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### Lesson plan

# The Case of the Missing Rectangle Side

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#### Learning Objectives

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.

#### Introduction

*(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.

**Beginning**

- Allow students to discuss their ideas in partners in their home language (L1) or their new language (L2).
- Provide visuals and vocabulary cards in their L1 or L2 for the new terms.
- Give them sentence frames to help them explain the meaning of the word "area."

**Intermediate**

- Have them restate the meaning of the word "area" and its equation for a rectangle in their L1 or L2.
- Ask them to relay the steps you used to solve the area problem.

#### 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 Ã· 12 = 3**).

**Beginning**

- Let students work in partners while they solve the area problems.
- Ask them to explain the steps they used to solve the problems in their L1 or L2.
- Provide sentence frames with keywords to help in their explanations.
- Have them copy your teacher markings for the area solutions.

**Intermediate**

- Have ELs explain their process for solving the area of a rectangle to their partner in their L1 or L2. Allow them to use their vocabulary cards for assistance.
- Ask them to restate to their partners the inverse relationship between multiplication and division.

#### 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.

**Beginning**

- Ask students to explain their answer in their L1 or L2. Allow them to draw pictures with graph paper to support their answer.

**Intermediate**

- Write out the steps for finding the missing side on the board.
- Allow students to offer alternative processes (e.g., inverse of multiplication, guess and check, counting squares with graph papers, etc.).

#### 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.

**Beginning**

- Provide a real-world scenario for the four rectangles and ask students to solve for the missing side. For instance, they need to put a ping-pong table in the recreation center. They know the area is 72 feet squared with the length measuring 12 ft. What is the width they need to accommodate at the recreation center?
- Allow students to draw their answer on graph paper to support their answer.

**Intermediate**

- Provide an example of a real-world scenario for one of the four rectangles.
- Have them create a real-world scenario for one of the rectangles that would involve them not knowing one of the sides of a rectangular object. Allow them to share it in their L1 or L2.

#### Differentiation

**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.

#### Assessment

*(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.

**Beginning**

- Encourage them to use their vocabulary cards during their explanations.

**Intermediate**

- Provide scrap or graph paper to help them complete their assignment.

#### 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.

**Beginning**

- Write the key ideas from the student-shared story problem on the board for ELs to reference. Sketch visuals next to unfamiliar words and allow the students to complete them on their own.

**Intermediate**

- Have students complete the word problem and turn and talk to a sympathetic partner before sharing their answers aloud with the class or group.