Guided Lessons

# The Case of the Missing Rectangle Side

Your students will become junior math detectives as they hunt down the missing side of a rectangle by applying the area formula for rectangles. The only clues they have are the rectangle's area and the measure of one side.
Need extra help for EL students? Try the Area Arrangements pre-lesson.

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Need extra help for EL students? Try the Area Arrangements pre-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 area underneath 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: Practice 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.