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# Fractional Tape Diagram Descriptions

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This lesson can be used as a pre-lesson for the Fractions and Word Problems lesson plan.

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This lesson can be used as a pre-lesson for the Fractions and Word Problems lesson plan.

Students will be able to write about their tape diagrams that show fractions.

##### Language

Students will be able to explain and write about their tape diagrams using sentence frames and visuals.

(3 minutes)
• Display Card A from the Tape Diagram Descriptions worksheet. Ask students to turn and talk to one another about what they see in the card and what the visual describes. Look for key vocabulary shown on the Vocabulary Cards or Glossary, and write the terms they use as you hear them.
• Ask a volunteer to describe the picture aloud and write some of the phrases they use that emphasize the description of the tape diagram (e.g., "It has ____. These are ____. ____ (number) rectangles are shaded while ____(number) are white. The total sum of the pieces is ____.The tape diagram represents ____.").
(8 minutes)
• Model adding the pieces from Card A to get the improper fraction 19/6. Use descriptive phrases from the Tape Diagram Descriptions worksheet to share the information (e.g., "The sum of the parts of the tape diagram is 6/6 + 6/6 + 6/6 + 1/6 = 19/6.").
• Have students turn and talk to their elbow partners, restating the process you used to find the improper fraction. Write down some of the sentences they use in their descriptions and then share some of them aloud with the class after the partner discussions. For example, "First, I added all the shaded parts up in each of the tape diagrams to get the numerator. Then, I added up the total parts of one tape diagram to get the whole amount, or the denominator. My improper fraction is 19/6."
• Tell students to vote on which example is the best based on clarity and specificity of the sentence. They can hold up their fingers for 1â€“5, where five is the most detailed and one is the one that needs the most improvement.
• Ask students to discuss how they might find the mixed number for the tape diagram in partners. Correct any misconceptions and model describing the process of finding the mixed number (e.g., "First, I added the whole tape diagrams pieces that were fully shaded (3) and then I added the parts from the last whole (one of six, or 1/6). Lastly, I added them together and my total was 3 1/6.").
• Write out a descriptive paragraph on the teacher copy of the Tape Diagram Descriptions page for Card A while you describe the tape diagrams shown in Card A.
(7 minutes)
• Display Card F from the worksheet Tape Diagram Displays. Tell students they will now orally practice using the language frames to describe what they see in the card. Allow them to use the sentence frames from the Tape Diagram Descriptions page.
• Display your teacher copy page and listen for students' explanations. Fill in the section on your teacher copy as you listen to their conversations.
• Have a student read the teacher copy aloud to the class. Ask for student input on how to make the explanation better. Make the appropriate adjustments as a whole class.
(12 minutes)
• Tape the pre-cut tape diagrams from the Tape Diagram Displays worksheet around the room and distribute a copy of the Tape Diagram Descriptions the worksheet.
• Have students walk around and complete 1â€“4 paragraph frames with the descriptive sentences of the tape diagram they're evaluating. Make sure students write in the boxes that correspond with the same letter on the tape diagram card. (Note: emphasize quality over quantity and allow students to complete fewer paragraph frames if necessary.)
• Allow students to work in partners in which they create their own sentences for one card and then share with each other. Encourage them to read the whole paragraph to each other before offering input, such as, "I like how you ____. What do you think about adding/taking away ____?"
• Choose volunteers to read their paragraph while standing next to the referenced tape diagram. Have listeners put a thumb up if they agree with the description or a thumb sideways if they have a suggestion or something to add to the description. Give the students time to add information.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide bilingual reference materials to assist in their vocabulary word acquisition.
• Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
• Tell them to cut out the tape diagrams and use them in their conversations before they write their descriptions in their paragraph frames.
• Group the sentence frames and have them work on one idea at a time. For example, have them focus on sentence stems with what the tape diagram looks like. Then, practice with the sentence stems that focus on the addition and equation, etc.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Have student write their descriptions from a list of sentence stems and allow them to to have more flexibility regarding their transition choices.
• Challenge them to complete their assessments without using the provided sentence frames, or give them sentence stems instead (e.g., "The improper fraction...").
• Make sure they are sharing their description paragraphs aloud to model phrasing and word choice for their peers.
• Have confident mathematicians add another sentence to the paragraph frame discussing how to simplify the fractions, or how to convert between the improper fraction to the mixed number if time remains.
(5 minutes)
• Distribute one of the tape diagrams from the Tape Diagram Displays worksheet to each student.
• Ask students to use a section from the Tape Diagram Descriptions to complete a descriptive paragraph of the mixed numbers represented in the tape diagrams. (Note: allow struggling students to repeat cards they've already completed and note their improvement as part of their assessment.)
• Distribute Cards A, B, and E for struggling students and Cards C, D, and F for those who are ready for a challenge.
(5 minutes)
• Ask students to think about what makes one descriptive paragraph better than the other. Allow them to share their ideas with their partners (e.g., specific information, adjectives, numbers or key term references, shapes described, etc.).
• Write a descriptive paragraph for one of the more challenging tape diagrams that is lacking specific vocabulary (tape diagram, mixed number, fractional units, etc.) and ask students to improve it.
• Have students share their suggestions aloud after you've read the paragraph aloud. Mark the edits in a different color as you make changes.

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