benchmark and an equivalent decimal."
Play Order Showdown: teams draw four fraction, mixed-number, or decimal cards, order them, and earn a point after a correct justification.
Give four hiking distances written as decimals, improper fractions, and mixed numbers; students rank them and explain which trail is longest.
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