The Case of the Missing Rectangle Side
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.
- 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.
Explicit Instruction/Teacher modeling(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).
Guided Practice(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.
- Check their answers.
Independent working time(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.
- 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.
- 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.
- 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.
Review and closing(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.