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# Fractions: All Lined Up

In this lesson, students will practice identifying and modeling equivalent fractions by using number lines.

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Students will be able to draw and partition number lines to show fractions. Students will be able to label pairs of number lines to show equivalent fractions, including whole numbers.

(5 minutes)
• Explain to your students that they are going to learn how to use a number line to show equivalent fractions.
• Remind them that numbers can have lots of names. Give them examples. Possible examples include: 5 = 3 + 2, 4 + 1, 5 x 1, and five tally marks.
• Define equivalent, or equal, fractions as fractions that name the same parts or point on a number line. For example, three-sixths and one-half are equivalent fractions.
(10 minutes)
• Pose an example question, such as: How many sixths does it take to equal two-thirds?
• Show your students how to draw a straight horizontal line with arrows at the ends. Mark the horizontal line with two vertical lines at the beginning and end to designate the starting and end points.
• Label the starting point 0 and the end point 1.
• Partition, or divide, the line into 3 equal parts, being sure to stress that only two lines are drawn to make three parts.
• Show students one-third, two-thirds, and three-thirds on the number line, and label two-thirds with the fraction.
• Draw a new number line, but partition it into sixths, stressing that five lines are drawn to make six parts.
• Line up this number line with the thirds number line.
• Show students the line on the sixths number line that lines up with two-thirds.
• Have students help count to that line, and label that fraction on the number line.
• On the board, show that two-thirds equals four-sixths.
(10 minutes)
• Pose another question to your students, such as How many fourths equal six-eighths?
• Have your students draw a number line with the start and end points labeled.
• Ask your students how many lines they need to draw to partition the line into eights.
• Have your students partition the line and label six-eighths.
• Instruct your students to draw a second number line with the start and end points labeled, lining the start and end points with the previous number line.
• Have students work with a partner to label the second number line, and have them write the number sentence that shows the equivalent fractions.
(5 minutes)
• Have students work on their own to find another equivalent fraction. For example, How many fifths equal four-tenths?
• Enrichment: Give your students three pairs of fractions to compare.
• Support: Have your students use a candy bar to divide into sections. Direct them to break one bar into two pieces and the other into four pieces, and show them that one whole bar is equivalent to 1.
(10 minutes)
• Have your students complete a task that evaluates someone else's process. For example, show two number lines that are incorrectly drawn or labeled.
(5 minutes)
• Have your students form groups and create charts to show how to compare fractions using a number line.