Maryland Math 4.NOS.D.9

4.NOS.D.9 is a cluster heading. These are the individual standards under it.

• 4.NOS.D.9.a

  Identify and generate equivalent fractions using representations and the Identity Property of Multiplication.

• 4.NOS.D.9.b

  Explain why fractions are equivalent (c/d = (n × c)/(n × d)).

01

What Students Need to Do

Students use fraction strips or drawings to show when two fractions name the same amount. They make equivalent fractions by multiplying the numerator and denominator by the same number, which means multiplying by 1.

02

What Mastery Looks Like

A student draws equal-length bars to show that 3/4 and 6/8 cover the same amount. They write 3/4 × 2/2 = 6/8 and explain that 2/2 equals 1, so the value stays the same.

03

Common Misconceptions

Some students add the same number to the top and bottom, treating 1/2 as equal to 2/3. Others multiply only the numerator or compare shaded parts in drawings with different-sized wholes.

04

How to Assess It

Exit ticket: Draw equal-length bars to show whether 2/3 equals 4/6. Write a multiplication equation and explain why the value stays the same.

1. 01

   Fold equal-length paper strips into thirds and sixths, shade 2/3 and 4/6, and place them side by side.

2. 02

   Ask, "Why does 3/4 equal 6/8 but not 4/5?" Have students explain with a drawing and an equation.

3. 03

   Give pairs cards showing fractions, shaded bars, and equations; have them match 2/3, 4/6, and 2/3 × 2/2.

4. 04

   Use a ruler to mark 1/2 inch and 2/4 inch, then explain why both marks land in the same place.

• 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.b

  Identify and generate equivalent fractions, (e.g., 1/2 = 2/4, 4/6 = 2/3.) and explain why the fractions are equivalent using concrete materials, drawings, numbe...