Name: ______________________________________ Class: ______________ Date: ____________

Unit 6: Say it with Symbols

Practice Ace Problems

Directions: Please complete the necessary problems to earn a maximum of 8 points according to the

chart below. Show all of your work clearly and neatly for credit- which will be earned based on

completion rather than correctness.

I can determine when algebraic expressions are equivalent and write algebraic expressions in useful equivalent forms.

Lesson Practice problems Options Maximum

Points

Lesson 1: Writing Equivalent Expressions

1, 2, 3, 4

3 Points

Lesson 2: Determining Equivalence

Lesson 3: Distributive Property

6, 10, 11, 12, 13, 14 5 Points

______/ 8 Points

Name: ______________________________________ Class: ______________ Date: ____________

1. Use the diagram below to answer questions (a) – (c).

a. How many 1-square-foot border tiles do you need to surround a pool that is 10 feet long

and 5 feet wide? (Use the diagram to help you.)

b. Write an algebraic expression for the number of border tiles need to surround a pool that is

L feet long and W feet wide.

c. Write a different (but equivalent) expression for the number of tiles needed for the situation

in part (b). Explain why your expressions are equivalent (use mathematic steps to help

explain).

2. A square hot tub has side length of s feet. Someone makes a border by placing 1-square-foot

tiles along the edges of the tub and triangular tiles at the corners, as shown below. He makes

the triangular tiles by diagonally cutting the square tiles in half.

a. Suppose the hot tub has side lengths of 7 feet. How many square tiles will it take to create

the border?

Name: ______________________________________ Class: ______________ Date: ____________

b. Write an algebraic expression for the number of square tiles N needed to build this border

for a square tub with side lengths of S feet.

c. Write a different (but equivalent) expression for the number of tiles N needed to build this

border for a square tub with side lengths of S feet. Explain why your expressions are

equivalent.

d. Is the relationship between the number of tiles and side length linear or nonlinear? Explain!

3. A rectangular pool is L feet long and W feet wide. Someone makes a border by placing 1-square-

foot tiles along the edges of the pool and triangular tiles on the corners, as shown below. He

makes the rectangular tiles by diagonally cutting the square tiles in half.

a. Suppose the pool is 30 feet long and 20 feet wide. How many square tiles does the tiler

need for the border?

b. Write two different algebraic expressions for the number of square tiles N needed to make

the border for a pool L feet long and W feet wide.

Name: ______________________________________ Class: ______________ Date: ____________

c. Explain why your two expressions are equivalent. (Use mathematical steps to show.)

4. Below are three more expressions students wrote for the number of border tiles needed to

surround the square pool in Problem 1.2.

a. Use each expression to find the number of border tiles N if s = 0. (Substitute 0 in place of S

for each expression and simplify!)

b. Do you think the three expressions are equivalent? Explain why or why not.

c. Use each expression to find the number of border tiles if s = 12. Do your results change your

answer to part (b)? Why or why not?

d. Is testing specific values a valid method for determining whether two or more expressions

are equivalent? Why or why not?

Name: ______________________________________ Class: ______________ Date: ____________

6. Each expression below represents the surface area for part of the pool.

a. Which expression(s) could represent the area of the diving section?

b. Which expression(s) could represent the area of the swimming section?

c. Write an equation that represents the total surface area A of the pool.

A =

d. What kind of relationship does the equation in part (c) represent? (linear, exponential,

quadratic?)

10. Use the Distributive Property to write each expression in expanded form.

a. 3(x + 7) b. 5(5 – x)

c. 2(4x – 8) d. (x + 4)(x + 2)

Name: ______________________________________ Class: ______________ Date: ____________

11. Use the Distributive Property to write each expression in factored form.

a. 2x + 6 b. 14 – 7x

c. 2x – 10x d. 3x + 4x

12. Are each of the following pairs of expressions equivalent? If so, describe which property allows them

to be congruent (Distributive or Commutative Properties?).

a. 3x + 7x and 10x b. 5x and 5x – 10x

d. 4(1 + 2x) – 3x and 5x + 4 d. 5 – 3(2 – 4x) and -1 + 12x

13. Here is one way Maleka proved that 2(s + 2) + 2s is equivalent to 4s + 4.

What properties justify each step?

(1)

(2)

(3)

(4)

Name: ______________________________________ Class: ______________ Date: ____________

14. Find three equivalent expressions for 6x + 3.

Exit Ticket Level of Understanding

After finishing this investigation you should be comfortable doing the following: -Writing equivalent expressions and determining if expressions are equivalent.