Learn to identify and evaluate expressions. WARM-UP Please answer the questions below showing all...

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


#2. A false equation

3 + 5 = 6


#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 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.


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


Try This: Example 1A


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



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


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


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.


Course 1


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


Course 1


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.


Course 1

Lesson Quiz: Part 2

3. Evaluate 8x for x = 5.

4. Evaluate 4x – 1 for x = 12.

40

47


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!

Learn to identify and evaluate expressions. WARM-UP Please answer the questions below showing all...

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