Reason and develop an understanding of how to place equivalent fractions on a number line.
- A length of ribbon for each student (About 10-12 inches) (If you prefer to do the lesson whole class rather than individually, use clothesline and clips to make a large version of this number line)
- 16 paper clips
- One of the following: 16 strips of cardstock, or 16 Post-it flags, or a copy the "Ribbon Task" activity sheet for each student (have students cut out the fraction cards)
- Pens or markers (if students make their own fraction cards rather than cut out the ones on the activity sheet)
- Set of Cuisenaire rods for each student
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Lesson 4, Ribbon Task Activity Sheet
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Lesson 4, Ribbon Task Answer Key
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Assessment Activity Sheet
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Assessment Activity Answer Key
Introduce
Review equivalent fractions with Cuisenaire rods.
Direct students to think about what they did in the previous lesson and model 2 equivalent fractions using the Cuisenaire rods. Put the work of one student on the document camera and discuss as the class the fractions that are shown.
Throughout the lesson be sure to encourage students to use the key vocabulary: equivalent fractions, numerator, denominator. Repeat with the work of another student and be certain that equivalent fractions based on the brown rod are shared. The work with the brown rod will tie in with the number line work in this lesson. Have the students put the Cuisenaire rods back in the container and set them aside until the end of the lesson.
Explore
Provide students with the Lesson 4, Ribbon Task Activity Sheet (all downloadables can be found in the Materials section above) and have them complete it in pairs.
The Ribbon Task
Give each child:
- A length of ribbon for each student (About 10-12 inches)
- 16 paper clips per student
- One of the following: 16 strips of cardstock, or 16 Post-it flags, or a copy of the “Ribbon Task” activity sheet for each student (have students cut out the fraction cards)
- Pens or markers (if students make their own fraction cards rather than cut out the ones on the activity sheet)
Britt wants to show the fractions she has been learning about on her ribbon. She is having a hard time. Can you help her put 0, 1/2, 2/2, 1/4, 2/4, 3/4, 4/4, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8, and 1 on her ribbon? Be ready to justify each fraction position. (SMP 3)
Start the task with private "think time" followed by small group sharing. Once students have all the fractions placed on the ribbon, ask them to select one fraction and write a justification for why they placed that fraction in that position. This can be in a math journal or on a large index card. As students write their justification, select students to share their justification, focusing on the position of the fractions on the number line. After a student shares, ask the other students to consider the reasoning provided (SMP 3).
One option for sharing is to have a ribbon in the front of the room, use a class set of fraction cards and strategically call on several students to share their justification for where they placed a particular fraction. Another option for sharing is to have students clip their ribbon to a whiteboard or clip board to bring to the front of the room to share.
After students shared how they placed the fractions on the number line, focus the discussion on the structure of the fractions and their equivalence (SMP 7), using the following example questions.
AskL:
- “I noticed that you placed 4/8 and 1/2 at the same point. Why did you do that?” [These fractions are the same amount, and the same distance from zero.]
- “What do you notice about the structure of the fractions at the 1/2 mark?” [We want to students to be able to say that the numerator is always half of the denominator. They may express this in different ways.] “Will fractions that are equivalent to 1/2 always have this structure?” [Yes]
- “Why did you place the 1/4 exactly in the middle of 0 and 1/2?” [1/4 is half of a half, or two ¼’s make a half.]
- “What numbers did you place with the 1 whole? Why? What do you notice about the structure of fractions at the 1 whole mark?” [Fractions that are equivalent to one whole have numerators and denominators that are the same.]
- “Name a fraction on your ribbon that does not have another fraction in the same position. Why is this the case?” [Tell students there are in fact many fractions in this position but they have not learned about them yet.]
Synthesize
The purpose of the summarize/synthesize activity is to help students coordinate their work with Cuisenaire rods and number lines and demonstrate their understanding of fraction equivalence (SMP 7).
Pass out the Assessment Activity Sheet and a set of Cuisenaire rods to each student. Have them work individually to answer questions 1-6 on the activity sheet. Be sure to circulate and monitor student progress. Students may need questions read aloud, as well as prompting or guidance on the first question or two in order to understand the design of the activity.
For those that finish early the activity can be extended by asking them to find equivalent fractions other than those equivalent to ½. Another extension would include having them generate other fractions equivalent to ½ beyond the fractions they have been working with so far (i.e. 5/10).
Summarize by having students pair-share their answer to question 5 and then call on one or two students to share whole class. It is important that they recognize that in the fractions equivalent to ½ the numerator is always half of the denominator. Be sure to focus on the important vocabulary.
Assessment
See the above summarize/synthesize activity and look at the students’ work on the Assessment Activity Sheet.
Teacher Reflection
- How do you know which students can identify that equivalent fractions occupy the same position on the number line? What activities are appropriate for students who have not yet developed this understanding? Which students understand and can explain the structure of fractions that are equivalent to one-half?
- How do you know which students can place fractions on the number line? What activities are appropriate for students who have not yet developed this understanding?
- What parts of the lesson went smoothly? What parts should be modified for the future?
Leave your thoughts in the comments below.