Show Me Equivalent Fractions!
Learning Objectives
Students will be able to find equivalent fractions using number lines and bar models.
Lesson
Introduction (5 minutes)

Hook students with a scenario: Imagine that you’re at a birthday party and your favorite cake is being served. Would you rather have 2/10 of the cake or 1/5 of the cake?

Have students discuss the scenario with a partner. Call on a student to share and justify their answer (i.e. 2/10 and 1/5 are equivalent fractions, so you would be getting the same amount of cake either way).

Show students a visual: Draw two circle models or fill in fraction circles to display a model of each fraction (see resources). Explain that the two fractions are equivalent, or equal, because they both represent the same amount of cake.
 Explain: There are many ways to draw models of fractions. Circle models are common, but they aren’t always easy to draw. Today we are going to explore two different ways to draw equivalent fractions.
Explicit Instruction/Teacher Modeling (8 minutes)

Tell students that drawing number lines is one way they can draw a model of equivalent fractions (see resources for example number lines).

Draw and label a number line that is divided into fourths. Place a dot on the 1/4 mark.

Directly below the number line, draw and label a second matching number line, ensuring that zero and one are aligned. Divide the second number line into eighths, ensuring that the marks are aligned appropriately with the above number line.

Ask students to look at the number lines to identify a fraction that is equivalent to 1/4. Have students justify their answers, or provide a justification (i.e. “I can tell that 2/8 is equivalent to 1/4 because both fractions are the same distance from zero.”) Place a dot on the 2/8 mark.

Use a highlighter to emphasize the distance from zero on each number line.

Tell students that bar models are another way to show equivalent fractions (see resources for example bar models).

Draw a rectangle and divide it into fourths. Label each section 1/4. Shade in one section (1/4).
 Directly below the first bar model, draw a second matching rectangle and divide it into eighths, ensuring that the half and quarter marks are aligned with the first bar model. Label each section 1/8. Shade in two sections (2/8).
Guided Practice/Interactive Modeling (12 minutes)

Hand out the Number Line and Bar Model worksheets.

Review the sample problems on each worksheet.

Have students work with a partner to complete the worksheets.

Circulate the room as students work and provide support as needed.
 When students are finished, review the worksheets as a class.
Independent Working Time (15 minutes)

Hand out a sheet of 8½ x11 paper to each student

Have students count off 16. Assign each number a different problem (i.e. “if you are a number one, draw number lines and bar models to show a fraction that is equivalent to 3/4”).

Write each problem on the board for student reference.

Have students construct their own number lines on one side of their paper and bar models on the other side to show equivalent fractions.

Organize a jigsaw review: Group students according to which number problem they modeled and have them share their number lines and bar models as a group (e.g. Students who modeled problem one would check their work with other ‘one’s.)
 Instruct students in each jigsaw group to pick one model from their group to share with the class.
Extend
Differentiation
Support:
 Provide additional practice with predrawn number lines or bar models.
Enrichment:
 Have students draw multiple models and/or number lines showing several equivalent fractions (i.e. 1/3, 2/6, 3/9, and 4/12).
Review
Assessment (5 minutes)

Give two unequivalent fractions and ask students if they are equivalent. Have students justify their answer with a bar model or number line (i.e. is 3/5 equivalent to 8/10?)

Then, ask students to identify an equivalent fraction on their number line or model (i.e. what fraction on your number line is equivalent to 8/10?)
 Ask students to name other pairs of equivalent fractions and record their responses on the board or on a chart.
Review and Closing (5 minutes)

Show the Equivalent Fractions video to review the concept of equivalent fractions (see link in resources).
 Ask & Discuss: Why might it be helpful to draw equivalent fractions?