## An Expression for Area

## Opening

# An Expression for Area

Write an expression for the area of the shaded part of the figure.

Write an expression for the area of the shaded part of the figure.

Detect errors that can be made when simplifying expressions.

Karen, Lucy, Jack, and Marcus each simplified the expression he or she wrote for this problem.

- Whose solution is correct?
- What mistakes did the other students make?

- When you simplify an expression, write an equivalent expression that is as simple as possible. It should not contain any parentheses. It should have only one term with each variable and only one number without a variable. Examples:

2(*x*– 4) = 2*x*– 8

and

*x*+ 5*x*+ 4*x*= (1 + 5 + 4)*x*= 10*x* - Can you use the distributive property to rewrite expressions?
- Remember: Multiplying two negative integers results in a positive product.

- Summarize the mistakes made by three of the students.
- For the correct answer, prove that all steps are equivalent expressions by using substitution.

Look again at the shaded figure.

- Which of these numbers make sense for a value of
*x*?

4.5, 2, $6\frac{1}{2}$, 14

- Explain your reasoning.

Take notes about your classmates’ strategies for simplifying expressions.

As your classmates present, ask questions such as:

- How did you know to multiply/add those numbers?
- Did you check for equivalent expressions by substitution?
- Did you consider whether your answer makes sense?
- Can you explain that step again?

Are each of the following expressions equivalent to (10*x*)(8) − 6(*x *− 3)?

Explain why or why not.

- (8)(10
*x*) − [6(*x*− 3)] - (8)(10
*x*) + (−6)[*x*+ (−1)3]

Check your work by substituting the value 10 for the variable *x*.

Check your work by substituting the value 10 for the variable *x* .

Write a summary about simplifying expressions.

Check your summary:

- Do you explain how to use the distributive property to rewrite an expression?
- Do you discuss the importance of paying attention to plus and minus signs in multiplication?
- Do you describe how to check whether two expressions are equivalent?

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful.

**Something new I learned today is …**

**I still have questions about …**