Post on 20-Jan-2016
Learn to identify and evaluate expressions.
WARM-UP
Please answer the questions below showing all your work!
1.563 + 981 =
2.298 – 189 =
3.46 x 847=
4.2952 ÷ 24 =
1,044
109
38,962
123
Order of Operations - Warm UpSimplify.
1. 4 + 8 2 152. 87 10 5 x 33. 6(5 + 2) + 24. 35 7 5 + 2
5
8144
27
Do you want to see something
VERY scary!
Vocabularyvariableconstantalgebraic expression
Equation
A mathematical statement showing two expressions
are indeed, equal.
3 types of Equations
#1. A true equation
3 + 5 = 8
3 types of Equations
#2. A false equation
3 + 5 = 6
3 types of Equations
#3. A conditional equation
3 + X = 8We try to make these
equations true!
SOLVE
When you solve an equation or inequality you
find the value(s) of the variable that makes the
equation true.
SIMPLIFY
This is exactly what it sounds like. It is
expressing a mathematical statement
in the “simplest” form possible.
When you were in second grade you did
problems like this!
3 + 5 = You realized the box
represented the unknown number!
When you were in Third grade you did problems
like this!
3 + =8
When you were in Fourth Grade you did problems
like this!
? + 5 =8 You realized the
Question Mark was the same as the box!
When you were in Fifth Grade you did problems
like this!
n + 5 =8
Do you remember those “n”s? It
meant the same as the box and the question mark!
Now, you are in Sixth Grade…. problems look
like this!
3 + x =8
The X means the same as the, the “n”,
the box and the question mark!
Scary!
Do you want to see something
VARY scary!
Do you want to see something
VARY scary!
Do you want to see something VARIABLE
VARIABLE
A variable is a symbol, normally a letter of the
alphabet, that represents one or more numerical
values. It takes the place of a number!
The “X” is a variable!
Remember….
VARIABLE
A variable is a symbol, normally a letter of the
alphabet, that represents one or more numerical
values. It takes the place of a number!
Very Scary!
ALGEBRA
WARM-UP
• What is a variable?
• What is a constant?
• If X =4, then 5 + X = ?
We can use any letter we want as a variable except
for one. Do you know which letter we should
never use as a variable?
0 Because it looks like an “o”
“oh”
Check these out!
5 + y = 8
r – 3 = 11
6 + 4 = k
8 x a = 16
These are all variables!
These are easy equations to
solve!
These are all conditional equations!
5 + y = 8
r – 3 = 11
6 + 4 = k
8 x a = 16
Remember, our goal is to make
conditional equations into
TRUE EQUATIONS!
Check these out!
5 + y = 8 y = 3
y – 3 = 11 y = 15
6 + 4 = y y = 10
8 x y = 16 y = 2
y is worth a different amount
each time. It “varies”.
That is why we call it a variable!
A variable is a letter or symbol that represents a quantity that can change.
A constant is a quantity that does not change.
Constant or Variable?
Your Weight!
variable
Constant or Variable?
# of days in a week
constant
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.
To evaluate an algebraic expression, substitute a number for the variable and then find the value.
“EVALUATE” Doesn’t mean to let me know how much you like it or
hate it!
“EVALUATE” means to solve it!
We substitute the variable?
What does it mean to be a “substitute
teacher”?
1. Evaluate each expression to find the missing
values in the tables.
WARM-UP
x
10
7
5
x
1
3
5
7
21
35
x – 5
2. Find an expression for the table.
5
2
0
7x
3. Evaluate 8x for x = 5.
4. Evaluate 4x – 1 for x = 12.
40
47
If X = 5, then…
8 - X = ?= 3
If X = 2, then…
5 + X = ?= 7
If X = 4, then…
3 x = 32 ?
If X = 4, then…
3 x = 12
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
If X = 5, then…
3 x = 35 ?
If X = 5, then…
3 x = 15
If X = 5, then…
2 x = ?
If X = 5, then…
2 x = 10
If X = 10, then…
X2
?
?
If X = 10, then…
X2
?
5
If X = 12, then…
X6
?
?
If X = 12, then…
X6
?
2
Evaluate the expression to find the missing values in the table.
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.
Evaluate the expression to find the missing values in the table.
Additional Example 1B: Evaluating Algebraic Expressions
Substitute for z in z 5 + 4.z z 5 + 4
20
45
60
8 z = 20; 20 5 + 4 = 8
z = 45; __ 5 + 4 = __
z = 60; __ 5 + 4 = __
13
16
45 13
60 16
The missing values are 13 and 16.
Try This: Example 1A
Evaluate the expression to find the missing values in the table.
Substitute for x in x 9.x x 9
18
36
54
2 x = 18; 18 9 = 2
4
6
4
54 6
x = 36; 9 =
x = 54; 9 =
36
The missing values are 4 and 6.
Evaluate the expression to find the missing values in the table.
Try This: Example 1B
Substitute for z in 8 z + 2.z 8 z + 2
7
9
11
58 z = 7; 8 7 + 2 = 58
z = 9; 8 __+ 2 = __
z = 11; 8 __ + 2 = __
74
90
9 74
11 90
The missing values are 74 and 90.
Multiplication and division can be written without using the symbols and .
Instead of . . . You can write . . .
x 3x 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
Find an expression for the table.
Additional Example 2A: Finding an Expression
39 13 = 3
n
39
52
65
3
4
5 65 13 = 5
52 13 = 4
n 13
An expression is n 13, or .n13
2-1 Variables and Expressions
Course 1
Find an expression for the table.
Additional Example 2B: Finding an Expression
7 • 4 = 28
p
4
6
8
28
42
56 7 • 8 = 56
7 • 6 = 42
7 • p
An expression is 7 • p, or 7p.
2-1 Variables and Expressions
Course 1
Find an expression for the table.
21 3 = 7
u
21
42
63
7
14
21 63 3 = 21
42 3 = 14
u 3
An expression is u 3, or .u3
Try This: Example 2A
2-1 Variables and Expressions
Course 1
Find an expression for the table.
Try This: Example 2B
4 • 5 = 20
n
5
8
11
20
32
44 4 • 11 = 44
4 • 8 = 32
4 • n
An expression is 4 • n, or 4n.
2-1 Variables and Expressions
Course 1
Lesson Quiz: Part 2
3. Evaluate 8x for x = 5.
4. Evaluate 4x – 1 for x = 12.
40
47
2-1 Variables and Expressions
Course 1
Lesson 2-7
Write this in
Your planner!
Today’s Assignment
Lesson 2-1
Let’s Look Closer at
5 + y = 8This is a Conditional Equation! We
want to make it into a True Equation! We can tell just by glancing at it that y = 3. But, now we have to try to do
something that is difficult.
Pretend you don’t know that y = 3!