# Comparing Tape Diagrams

This lesson can be used as a pre-lesson for the Illustrating Fraction and Whole Number Products with Tape ModelsLesson plan.

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This lesson can be used as a pre-lesson for the Illustrating Fraction and Whole Number Products with Tape ModelsLesson plan.

Students will be able to use tape diagrams to create equivalent expressions involving whole numbers, fractions, and multiplication.

##### Language

Students will be able to compare tape diagrams that have whole numbers and fractions using group discussions and visuals.

(5 minutes)
• Draw a tape diagram for 3/4 with 3 rectangles filled and one clear and ask students tell their partner the number the tape diagram represents. Choose a student to share aloud the answer.
• Write the student-friendly language objective on the board and have students choral read it with you: "I can compare tape diagrams that have whole numbers and fractions using group discussions and visuals." Challenge students to raise their hand when they hear a vocabulary term they would like to define (e.g., "tape diagrams," "whole numbers," "visuals," "fractions").
• Distribute the vocabulary cards and ask students to help you define the terms from the language objective. Draw visuals on their cards to represent each of the terms.
• Tell students that today they will compare tape diagrams that show different information visually.
(8 minutes)
• Show the vocabulary card for the word CompareAnd ask students to share some phrases they use when they compare two things. Write their responses on the board and allow students to correct each other when necessary (e.g., "____Is easier/harder than ____Because ____," or "They are alike/different because ____.").
• Draw the two example tape diagrams from the Types of Tape Diagrams Assessment worksheet without the fractions or the expression, and have students turn and talk about what they observe about the two cards (e.g., have rectangles, separated into 6 groups, Example 2 has 6 total dots with one dot in each small rectangle, both tape diagrams have smaller pieces inside of the larger rectangle, etc.).
• Write down some of the student conversations you overhear from their partner conversations on chart paper titled "Compare and Contrast Language." Choose a student to read aloud some of the phrases you wrote on the chart paper.
• Redo both examples on separate chart papers. Start by drawing the tape diagrams, partitioning them, and then think aloud how to get a fraction for Example 1 using a realistic example to represent the numbers in the tape diagram. For example:
• "Charlie bought a birthday cake and had 3/6 leftover."
• "There are six small rectangles, or pieces of cake in one larger rectangle, or the whole cake. There are no other additional markings, so this is similar to a fraction strip and equals one whole cake. Since there are six groups, I can label each small rectangle 1/6. Three of the 1/6s are shaded, so I can add 1/6 + 1/6 +1/6 = 3/6And simplify it to 1/2."
• Think aloud how to get the expression for Example 2 as you write on the next chart paper using a realistic example to represent the numbers in the tape diagram. For example:
• "Veronica has a cake and shares it with her six friends. Each friend gives 1/6 of their cake to their little brother."
• "There is one large rectangle, or cake, that equals one separated into sixths, so I know we are dealing with fractions. We have 6 sections with 1 dot in each section, so that is 6 x 1 = 6Total dots. There is only one dot in each, so that is the numerator, and the total number of dots is 6, or the denominator. The fraction is 1/6. Since there are 6 total groups, the expression will be 6 x 1/6."
• Ask students to look at the two charts and rethink some of the ways the tape diagrams are the same or different. Add more similarities and differences to the Compare and Contrast Language chart paper and start creating separate sentence frames from the student discussions:
• "One difference/similariarity is ____."
• "The first tape diagram has/shows ____While the second tape diagram has ____."
(7 minutes)
• Have students help you create a Venn diagram on the board comparing the two types of tape diagrams.
• Model using some comparative sentences while you write some of the differences and similarities in the Venn diagram (e.g., "Example 2 has a large rectangle that shows a whole number and fraction, while Example 1 has a large rectangle that shows a fraction."). Continue to add examples of comparative language to the chart paper Compare and Contrast Language.
• Ask for student input as well and write their answers in the Venn diagram. Afterwards, have one student model finding the fraction for Example 1 and another student model finding the expression for Example 2. Encourage them to explain their thinking.
(8 minutes)
• Distribute the pre-cut card sets so that each group gets one card that shows a fractional representation (cards A, C, and E) and one card that shows a multiplication expression (cards B, D, and F).
• Ask students to describe what they see in the cards and then compare the two cards in their groups.
• Give them a sheet of copy paper so they can recreate both diagrams and then create a Venn Diagram on the back of their paper using the comparative language from their previous discussions (see the chart paper Compare and Contrast Language).
• Choose a volunteer group to share their creation of the tape diagrams. Ask them to focus on how they created the expression and the fraction:
• "I added/counted the ____. The denominator is ____Because ____. The numerator is ____Because ____. The fraction is ____. For the second tape diagram, the whole number is ____Multiplied by ____. I added/counted the ____And added/counted the ____. I got the fraction ____. Card ____Is ____While Card ____Is ____."

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 on their vocabulary cards.
• Have students use whiteboards throughout the lesson and allow them to have two markers to help them visually differentiate between the two tape diagrams. Tell students to refer to their whiteboard drawings in their conversations.
• Tell students to use the example sentence frames and new vocabulary terms in their conversations.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Choose them to share their explanations first to model language use.
• Ask them to give more comparative sentence stems to add to the chart.
• Have students explain the two different tape diagrams and how to draw them using sequencing words and key vocabulary.
• Challenge them to create a word problem to correspond with the Two Types of Tape Diagrams cards.
(7 minutes)
• Distribute the Types of Tape Diagrams Assessment worksheet and read through the instructions. Ask a volunteer to explain the two examples using language from today's lesson. (Note: these are the same examples they saw in the Explicit section.)
• Have students write the fraction or expression for each of the tape diagrams from two questions.
• Allow students to discuss their answers with their elbow partners and then use comparative language as they describe what they see in both of the tape diagrams.
• Encourage students to use the language from the Compare and Contrast Language chart paper.
(5 minutes)
• Conduct a 3-2-1Activity and ask students to label the back of their assessment worksheet numbers 1–3. Have students write down:
• ThreeKey vocabulary terms they need to compare the two tape diagrams
• TwoPhrases they use in their comparisons
• OneQuestion they have about the tape diagrams
• Choose volunteers to share their question and ask other students to answer the questions. Correct misconceptions as necessary.

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