### Lesson Plan

# Using Properties to Identify Equivalent Expressions

In this Adventures in Expressions and Equations lesson, students will generate equivalent expressions using the distributive property in the context of professional skydiving.

Grades

6–8

Duration

40 MINUTES

### Objectives

**Students will:**

- Add linear expressions with rational coefficients
- Subtract linear expressions with rational coefficients
- Factor linear expressions with rational coefficients
- Expand linear expressions with rational coefficients
- Use the distributive property to rewrite expressions
- Compare expressions to determine whether they are equivalent

### Materials

- A Interview With a Skydiver: Generating Equivalent Expressions printable
- Answer Key: Adventures in Expressions and Equations printable

### Set Up

- Make a class set of the Interview With a Skydiver: Generating Equivalent Expressions printable.
- Print a copy of the Answer Key: Adventures in Expressions and Equations printable for your use.

### Lesson Directions

### Introduction to New Material

**Step 1:** Display the following image, and ask students to come up with an expression that represents the area of the image. (13 x 10)

Ask students:* ***What is the area of the rectangle?** (130 units)

**Step 2:** Display the following image, and ask students to come up with an expression that represents the area of the image. (100 + 30, or 10 x 10 + 10 x 3)

Ask students:

**What is the area of the image?**130 units**How are these images similar? How are they different?**

**Step 3:** Use the same process to discuss the following sets of images:

Set 1 |

Set 2 |

**Step 4:** Tell students that writing these equivalent expressions for the areas of rectangle pairs is a visual model of the distributive property. Display the first pair of rectangles. Recall that the first rectangle’s area was described as 10 x 13. This could also be considered as 10 x (10 + 3). If you distribute “10 x” to both the terms in (10 + 3), the expression will now be 10 x 10 + 10 x 3, which is the area of the second set of rectangles. We know these two expressions are equivalent because they both equal 130.

**Step 5:** Display various other examples of how to use the distributive property for students. For example:

**Step 6:** Have students practice some examples on their own. Tell them to use the distributive property to write equivalent expressions for the following:

- 16 (
*m*– 4) - (33 – 3) x 6
- 8 (0 –
*x*) - 2 x (
*g*+ 7) - (3 +
*z*)(15*y*)

**Step 7:** Have students then consider the following word problems about canoe equipment. They can work in pairs to generate expressions.

**Word Problem #1:** A single canoe costs $850. A paddle costs $130. A personal flotation device costs $80. A helmet costs $45.

- Write an expression that describes how much it will cost to buy one set of canoe equipment.
- Use the distributive property to write two equivalent expressions that describe how much it will cost for you and your best friend to buy two sets of canoe equipment.
- You and your friend each decide to also buy attachable cameras to film your ride. Each camera costs
*d*. Modify your equivalent expressions from above to include attachable cameras for you and your friend.

**Word Problem #2: **Each month, you earn $200 waiting on tables at a restaurant, $100 mowing your neighbor’s lawn, and $140 babysitting. You spend $30 on your cell phone bill, $60 on lunches, and $80 on bus fare each month.

- Use the distributive property to write two equivalent expressions describing how much money you save each month.
- You work for
*m*months. Use the distributive property to write two equivalent expressions describing the amount of money you save over the*m*months.

**Word Problem #3:** Each month your friend earns $80 delivering newspapers, $90 walking dogs, and $250 working at a grocery store. She spends $45 on her cell phone bill and $65 on lunches each month. She works for *m* months. Use the distributive property to write two equivalent expressions describing the amount of money she saves over *m* months.

**Word Problem #4: **Simplify the expressions you wrote in questions 7 and 8.

- How much money do you save over
*m*months? - How much money does your friend save over
*m*months? - How much money do you and your friend save in all over
*m*months?

**Word Problem #5: **You decide to hold off on buying the attachable cameras. You pool your money together to buy two sets of canoe equipment.

- How much money do you and your friend need to save to buy the two sets of equipment?
- Write an equation that will help you determine how many months you and your friend will need to save in order to buy the equipment.
- How many months do you and your friend need to save?

### Guided Practice

**Step 8:** Show students the following pairs of expressions. Ask students to determine whether the expressions are equivalent, and have them provide reasoning for their answers:

- 7(
*k*– 4) = 7 +*k*– (7 + 4) - 17
*g*– 2*g*+5*j*= 15*g*+ 5*j* - 6
*h*+ 9*h*=*h*(6 + 9) - 4.5
*y*+ 6.5*z*– 3.5*z*= 7.5*yz*

**Step 9: Checking for Understanding:** Review students’ answers as a class and respond to any questions.

### Independent Practice

**Step 10:** Assign the Interview With a Skydiver: Generating Equivalent Expressions printable worksheet for classwork or homework.

**Step 11: Checking for Understanding:** Review the answers to the Interview With a Skydiver: Generating Equivalent Expressions printable, which are provided on page 2 of the Answer Key: Adventures in Expressions and Equations printable. Make sure students explain their mathematical thinking. Address any misconceptions that may arise.

### Standards

**Grade 7**: Distributive Property, Linear Expressions, Writing Expressions for Real-World Problems (CCSS 7.EE.A.1)**Grade 6–8**: Making Sense of Problems, Reasoning Abstractly and Quantitatively, Constructing Viable Arguments, Modeling, Making Use of Structure (CCSS Practice MP1, 2, 3, 4, 7)