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2-2 Variables and Expressions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
2-2 Variables and Expressions
Warm UpSimplify.
1. 4 + 7 3 1
2. 87 15 5
3. 6(9 + 2) + 7
4. 35 7 5
24
84
73
25
2-2 Variables and Expressions
Problem of the Day
How can the digits 1 through 5 be arranged in the boxes to make the greatest product?
4 3 1
5 2
2-2 Variables and Expressions
MA.6.A.3.1 Write and evaluate mathematical expressions…given situations.
Sunshine State Standards
2-2 Variables and Expressions
A variable is a letter or symbol that represents a quantity that can change.
A constant is a quantity that does not change.
2-2 Variables and 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 10 + 3 5
To evaluate an algebraic expression, substitute a number for the variable and then find the value by simplifying.
2-2 Variables and Expressions
Evaluate the expression to find the missing values in the table.
Additional Example 1A: Evaluating Algebraic Expressions
Substitute for y in 5 y.y 5 y
16
27
35
80 y = 16; 5 16 = 80
135
175
27 135
35 175
y = 27; 5 =
y = 35; 5 =
The missing values are 135 and 175.
2-2 Variables and Expressions
Evaluate the expression to find the missing values in the table.
Additional Example 1B: Evaluating Algebraic Expressions
z z 5 + 4
20
45
60
20 z = 20; 20 5 + 4 = 20
z = 45; __ 5 + 4 = __
z = 60; __ 5 + 4 = __
13
16
45 13
60 16
The missing values are 13 and 16.
Substitute for z in z 5 + 4.
2-2 Variables and Expressions
Check It Out: Example 1A
Evaluate each expression to find the missing values in the table.
t 8t
10
20
30
80
160
240
2-2 Variables and Expressions
Evaluate each expression to find the missing values in the table.
Check It Out: Example 1B
m 52 - 2 m
4
7
10
17
11
5
2-2 Variables and Expressions
Evaluate each expression to find the missing values in the table.
Check It Out: Example 1C
n n ÷ 6 - 4
60
48
36
6
4
2
2-2 Variables and Expressions
Evaluate each expression to find the missing values in the table.
Check It Out: Example 1D
b 3 (2 + b)
3
6
9
15
24
33
2-2 Variables and Expressions
You can write multiplication and division expressions without using the symbols and .
Instead of . . . You can write . . .
x 3 x 3
35 ÷ y
x(3) 3x
35y
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
2-2 Variables and Expressions
A rectangle is 4 units wide. How many square units does the rectangle cover if it is 3, 4, 5, or 6 units long?
Additional Example 2: Evaluating Expressions with Two Variables
Make a table to help you find the number of square units for each length.
3 x 4 = square units
20
16
l w l x w
3 4 12
4 4
5 4
6 4
The rectangle will cover 12, 16, 20, or 24 square units.
4 x 4 = square units
5 x 4 = square units
6 x 4 = square units
12
16
20
2424
2-2 Variables and Expressions
Complete the table.
Check It Out: Example 2A
z 8 z + 2
7
9
11
58
74
90
2-2 Variables and Expressions
A rectangle is 7 units wide. What is the area of the rectangle if it is 8, 9, 10, or 11 units long?
Check It Out: Example 2B
7 · 8 = 56 square units;
7 · 9 = 63 square units;
7 · 10 = 70 square units;
7 · 11 = 77 square units
2-2 Variables and Expressions
A rectangle has a length of 13 units. The perimeter of a rectangle is twice its width plus twice its length. Complete the table to find the perimeter of the rectangle if its width is 5, 6, 7, or 8 units wide.
Check It Out: Example 2C
w
l = 13
2-2 Variables and Expressions
Check It Out: Example 2C Continued
w2 13 + 2 w
5 36 units6
7
8
38 units
42 units
40 units
2-2 Variables and Expressions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-2 Variables and Expressions
1. Evaluate the expression to find the missing values in the table.
Lesson Quiz
2. A rectangle is 6 units wide. What is the area of the rectangle cover if it is 2, 3, 4, or 5 units long?
95
44
20
12
l w l x w
2 6
3 6
4 6
5 6
18
24
30
x x2 – 5
10
7
5
2-2 Variables and Expressions
1. Evaluate the expression to find the missing values in the table.
A. 67, 97, 112
B. 67, 77, 92
C. 47, 77, 92
D. 47, 77, 112
Lesson Quiz for Student Response Systems
x 5x + 22
9
15
18