Download 1-1 Variables

1-1 Algebraic Expressions and the
Order of Operations
Pg 4
Copyright © 2012 by Reynolds Industries. All rights Reserved
Vocabulary and Key Concepts
Define each:
 Variable Algebraic Expression Simplify Evaluate Order of operations-
Algebraic Expressions:
Give me an example of an Algebraic Expression:
Example 1:
 Suppose your after-school job pays $8 an hour.You work a
different number of hours a week. Define a variable. Write
an algebraic expression for your weekly earnings.
Example 2: (Evaluate)
 Evaluate n – 5 for n = 27.
Part 2: Order of Operations
 PEMDAS!
 Work inside grouping symbols.
 Multiply and divide in order from left to right.
 Add and subtract in order from left to right.
Example 3:
 Evaluate n + (13 – n)
5 for n = 8.
Example 4:
 A fitness club charges $100 activation fee and $33 for each
month. Write an expression to model the total cost and then
evaluate the expression for 1 to 6 months of membership.
Problem Set
 Pg 8-9
 Exercises #’s 1 – 9, 18 – 26, 31 – 34, and 43-45 all
1-2 Use a problem-solving plan
Pg 12
Copyright © 2012 by Reynolds Industries. All rights Reserved
Key Concepts
A problem solving plan:
 Read to understand the problem.
 Plan how to solve the problem, and then solve it.
 Look back and check to see if your answer makes sense.
Example 1:
 An air-traffic controller needs to find the difference between
the altitudes of two airplanes. Airplane A is 3,800 ft above the
clouds. Airplane B is at an altitude of 5,500 ft above the
ground. The clouds are at 12,000 ft altitude. What is the
difference in the altitudes of Airplane A and Airplane B.
Example 2:
 In a local school-committee election, a total of 250 votes
were cast for two candidates. Candidate A won the election
by 10 votes. How many votes did Candidate A receive?
Problem Set
 Pg 14
 Exercises #’s 1, 2, 4, 6 and 8
1-3 Integers and Absolute Values
Pg 16
Copyright © 2012 by Reynolds Industries. All rights Reserved
Vocabulary and Key Concepts
 Opposites- two numbers who are the same distance away
from zero. Ex. -5, and 5
 Integers- are whole numbers and their opposites.
…-3,-2, -1, 0, 1, 2, 3…
 Absolute Value- is the distance away from zero on a number
line. Represented by two bars. |x|
Example 1:
 Graph the points 5, -4, -2, and 0 on a number line.
Example 2:
 Find the absolute value.
|6|
|-6|
Example 3:
 Evaluate each expression for the given value.
|a| for a = -2
3|c| for c = -3.5
Example 4:
 Order from least to greatest.
-2, 3, -6, -17
Example 5: (Real world)
 Which continent has the lowest
recorded temperature? Explain.
Problem Set
 Pg 18 – 20
 #’s 2, 8, 16, 18, 24, 26, 40, 44, 46, 54, and 61 – 67
1-4 Adding and Subtracting Integers
Pg 22
Copyright © 2012 by Reynolds Industries. All rights Reserved
Key Concepts
 Adding Integers Rules: (Think number line)
 Same Sign: The sum of the two positive integers is positive. The
sum of two negative integers is negative.
 Adding and keep sign!!
 Ex. 10 + 11
or
-6 + (-11) =
 Different Signs: Find the absolute value of each. Subtract the
lesser absolute value from the greater. The sum has the sign of
the integer with the greater absolute value.
 Subtract and keep sign from larger absolute value!!
 Ex. -10 + 5 =
or
8 + (-3) =
Example 1:
 Add
A) 3 + (-5)
B) -5 + (-6)
C) -32 + (-17)
D) -16 + 62
Key Concepts
 Subtracting Integers Rules:
 To subtract an integer, add its opposites.
 Ex. 5 – 7
or
5 – (-7)
Example 2:
 Which content has the lowest
recorded temperature? Explain.
Example 3: (Real World)
 A group of archaeologists leaves a site in Jordan and descends
647 m to the shore of the Dead Sea. Their initial elevation
was 251 m above sea level. What is the elevation of the Dead
Sea?
Problem Set
 Pg 25-26
 #’s 2-36 evens, and 53-58 all
1-5 Multiplying and Dividing Integers
Pg 28
Copyright © 2012 by Reynolds Industries. All rights Reserved
Key Concepts
 Multiplying Two Integers:
 Same Sign: The product of two integers with the same sign is
positive
 Ex. 10•11
or
-6•(-11) =
 Different Signs: The product of two integers with different signs
is negative.
 Ex. -10•5 =
or
8•(-3) =
Key Concepts
 Dividing Two Integers: (Exact same as multiplication)
 Same Sign: The quotient of two integers with the same sign is
positive
 Ex. 8/2
or
-12/(-6) =
 Different Signs: The quotient of two integers with different
signs is negative.
 Ex. -10/5 =
or
8/(-4) =
Example 1:
 Simplify.
A) 3•(-5)
B) -55/(-11)
C) 32/(-16)
D) -16•8
Example 2: (Real life)
 A hiker descended 360 feet in 40 minutes. What was the hiker’s
average change in elevation per minute?
A little gimmick.
Problem Set
 Pg 31-32
 #’s 2-30 evens
1-6 Using Integers with Mean,
Median, and Mode
Pg 33
Copyright © 2012 by Reynolds Industries. All rights Reserved
Vocabulary and Key Concepts
 Measure of Central Tendency- is a single central value that





summarizes a set of data.
Mean- the average. (the meanest process)
Median- is the middle value when list is in numerical order.
(middle of the road)
Mode- the item that occurs the most. (mode, most)
Range- the difference between the greatest and least value.
Outlier- a data item that is either much larger or smaller than
the rest of the data. (out there!)
Example 1:
 Find the mean, the median, the mode, and the range of the scores.
Example 2: (Outlier)
 Find the absolute value.
|6|
|-6|
Example 3: (Best measure)
 Evaluate each expression for the given value.
Problem Set
 Pg 36
 #’s 2, 7, 14, 16 – 21, and 23(Tricky)
1-7 Powers and Exponents
Pg 39
Copyright © 2012 by Reynolds Industries. All rights Reserved
Vocabulary and Key Concepts
 Factor- an integer that divides another integer with a
remainder of 0.
 Exponent- tells how many times a number, or base, is used as
a factors.
 Base- is the number that is being used as factors.
 Power- is an expression using a base and an exponent.
25
Example 1:
 Write using exponents.
a) 3•3•5•5•5
b) 4•4•x•x•y
Example 2:
 Simplify each expression.
a) (-5)4
b) -54
Review Order of Operations
Example 3:
 Simplify.
a) 26 – (2•5)2
b) -4 + 6•32
Example 4:
 Evaluate each expression for x = -2.
a) 5x3
b) (5x) 3
Problem Set
 Pg 42
 #’s 2-40 evens
1-8 Properties of Numbers
Pg 45
Copyright © 2012 by Reynolds Industries. All rights Reserved
Key Concepts
 Commutative Properties of Addition and Multiplication
(order)
Arithmetic
7 + 12 = 12 + 7
7·12 = 12·7
Algebra
a+b=b+a
a·b = b·a
 Associative Properties of Addition and Multiplication
(grouping)
Arithmetic
(4 + 3) + 7 = 4 + (3 + 7)
(4·7)·3 = 4·(7·3)
Algebra
(a + b) + c = a + (b + c)
(a·b)·c = a·(b·c)
Key Concepts
 Identity Properties of Addition and Multiplication
Arithmetic
7+0=0+7=7
8·1 = 1·8 = 8
Algebra
a+0=0+a=a
a·1 = 1·a = a
Example 1:
 Identify each property.
a)
14 + (12 + 16) = 14 + (16 + 12)
b)
14 + (12 + 16) = (14 + 12) + 16
Example 2:
 Use mental math and these properties to simplify.
A)2.5 + 5.4 + 7.5
B)26 + (-12) + 34
C) -5·7·8
D) -4·356·(-25)
Key Concepts
 Distributive Property
Arithmetic
3(2 + 7) = 3·2 + 3·7
(2 + 7)3 = 2·3 + 7·3
5(8 – 2) = 5·8 – 5·2
(8 – 2)5 = 8·5 – 2·5
Algebra
a(b + c) = ab + ac
(b + c)a = ba+ ca
a(b – c) = ab – ac
(b – c)a = ba – ca
Example 3:
 Find the product.
A)5 ( k – 4)
B)(n + 14) (-8)
Example 4:
 Simplify:
A) 27·12 + 73·12
B)105· 8 – 5·8
Problem Set
 Pg 49
 #’s 2-38 evens