1.2 - Writing Numerical Expressions

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Assignment List
Textbook Lesson or Topic
Date
Assignment
9.1
Powers and Exponents
p.473, #1-7, 12-24
10.1
Squares and Square Roots
p.540-542, #11-30,32-33, 44-47
9.1 and 10.1 Review
p.829, (9-1) #1-14
p.832, (10-1) #1-9, 19-27
1.1
Numerical Expressions
(PEMDAS)
p.8-9, #18-29,39,40
Substitution
p.14, #22-29, 32-37
1.2
Writing Numerical Expressions
p.8-9, #12-17, 41,42
1.2
Writing Algebraic Expressions
p.14-17, #1-4, 12-17,30,45-48
1.3
Properties
p.21-23, #2-7,17-24,49-51
Simplifying Expressions
P.21-23, #25-36,49-52
1.1, 1.2, 1.3 Review
p.24, #1-25 (skip #7)
Unit Review
study guide
Test
no homework
Place Value
1
4 . 2
5
6
3
9.1 - Powers and Exponents
Exponent: how many times a number is used as a factor
Power: a number that is expressed using an exponent
3
4
Base: the number that is multiplied
The negative sign out front!
-54 (exponent only applies to the 5)
(-5)4 (exponent applies to the -5)
*bring negative sign to the answer
Any number to the zero power defined as 1.
Zero to the zero power is undefined (cannot be done).
Write each expression using exponents.
6 • 6 • 6 • 6 • 6• 6 • 6
(-2)(-2)(-2)• t • t •q
4(−x)(−x)(−x)
(c – d)(c – d)
1 1 1 1
    
2 2 2 2
3m(n) • 2n • m • 4n
Write each expression in expanded form.
1
( ‒ )3
7
46
(x-2)2
10.1 - Squares and Square Roots
PERFECT SQUARE: the square of an integer
SQUARE ROOT: one of the two equal factors of a number
[52 = 25, so 5 is the square root]
RADICAL SIGN (√ ): used to indicate a positive square root
Rules
49
( no sign in front, just do it)
 16
(– in front, put – in the answer)

100
 81
(  , put the  in the answer)
(– inside, cannot be done)
Find each square root.
 4
64
 36
 121
Use a calculator to find each square root to the nearest tenth.
23
 46
A baseball diamond is actually a square with an area of 8100 square feet. Most baseball teams cover
their diamond with a tarp to protect it from the rain. How long is the tarp on each side?
Walter found a piece of paper at the store that will cover 256 square feet. If he lays the paper on the
gym floor, what is the possible maximum length that each side of the paper?
1.1 - Numerical Expressions
Operation: addition, subtraction, multiplication, division
Numerical Expression: A combination of numbers and operations
Evaluate: To calculate or solve
Order of Operations (PEMDAS): Rules that are followed when more than one operation
is used in an expression
P
E
M
D
A
S
Evaluate each numerical expression
6+8×2
24 ÷ 8 × 3
5(4 + 6) – 7 ∙ 7
3(18  6)  2(4)
49  31
19  14
(3 + 4)(6 – 5 + 8)
7(40 ÷ 5) ‒ 2
6÷2•3
2+4•7–5•2+6•3
(6)7 + 3
4[(12-4) + 2]
Substitution Practice!
Follow the rules of PEMDAS to evaluate each expression.
e = 3 and f = 9
a = 4 and b = 8
6–e+f
ab
16
x = 8, y = 10 and z = 2
a = 4 and c = 12
x + y – 2z²
15 ‒ 3a + 2c
a = 5, b = 2, and c = 3
x = 8, y = 10 and z = 2
6(a – c)⁴
3(x + z)
1.2 - Writing Numerical Expressions
Numerical Expression: contains only numbers, no variables
Write a numerical expression for each phrase. Find the value.
The quotient of eighteen and six.
The total number of photos if there are nine photos in the camera plus four more.
Madison earns an allowance of $5 per week. She also earns $4 per hour babysitting, and usually
babysits 6 hours each week. Find the total amount of money she earns in one week.
Eleven less than twenty two.
Seven less than the product of two and eight.
The quotient of zero and four.
The quotient of four and zero.
1.2 - Writing Algebraic Expressions
Algebra: mathematical expression or equation that uses numbers and symbols
Variable: a letter or symbol used to represent a value
Algebraic Expression: contains at least one variable and one number
Translate each phrase into an algebraic expression. Use any variable.
Two miles less than the athlete ran.
Five points more than the points scored by field goals if each goal is worth 3 points.
35 more than the number of tickets sold.
The difference of six times a number and 10.
East Junior High sold tickets for a school play. The price of an adult ticket was $3, and the price
of a student ticket was $1.
a. Write and algebraic expression that represents the total amount of money collected.
b. Suppose 70 adult tickets and 85 student tickets were sold. How much money was collected?
Ms. Kay is going to take all her students to the movies. The price for transportation totaled $85.
A ticket for each student will cost $5 and each student will get $12 to spend on snacks.
a. Write and algebraic expression that represents the total amount of money Ms. Kay will spend.
b. Suppose there are 150 students. How much will Ms. Kay spend?
1.3 Properties
Properties: statements that are true for any number
Property
Example
Trigger Word
Commutative +
Commutative •
Associative +
Associative •
Additive
Identity
Multiplicative
Identity
Multiplicative
Property of Zero
Name the property shown
1) 8 + 2 = 2 + 8 ____________________________________________
2) 14 + (9 + 10) = (14 + 9) + 10 ______________________________________
3) (2 • 3)x = 2(3 • x) _______________________________________
4) 5 • 7 • 2 = 7 • 2 •5 ______________________________________
1.3 Simplifying Expressions
Simplify Algebraic Expressions: perform all possible operations
13 + (27 + a)
10a(6)
Property:
Property:
Pull apart:
Pull apart:
Snap together:
Snap together:
x(6 • 9)
18 + (h + 15)
Property:
Property:
Pull apart:
Pull apart:
Snap together:
Snap together:
(z + 4) + 12
y(4)(5)
Property:
Property:
Pull apart:
Pull apart:
Snap together:
Snap together:
12 (10 • z)
10 + (p + 18)
Property:
Property:
Pull apart:
Pull apart:
Snap together:
Snap together:
4w(9)
x(11 • 3)
Property:
Property:
Pull apart:
Pull apart:
Snap together:
Snap together:
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