Maryland Math 4.NOS.D.10

4.NOS.D.10 is a cluster heading. These are the individual standards under it.

• 4.NOS.D.10.a

  Use benchmark numbers (e.g., 1/2, 1), common numerators, and common denominators to compare.

• 4.NOS.D.10.b

  Record comparisons with symbols >, =, <.

• 4.NOS.D.10.c

  Justify comparisons using representations and reasoning.

01

What Students Need to Do

Students compare fractions with different numerators and denominators that refer to the same-sized whole. They use one-half, one whole, or equivalent fractions with matching numerators or denominators. They write >, <, or = and explain their choice with a drawing or number line.

02

What Mastery Looks Like

A student writes 2/3 > 3/5 and shows why using equal-sized fraction bars. They can rename the fractions as 10/15 and 9/15, then explain why the bars must represent the same-sized whole.

03

Common Misconceptions

Students may think a larger denominator means a larger fraction, so they choose 3/5 over 2/3. Some compare shaded parts of different-sized wholes as if the wholes matched. Others reverse > and <.

04

How to Assess It

Exit ticket: Draw equal-sized bars to compare 2/3 and 3/5. Write >, <, or =, explain your choice using fifteenths, and tell why the bars must be the same size.

1. 01

   Give pairs equal-sized paper strips to fold and shade 2/3 and 3/5, then have them align the strips and write a comparison.

2. 02

   Ask, 'Which is greater, 3/4 or 4/6?' Have students draw equal-sized bars and explain their comparison using twelfths.

3. 03

   Give pairs cards showing 2/3 versus 3/5 and 3/4 versus 4/6; race to place the correct symbol and sketch proof.

4. 04

   Show a small pizza with 3/4 eaten and a large pizza with 2/3 eaten; ask whether fractions alone reveal more pizza eaten.

• 3.NOS.F.13

  Explain equivalence of fractions and compare fractions by reasoning about their size, recognizing that comparisons are valid only when the two fractions refer t...

• 3.NOS.F.13.d

  Compare two fractions with the same numerator or the same denominator by reasoning about their size. Record the results of comparisons with the symbols >, =, or...

• 4.NOS.E.12

  Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with like denominators.