Lesson: Compare fractions with area model and number line

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 Source: https://www.geogebra.org/m/QqFyBqcV

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In this lesson students will use the area model and number line to compare fractions. Ultimately, during this lesson students will be able to use number sense and the three-part definition of a fraction to compare fractions that have the same numerator or the same denominator.

Example 1: Compare $\frac{3}{8}$ and $\frac{5}{8}$ using the area model and number line.

To compare the two fractions, let's represent them using an area model and a number line.

 We can see that $\frac{3}{8}$ is less than $\frac{5}{8}$.

Example 2: Compare $\frac{5}{6}$ and $\frac{3}{6}$ using the area model and number line.

 Instead of writing $\frac{5}{6}>\frac{3}{6}$, we could have also written $\frac{3}{6}$. The important thing to remember is that the "alligator" always eats the larger number. 

 Lead a whole class discussion to guide students to see that for fractions that have the same denominator, the underlying unit fractions are the same size, so the fraction with the greater numerator is greater because it is made of more unit fractions. For example, a line segment from 0 to $\frac{3}{4}$ is shorter than the line segment from 0 to $\frac{5}{4}$ because it measures 3 units of $\frac{1}{4}$ as opposed to 5 units of $\frac{1}{4}$ . Therefore $\frac{3}{4}$.

 Example 3: Compare $\frac{1}{4}$ and $\frac{1}{6}$ using the area model and number line.

Example 4: Compare $\frac{2}{3}$ and $\frac{2}{5}$ using the area model and number line.

Example 5: Compare $\frac{3}{6}$ and $\frac{3}{4}$ using the area model and number line.

Continue leading a whole class discussion so that students see that for unit fractions, the one with the larger denominator represents a smaller fraction, since the more (identical) pieces the whole has been cut into, the smaller the pieces must be. From this they reason that for fractions that have the same numerator, the fraction with the smaller denominator is greater. For example, $\frac{2}{5}>\frac{2}{7}$ because 2 copies of $\frac{1}{5}$ is more than 2 lengths of $\frac{1}{7}$ .

Press [Next] to begin the 4 practice problems.