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# Area Arrangements

Students will use the inverse relationship between multiplication and division to complete an area formula in a real-world situation. Use this lesson on its own or as support for the lesson The Case of the Missing Rectangle Side.
This lesson can be used as a pre-lesson for the The Case of the Missing Rectangle Side lesson plan.

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This lesson can be used as a pre-lesson for the The Case of the Missing Rectangle Side lesson plan.

Students will be able to find the missing side of a rectangle given the rectangle's area and measure of one side by applying the area formula.

##### Language

Students will be able to explain how to use the area formula with key vocabulary and visuals.

(5 minutes)
• Distribute the vocabulary card for the word area and ask students to label the sides based on the equation on the card.
• Let them turn and show their answers to their elbow partners.
• Ask for a volunteer to explain how they labeled the sides. Rephrase their explanation using key vocabulary terms (i.e., "width," "length," "square units," etc.).
• Have a student read the student-friendly language objective: "I can explain how to use the area formula with key vocabulary and visuals."
(7 minutes)
• Review the definition of the word area and discuss how the formula inverse is Area ÷ a side = the other side. Model the inverse with the values on the vocabulary card for area.
• Have an advanced student read the length and width vocabulary cards while the rest of the class choral reads it.
• Display the worksheet Area: Arranging the Carnival. Explain that they have to organize the games for the carnival. Tell them there is a limited amount of area, so they will have to be selective in which games they add to the carnival. They have a total area of 22 ft x 32 ft = 704 square feet.
• Model finding the missing side of a rectangle's area. Then, draw the rectangle on the graph paper, labeling the length and width and checking your answer by adding the square units.
• Choose an advanced student to restate the steps you used to find the missing side (i.e., inverse division operation). Write down some key sentence frames given the advanced student's explanation or correct misconceptions and write the correct phrasing on the board.
(10 minutes)
• Do the next problem in the Area: Arranging the Carnival worksheet. Before trying the inverse operation, ask them to make guesses about the missing side measurement and have them consider why they cannot have more than one value, even though there are different factors for the given area. Define factor with the vocabulary card if necessary.
• Model verifying the side guesses using the inverse operation and sketching the rectangle on the grid.
• Distribute the Area: Arranging the Carnival worksheet and scrap paper, and ask students to find the values of the other missing sides.
• Have advanced students share their answers and explain how they know their answer is correct. Rephrase the students' answers with some of the following sentence frames:
• "First, I ____. Then, I ____."
• "The inverse operation for this area equation is ____."
• "I know I have the correct answer because ____."
• Monitor student conversations throughout the whole lesson using the Formative Assessment: Peer Explanations Checklist to jot down student explanations.
(6 minutes)
• Have students choose which activities they'll add to the carnival and draw them in the grid.
• Ask students to turn and talk to their partner about how they drew the rectangles on the grid and labeled their rectangles. Encourage them to use the sentence frames from the board that emphasize the steps they used to draw their rectangles and how they know their answers are correct.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions.
• 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.
• Provide reference materials in their L1 to assist in their vocabulary word acquisition.
• Allow students to label the vocabulary cards as they understand the meanings and add definitions for their L1 on their Glossary.
• Preteach a lesson on the inverse relationship between multiplication and division, or on the relationship between perimeter and area and how perimeter and area changes with side measurement changes.

• Challenge students to create new perimeters but use the same area for some of the activities. Ask them to think about how they would be able to fit all the activities on the grid (e.g., eliminate the minimum 2-units restriction, make the areas smaller by changing the dimensions, etc.).
• Ask them to share their mathematical processes with beginning students and let them serve as student teachers when other students need help.
(7 minutes)
• Tell students they'll now evaluate their choice of activities for the carnival. Write the following questions on the board:
• "How many activities could you fit into the gymnasium?"
• "Were you able to include all the activities you wanted for the carnival?"
• "Were the areas for the activities realistic? Why or why not?"
• Ask a confident advanced EL to share their answers for their own carnival and write down sentence frames for each of the questions based on the EL's explanation. Then, have students turn and talk to their partners to share their responses.
• Monitor student conversations throughout the whole lesson using the Formative Assessment: Peer Explanations Checklist to jot down student explanations.
(5 minutes)
• Choose two examples of student explanations you wrote on the Formative Assessment: Peer Explanations Checklist worksheet and write them on the board.
• Remind students that they reviewed a few ways to find the missing side of a rectangle (e.g., inverse operations, using a grid to count the square units, and guessing the sides based on factors for the listed area) and ask them to explain which method they used the most. Have them turn and talk to their partners.
• Explain that understanding how area works in real-world scenarios, like a carnival, can help understand using area to multiply or divide larger numbers.