1. Variables and Expressions
2-1
Variables and Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
Course 1

2. Warm Up
Simplify.
 3  1
2. 87  15  5
3. 6(9 + 2) + 7
4. 35  7  5

3.  Problem of the Day How can the digits 1 through 5 be arranged
in the boxes to make the greatest product? 

4. Learn to identify and evaluate expressions.

5. Vocabulary
variable
constant
algebraic expression

6. A variable is a letter or symbol that represents a quantity that can change.
A constant is a quantity that does not change.

7. Algebraic Expressions NOT Algebraic Expressions
An algebraic expression contains one or more variables and may contain operation symbols. So p  7 is an algebraic expression.
Algebraic Expressions
NOT Algebraic Expressions
150 + y
85 ÷ 5
35  w + z
 5
To evaluate an algebraic expression, substitute a number for the variable and then find the value.

8. Additional Example 1A: Evaluating Algebraic Expressions
Evaluate the expression to find the missing values in the table. y
5  y 16 27 35 80
Substitute for y in 5  y.
y = 16; 5  16 = 80
y = 27; 5  = 27
y = 35; 5  = 35
The missing values are 135 and 175.

9. Additional Example 1B: Evaluating Algebraic Expressions
Evaluate the expression to find the missing values in the table. z
z  20 45 60
Substitute for z in z 
z = 20; 20  = 20
z = 45; __  = __ 45
z = 60; __  = __ 60

10. Check It Out: Example 1A
Evaluate the expression to find the missing values in the table. x
x  9 18 36 54 2
Substitute for x in x  9.
x = 18; 18  9 = 2
x = 36;  9 = 36
x = 54;  9 = 54

11. Check It Out: Example 1B
Evaluate the expression to find the missing values in the table. z
8  z + 23 7 9 11 64
Substitute for z in 8  z + 23.
z = 7; 8  = 64
z = 9; 8  __+ 8 = __ 9
z = 11; 8  __ + 8 = __ 11

12. You can write multiplication and division expressions without using the symbols  and .
Instead of . . .
You can write . . .
x  3
x  3
x(3) 3x 35 y
35 ÷ y
When you are multiplying a number times a variable, the number is written first. Write “3x” not “x3.” Read 3x as “three x.”
Writing Math

13. Additional Example 2: Evaluating Expressions with Two Variables
A rectangle is 4 units wide. How many square units does the rectangle cover if it is 3, 4, 5, or 6 units long?
Make a table to help you find the number of square units for each length. l w
l x w 3 4 12 5 6
3 x 4 = square units
4 x 4 = square units
5 x 4 = square units
6 x 4 = square units

14. l w l x w Check It Out: Example 2
A rectangle is 3 units wide. How many square units does the rectangle cover if it is 2, 3, 4, or 5 units long?
Make a table to help you find the number of square units for each length. l w
l x w 2 3 6 4 5
2 x 3 = square units
3 x 3 = square units
4 x 3 = square units
5 x 3 = square units

15. 1. Evaluate the expression to find the missing values in the table. l
Lesson Quiz x
x2 – 5 10 7 5
1. Evaluate the expression to find the missing values in the table. l w
l x w 2 6 3 4 5
2. A rectangle is 6 units wide. How many square units does the rectangle cover if it is 2, 3, 4, or 5 units long?