Guided Lessons
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# Making Models with Different Denominators

Increase your students' knowledge of fractions with this lesson that has them compare fractions with different denominators.
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Students will be able to compare fractions with like numerators and different denominators.

(15 minutes)
• Before beginning the lesson, review numerator by defining it as the number on top of the fraction and denominator as the number on the bottom of the fraction that represents the total of the set, and finally define fraction as a specific portion of a set.
• Draw two circles on the board that are the same size. Divide one circle into 5 parts and one into 6 parts. Explain to the students that this is a model of two birthday cakes. Label one as chocolate and one as vanilla.
• Discuss with students that a piece from the chocolate cake is represented by the fraction 1/5 and that a piece from the vanilla cake is represented by 1/6. Ask students if they were given one piece from each cake, would the pieces be equal, or would one be larger than the other?
• Have students pair and share their ideas. Next, have students discuss as a group. Tell students that this is what they will learn about today.
(10 minutes)
• Write the fractions 1/5 and 1/6 side by side. Discuss with students how the numerators are the same but the denominators are different. Discuss that when we divide two equal wholes into more pieces, the size pieces become smaller. Tell students that it’s important to note the denominators of the fractions. Even though the denominator for 1/6 is greater, the fraction 1/5 is greater than the fraction 1/6.
• Give several more examples with numerators of 1. Draw models to support the discussion and help students justify their reasoning.
(15 minutes)
• Give each pair of students a set of 10 index cards. Have students divide each index card into different equal parts. Model for students making one card into 8 parts, one into 5 parts, etc.
• Have students choose two cards. Ask students to compare these two cards by writing the fractions in their notebooks and using the greater than, less than, or equal to symbols.
• Have students continue with this activity until they have compared all of their index cards.
(10 minutes)
• Distribute the Comparing Fractions worksheet to be individually completed.
• Walk around the classroom to assist struggling students and take any questions students may have.
• Enrichment: Have students try to compare and draw models for fractions with both different numerators and denominators.
• Support: Provide models for students in need of extra support.
(10 minutes)
• Circulate as students work with partners during the guided practice portion of the lesson.
• Give students several problems to solve using whiteboards. Have students draw models on the boards to share with a partner. Have students hold up boards as a quick visual assessment.
(5 minutes)
• Gather students together. Discuss with students how to compare the value of a fraction when both numerators are the same.
• Make sure to ask students to explain why a greater denominator does not mean a greater fraction.

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