Download Algebraic Expressions and Properties

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Algebraic Expressions and Properties
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Schedule:
Algebraic Expressions and Properties
This is the tentative order I plan on completing the lessons. Keep in mind, I
may choose to move even quicker (skip a day or two) or even slower
(add to this). I will surprise you with a POP QUIZ at some point during these
lessons. I will also give you a test at the end of the unit to see if you have
learned all of the information that I presented.
Be sure that you do not fall behind and come to class ready for your
math lesson each day.
Homework is NOT optional! It is required to be completed and submitted
the day it is due. NO EXCUSES!
1
Lesson
Algebraic Expressions
2
Writing Expressions
3
Properties of Addition and
Multiplication
4
The Distributive Property
HW
Lesson #1 – Note Taking Guide
Algebraic Expressions
An _____________ ______________ is an expression that may contain ____________,
__________________, and one or more ________________.
Part of an algebraic expression are
called ___________________.
Identifying Parts of an Algebraic Expression
Identify the terms, coefficients, and constants in each expression.
a.
5x + 13
b.
Terms:
2x2 + y + 3
Terms:
Coefficient:
Coefficient:
Constant:
Constant:
Your Turn
Identify the terms, coefficients, and constants in each expression.
1. 12 + 10c
2.
15 + 3w +
1
2
3.
Terms:
Terms:
Terms:
Coefficient:
Coefficient:
Coefficient:
Constant:
Constant:
Constant:
z3 + 9z
Writing Algebraic Expressions Using Exponents
Write each expression using exponents.
a. d
d
d
d
b.
1.5
h
h
h
What is the repeated factor?
What is the repeated factor?
How many times was it repeated?
How many times was it repeated?
Your Turn
Write the expression using exponents.
1.
j
j
j
j
j
j
2.
9
k
k
k
k
k
To check an algebraic expression, subsitute a number foreach variable. Then
use the order of operations to find the value of the numerical expression.
Evaluating Algebraic Expressions
a. Evaluate k + 10 when k = 25.
b. Evaluate 4
Your Turn
1. Evaluate 24 + c when c = 9.
n when n = 12.
2.
Evaluate d – 17 when d = 30.
Evaluating an Expression with Two Variables
2
Evaluate a ÷ b when a = 16 and b = .
3
Your Turn
Evaluate the expression when p = 24 and q = 8.
1. p ÷ q
2.
q+p
3.
p–q
4.
pq
Evaluating an Expression with Two Operations.
***Don’t forget about order of operations***
a. Evaluate 3x – 14 when x = 5.
b.
Evaluate z2 + 8.5 when z = 2.
3.
y2 – 7
Your Turn
Evaluate the expression when y = 6.
1. 5y + 1
2. 30 – 24 ÷ y
4.
1.5 + y2
Real-Life Application
You are saving money to buy a skateboard. You begin with $45 and you save
$3 each week. The expression 45 + 3w gives the amountof money you save
after w weeks.
a. How much will you have after 4 weeks, 10 weeks, and 20 weeks?
b. After 20 weeks, can you buy the skateboard? Explain.
Your Turn
What if in the skateboard example the expression for how much money
you have after w weeks is 45 + 4w. Can you buy the skateboard after 20
weeks. Explain.
Lesson #2 – Note Taking Guide
Writing Expressions
Some words imply math operations.
Writing Numerical Expression
Write the phrases as an expression.
a. 8 fewer than 21
b.
the product of 30 and 9
Writing Algebraic Expression
Write the phrases as an expression.
a. 14 more than a number x.
b. b. a number y minus 75
c. the quotient of 3 and a number z.
Your Turn
Write the phrase as an expression.
1. The sum of 18 and 35
2.
6 times 50
3. 5 less than a number b
4.
a number x divided by 4
6.
100 decreased by a number k.
5. the total of a number t and 11
Writing Algebraic Expression
The length of Interstate 90 from West Coast to the East Coast is 153.5 miles more
than 2 times the length of Interstate 15 from southern California to northern
Montana. Let m be the length of Interstate 15. Which expression can you use
to represent the length of Interstate 90?
Hint: Do you see any words that imply math operations?
a. 2m + 153.5
b.
2m - 153.5
c. 153.5 – 2m
d.
153.5m + 2
Real-Life Application
You plant a cypress tree that is 10 inches tall. Each year, its height increases by
15 inches.
a. Make a table that shows the height of tree for 4 years. Then write an
expression for the height after t years.
Year, t
Expression
Height (inches)
b. What is the height after 9 years, write and solve the expression.
Your Turn
1. Your friend has 5 more than twice as many game tokens as your sister. Let
t be the number of game tokens your sister has. Write an expression for
the nuymber of game tokens your friend has.
2. In the cypress tree example, what is the height of the cypress tree after 16
years. Write and expression and then solve.
Lesson #3 – Note Taking Guide
Properties of Addition and Multiplication
Expression with the same value, like 12 + 7 and 7 + 12, are __________________
___________________. You can use the __________________ and _______________
Properties to write equivalent expressions.
Key Ideas
Commutative Properties
Words: Changing the ___________ of addends of factors does not change
the sum or product.
Numbers: 5 + 8 = 8 + 5
Algebra: a + b = b + a
5
a
8=8
5
b=b
a
Associative Properties
Words: Changing the __________________ of addends or factors does not
change the sum or product.
Numbers: (7 + 4) + 2 = 7 + (4 + 2)
(7
4)
2=7
(4
Algebra: (a + b) + c = a + (b + c)
2)
(a
b)
c=a
(b
Using Properties to Write Equivalent Expressions
a. Simplify the expression 7 + (12 + x)
What property can I use?
b. Simplify the expression (6.1 + x) + 8.4
What property can I use?
c. Simplify the expression 5(11y)
What property can I use?
c)
Your Turn
Simplify the expression. Explain each step.
1. 10 + (a + 9)
2.
1
1
3
3
(c + ) +
3.
5(4n)
Addition Property of Zero
Words: The sum of any number and ______________ is that number.
Numbers: 7 + 0 = 7
Algebra: a + b = b + a
Multiplication Properties of Zero and One
Words: The product of any number and ______________ is 0.
The product of any number and ________ is that _____________.
Numbers: 9
0=0
Algebra: a
4
1=4
a
0=0
1=a
Using Properties to Write Equivalent Expressions
a. Simplify the expression 9
b. Simplify the expression 4.5
0
r
p.
What property can I use?
1.
What property can I use?
Real-Life Application
You and six friends play on a basketball team. A sponsor paid $100 for the
league fee, x dollars for each player’s T-shirt, and $68.25 for trphies. Write an
expression for the total amount the sponsor paid. (Make sure your expression is simplified.)
Your Turn
Simplify the expression. Explain each step.
1. 12 b 0
2.
1 m
24
`
`
`
3.
(t +15) + 0
3. In the basketball example, your sponsor paid $54.75 for trophies. Write an
expression for the total amount the sponsor paid.
Lesson #4 – Note Taking Guide
The Distributive Property
Key Ideas
Distributive Property
Words: To multiply a sum or difference by a number, multiply _________
number in the sum or difference by the number _________________ the
parentheses. Then evaluate.
Numbers: 3(7 + 2) = 3 x 7 + 3 x 2
Algebra: a(b + c) = ab + ac
3(7 - 2) = 3 x 7 - 3 x 2
a(b - c) = ab – ac
Using Mental Math
Use the Distributive Property and mental math to solve.
a. 8 x 53 = 8( _____ + _____ )
b.
7 x 97 = 7 ( ______ - ______)
Using the Distributive Property
1
3
2
4
Use the Distributive Property to find x 2
Extension 3.4 – Factoring Expressions
Factoring an Expression
Key Idea
Words: Writing a numerical expression or algebraic expression as a
product of factors is called ___________________________. You can
use the Distributive Property to factor expressions.
Numbers: 3
7 + 3
2 = 3(7 + 2)
Algebra: ab + ac = a(b + c)
3
7 - 3
2 = 3(7 - 2)
ab - ac = a(b - c)
Factoring a Numerical Expression
Factor 20 – 12 using the GCF.
Find the GCF of 20 and 12.
The GCF of 20 and 12 is ___________.
Write each term of the expression as a product of the GCF and the remaining
factor. Then use the Distributive Property to factor the expression.
20 – 12 = 4 ( ) - 4 (
=4(
-
)
)
Rewrite using GCF.
Distributive Property
Identifying Equivalent Expressions
Which expression is not equivalent to 16x + 24?
A.
2(8x + 12)
B.
4(4x + 6)
C.
6(3x + 4)
D.
(2x + 3)8
Factoring an Algebraic Expression
You receive a discount on each book you buy for your electronic reader. The
original price of each book is x dollars. You buy 5 books for a total of (5x – 15).
Factor the expression. What can you conclude about the discount?
Hint: Find the GCF of 5x and 15.
Your Turn
1.
12x – 4
2.
98 – 14x