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# The Case of the Missing Rectangle Side

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Do you need extra help for EL students? Try the Area ArrangementsPre-lesson.

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Do you need extra help for EL students? Try the Area ArrangementsPre-lesson.

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.

The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
(10 minutes)
• Prior to the lesson, draw a large rectangle to display.
• Tell students that today they will be on the case of the missing rectangle side.
• Inform them they will need their multiplication, division, and reasoning skills to solve the case.
• Display the large rectangle. Add to the fun by drawing a magnifying glass and tell students that they are officially on the case of the "missing rectangle side."
• Tell students that the only clues they have on the case is the area of the rectangle and the measure of one of the rectangle's sides.
• Write down the label AreaUnderneath the rectangle, defining it as the space inside the shape.
• Next, review the formula for area.
• Write down the area formula. Demonstrate an example of solving for area.
(10 minutes)
• Begin by writing down several area problems and model how to solve a few.
• Ask students to solve the rest of the problems with you and give you instructions.
• On your chart paper, draw a rectangle. List one side and display the area. Next to the unknown rectangle side, write an X. With student input, develop a formula for the missing side.
• Display your formula on your chart paper. For example, 12 x (X) = 36. Ask students how they think this formula can be solved.
• Discuss strategies and solve the problem.
• Remind students that multiplication and division have an inverse relationship, so if they're missing a multiple in a multiplication problem, they can use the stated product (e.g., 36) and create a division problem with the known factor (e.g., 36 ÷ 12 = 3).
(10 minutes)
• Draw another rectangle with an unknown side.
• Display one side and the area of the rectangle.
• Ask students to solve the problem on their own.
(15 minutes)
• Ask students to draw four rectangles on a piece of notebook paper.
• Direct your students to write down the area and the measure of one side next to the rectangle and an X for the missing side.
• Have students exchange papers with partners.
• Instruct your students to solve for all missing sides on their papers.
• After they have completed their work, have them return to their partners to correct the work.
• Have your students discuss any errors with each other.
• Walk around and monitor student discussions. Intervene with struggling students as necessary.
• Collect student work to assess.

Support:

• Students may struggle solving for the unknown side if they do not have strong basic multiplication and division skills. Work with them in a small group to review these skills.

Enrichment:

• Ask a small group to develop a real-life story problem in which there is an unknown variable for a rectangle where the area and one side is given. In the whole group, present the story problem the small group has written and have all students solve.
(10 minutes)
• Distribute the worksheet Rectangle Mania: practise Finding Length and ask students to find the missing side of the rectangle.
• Allow students to share their answers and correct their misconceptions.
(10 minutes)
• Take the story problems that your advanced students wrote during enrichment.
• Have students come up and read their story problem to the class.
• Solve the problems as a whole group.

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