Unit 2 Fraction Equivalence and Comparison (Family Materials)

In this unit, students deepen their knowledge of fractions. They explore the size of fractions, write equivalent fractions, and compare and order fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Near the end of the unit, ask your student to compare $\frac{3}{5}$ and $\frac{3}{7}$ .

Questions that may be helpful as they work:

How are the two fractions alike? How are they different?
What strategy did you use to compare?
Is there a different strategy that you could use to compare?

Section A Size and Location of Fractions

In this section, students revisit the meaning of fractions. They use fraction strips, tape diagrams, and number lines to represent fractions. Students compare fractions with the same numerators or the same denominators, and recall that equivalent fractions have the same size.

Students consider the size of fractions whose denominators are related, such as $\frac{1}{5}$ and $\frac{1}{10}$ , or $\frac{1}{6}$ and $\frac{1}{12}$ . They also compare fractions to benchmarks such as $\frac{1}{2}$ and 1. (For instance, they see that $\frac{3}{10}$ is less than $\frac{1}{2}$ and $\frac{3}{5}$ is more than $\frac{1}{2}$ .)

Section B Equivalent Fractions

Here, students take a closer look at equivalent fractions and reason using number lines. They show that fractions that are at the same point on the number line are equivalent.

Students then learn to tell if two fractions are equivalent without using number lines.

number line. 6 evenly spaced tick marks. First tick mark, 0. Point at second tick mark, 1 fifth. Last tick mark, 1.

Number line from 0 to 1. Evenly spaced by tenths. Point at 2 tenths.

number line. 16 evenly spaced tick marks. First tick mark, 0. Fourth tick mark, 3 fifteenths. Last tick mark, 1.

Number line. 20 tick marks. First tick mark, 0. Fourth tick mark, 4 twentieths. Twentieth tick mark, 1.

For example, they can explain that the fraction $\frac{2}{3}$ is equivalent to $\frac{8}{12}$ because the numerator and the denominator of $\frac{2}{3}$ are each multiplied by the same number, 4, to get $\frac{8}{12}$ . Students use such observations to identify and write equivalent fractions.

Section C Fraction Comparison

In this section, students compare fractions with different numerators and denominators using various strategies. For example, they may think about how far each fraction is from 0 on a number line, how each fraction compares to $\frac{1}{2}$ or 1, or think of the fractions in terms of the same denominator.

Students record the results of comparisons with symbols $>$ , $=$ , or $<$ . They then solve problems that involve comparing fractional measurements, such as lengths in fractions of an inch.