4.NF.2
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.
About the Math
Illustrative Mathematics Project (click picture)
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.
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.
About the Math
Illustrative Mathematics Project (click picture)
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.
- 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.
- Students can also draw pictures to represent the fractions making certain that the wholes are the same.
- When comparing fractions with the same numerators, such as 3/5 and 3/10, it should be obvious to the students because the numerator names the same number of parts so they need to look to the denominators and see that 3 out of 10 parts is less than 3 out of 5 parts.
- You can also compare each fraction to one. When comparing 5/6 and 7/8. Think that it takes 1/6 to get to one whole and it takes 1/8 to get to one whole. Since 1/8 is smaller than 1/6, 7/8 is larger than 5/6.
- You can compare fractions using a common denominator procedure. When comparing ¾ and 2/3, find the common denominator of 12 and calculate that ¾ = 9/12 and 2/3 is equal to 8/12 so ¾ > 2/3.