4.NF.2 - About the Math, Learning Targets, and Rigor

Grade 4 Fractions

4.NF.2

Full Standard

Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).
Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

4th Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

 

3rd Grade Students Learning 4th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number and fraction concepts.

 

Learning Targets

  • Explain that when comparing fractions they must refer to the same whole.
  • Compare fractions using benchmarks (7/8 > 3/10). 
  • Compare fractions by reasoning about their size and relationship (7/8 > 3/10)
  • Compare fractions by reasoning about their size when there are the same number of pieces (common numerator, 3/6 > 3/10).
  • Compare fractions by reasoning about the number of missing pieces (4/5 < 9/10).
  • Compare fractions by reasoning about the number of same-sized pieces (common denominator, 5/8 > 2/8).
  • Create equivalent fractions to compare using common denominators (if needed, 3rd quarter)).
  • Record comparison using >, <, or =.
  • Explain how fractions are compared.

 

About the Math

There are several ways to compare fractions. Before moving to the procedure of finding a common denominator, fraction sense, and reasoning should be the focus.

  • Explain that when comparing fractions they must refer to the same whole.

Students must demonstrate an understanding that comparison of fractions is grounded in the same whole be referred to in the comparison. Students should have opportunities to explore this. They can use real-world contexts such as the comparison of half of small pizza and half of a large pizza.  

  • Compare fractions using benchmarks (7/8 > 3/10). 

One way of comparing fractions is to look at benchmark fractions. Benchmark fractions are fractions that are easy to visualize such as ¼, ½ , ¾. So you look at fractions in relation to ½. When comparing the two fractions 7/9 and 3/8, students should think 7/9 is greater than ½ and 3/8 is less than ½ so 7/9 is greater than 3/8.

  • Compare fractions by reasoning about their size and relationship (7/8 > 3/10)

Sometimes we can compare fractions by their benchmarks. Other times we can compare fractions, with unlike denominators, by thinking about their distance from 0 or 1 or other familiar fractions. 7/8 is almost one whole. 3/10 is between 0 and 1/2. 7/8 is greater than 3/10. Note that this is similar to benchmark comparisons and that students do not have to differentiate between the strategies.

  • Compare fractions by reasoning about their size when there is the same number of pieces (common numerator, 3/5 > 3/10).

When comparing fractions with the same numerators, such as 3/5 and 3/10, it should be obvious to the students which is greater because they have the same number of parts. Knowing this, they can think about the relative size of denominators. Here, fifths are larger than tenths so three of them is larger than three tenths. 

  • Compare fractions by reasoning about the number of missing pieces (4/5 < 9/10).

We can think about the number of missing pieces to compare fractions. 4/5 and 9/10 are both missing one piece. Fifths are greater than tenths. Therefore, 9/10 is close to one whole than 4/5. 9/10 is greater than 4/5.

  • Compare fractions by reasoning about the number of same-sized pieces (common denominator, 5/8 > 2/8).

This strategy is the same as common denominators. Simply, we can compare two fractions with the same sized pieces by counting the number of pieces. 

  • Create equivalent fractions to compare using common denominators (if needed, 3rd quarter).

Students should be able to create equivalent fractions to compare fractions with unlike denominators. This should occur have other strategies and understandings have been developed. 

  • Record comparison using >, <, or =.

Fractions can be compared using the same symbols we use to compare whole numbers.

  • Explain how fractions are compared.

Students should understand the fundamental concepts of what fractions are and how they are related. Students should understand that counting pieces or that the number of parts in the whole do not determine which fraction is greater. 

Essential vocabulary for this standard includes numerator, denominator, fraction, greater than, less than, and equal.

Math in Minutes

The video links below demonstrate the way your student will learn specific concepts.

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Progression of Standard within Grade 4

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Explain that when comparing fractions they must refer to the same whole.
  • Compare fractions using benchmarks (7/8 > 3/10). 
  • Compare fractions by reasoning about their size and relationship (7/8 > 3/10)
  • Compare fractions by reasoning about their size when there are the same number of pieces (common numerator, 3/6 > 3/10).
  • Compare fractions by reasoning about the number of missing pieces (4/5 < 9/10).
  • Compare fractions by reasoning about the number of same-sized pieces (common denominator, 5/8 > 2/8).
  • Create equivalent fractions to compare using common denominators (if needed, 3rd quarter).
  • Record comparison using >, <, or =.
  • Explain how fractions are compared.
  • Explain that when comparing fractions they must refer to the same whole.
  • Compare fractions using benchmarks (7/8 > 3/10). 
  • Compare fractions by reasoning about their size and relationship (7/8 > 3/10)
  • Compare fractions by reasoning about their size when there are the same number of pieces (common numerator, 3/6 > 3/10).
  • Compare fractions by reasoning about the number of missing pieces (4/5 < 9/10).
  • Compare fractions by reasoning about the number of same-sized pieces (common denominator, 5/8 > 2/8).
  • Create equivalent fractions to compare using common denominators (if needed, 3rd quarter).
  • Record comparison using >, <, or =.
  • Explain how fractions are compared.

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 3 Grade 5
  • Explain  and generate equivalent fractions and compare fractions by reasoning about their size ( 3.NF.3
  • Solve word problems with +/- fractions (5.NF.2)

 

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