learn to identify and evaluate expressions. warm-up please answer the questions below showing all...
TRANSCRIPT
![Page 1: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/1.jpg)
Learn to identify and evaluate expressions.
![Page 2: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/2.jpg)
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
![Page 3: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/3.jpg)
![Page 4: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/4.jpg)
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
![Page 5: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/5.jpg)
Do you want to see something
VERY scary!
![Page 6: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/6.jpg)
Vocabularyvariableconstantalgebraic expression
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Equation
A mathematical statement showing two expressions
are indeed, equal.
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3 types of Equations
#1. A true equation
3 + 5 = 8
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3 types of Equations
#2. A false equation
3 + 5 = 6
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3 types of Equations
#3. A conditional equation
3 + X = 8We try to make these
equations true!
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SOLVE
When you solve an equation or inequality you
find the value(s) of the variable that makes the
equation true.
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SIMPLIFY
This is exactly what it sounds like. It is
expressing a mathematical statement
in the “simplest” form possible.
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When you were in second grade you did
problems like this!
3 + 5 = You realized the box
represented the unknown number!
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When you were in Third grade you did problems
like this!
3 + =8
![Page 15: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/15.jpg)
When you were in Fourth Grade you did problems
like this!
? + 5 =8 You realized the
Question Mark was the same as the box!
![Page 16: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/16.jpg)
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!
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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!
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Scary!
![Page 19: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/19.jpg)
Do you want to see something
VARY scary!
![Page 20: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/20.jpg)
Do you want to see something
VARY scary!
![Page 21: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/21.jpg)
Do you want to see something VARIABLE
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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!
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The “X” is a variable!
Remember….
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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!
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Very Scary!
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ALGEBRA
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WARM-UP
• What is a variable?
• What is a constant?
• If X =4, then 5 + X = ?
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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”
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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!
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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!
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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!
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A variable is a letter or symbol that represents a quantity that can change.
A constant is a quantity that does not change.
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Constant or Variable?
Your Weight!
variable
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Constant or Variable?
# of days in a week
constant
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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.
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To evaluate an algebraic expression, substitute a number for the variable and then find the value.
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“EVALUATE” Doesn’t mean to let me know how much you like it or
hate it!
“EVALUATE” means to solve it!
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We substitute the variable?
What does it mean to be a “substitute
teacher”?
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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
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If X = 5, then…
8 - X = ?= 3
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If X = 2, then…
5 + X = ?= 7
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If X = 4, then…
3 x = 32 ?
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If X = 4, then…
3 x = 12
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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
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If X = 5, then…
3 x = 35 ?
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If X = 5, then…
3 x = 15
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If X = 5, then…
2 x = ?
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If X = 5, then…
2 x = 10
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If X = 10, then…
X2
?
?
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If X = 10, then…
X2
?
5
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If X = 12, then…
X6
?
?
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If X = 12, then…
X6
?
2
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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.
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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.
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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.
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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.
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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
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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
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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
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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
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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
![Page 63: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/63.jpg)
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
![Page 64: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/64.jpg)
Lesson 2-7
Write this in
Your planner!
![Page 65: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/65.jpg)
Today’s Assignment
Lesson 2-1
![Page 66: 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=](https://reader035.vdocuments.us/reader035/viewer/2022062519/5697bf821a28abf838c85ba6/html5/thumbnails/66.jpg)
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!