Download 3 - SAS

PSSA – Assessment Coach
Mathematics- Grade 11
Chapter 1 Lesson 1
Orders of Operations and Number
Properties
Example 1: Order of Operations
• Find the value
• 6 ∙ (8+4) – 3
• 6∙8+4–3
• Why are the two values equivalent
Example 2: Algebraic Expressions
• Evaluate 5m – n ² ; where m = 4 & n = 3
Example 3: Number Properties
• Write 2 expressions that can be used to find
the area of the figure below
x
3
2x
Example 4: Inverse Operations
• For which value of w does the expression w -1
have an additive inverse?
– What does inverse mean?
• Think of a value for w that will make the expression
equal to 0
Example 5: Properties
• If r + s = s what is the value of s-r
– Remember the identity property of addition
• a+0=a
• Therefore r must equal ???
Lesson Practice
• P. 35 – 36 # 1-10
Chapter 1 Lesson 2
Powers, Roots, and Scientific
Notation
Example 1: Multiply Exponents
• Find the Area of a rectangle with a length of
b ^4 and the width is b^ 3
– Recall that A = l ∙w
• A = b ^4 ∙ b ^3
Example 2: Find the Product
• 2 ³ ∙ 2 ⁴∙ 4º =
Example 3: Negative Exponents
• Find the value of 3 ⁻³
Example 4 :Square Roots
• Estimate the square root of 23 w/o a calculator
• The area of a square is 256 in². if the length of a side of a
square is shortened by 1in , what is the effect on the are of
the square?
 Area of square = S²
 256 = S²
Example 5: Applying Powers
• If the number of hair a person loses each day
doubles every 6 hours, how many hairs are
lost in a day (24 hours)?
• Set up an exponent bⁿ
– The base is represented by the number be
repeatedly multiplied
• b=
– The exponent is represented by how many times
the hair loses is doubled
• n=
Example 6: Scientific Notation
• Scientific Notation is the product of :
 A number between 1-10
 10 to a given power
• Write 93,000,000 in scientific notation
• Write 0.000000005
• Find the difference: 8.8846 x 10⁴ - 7.4898 x 10⁴
Lesson Practice
• Text p. 44- 45 # 1-10
Chapter 1 Lesson 3
Irrational Numbers
Example 1: Recognizing Irrational Numbers
• Irrational Numbers : numbers that when in
decimal form do not terminate or repeat
 Terminating Decimals
 Repeating Decimals
• Name the following:
0.989898
0.673829…
0.75
Example 2: Applying Irrational Numbers
• Which of following can not be considered an
exact value (irrational number)?
– Perimeter
– C circumference
– Volume
– Area of a square.
Lesson Practice
• Page 50-51 # 1-9
Chapter 1 Lesson 4
Absolute Value and Integers
Example 1: Opposites
• Find the opposite of:
5
 -2
• Find the distance on a Number line for a
integer and it’s opposite:
 -9
4
Example 2: Absolute Value
• Absolute Value: the distance from 0.
• The meanings of “-”
 Find the absolute values
 /3/ =
 /-13/=
 - /-14/=
Basic Operations of Integers
• Adding Integers
 Same Sign: Add, keep the sign
 Different Sign: Subtract, keep the sign of the greater value
• Subtraction Integers
 Add, the opposite (see addition rules)
• Multiply Integers
 Same Signs = positive
 Different Signs = negative
• Divide Integers
 Same Signs = positive
 Different Signs = negative
Lesson Practice
• Page 58 # 1-10
Chapter 1 Lesson 5
Ratio and Proportions
Example 1: Express 4.5 lb/8 oz in simplest form
• Both values must be expressed in the same
units
 16 oz = 1 lb
• Simplify
Example 2: Comparing Fractions/Proportions
• Use cross products

Is
⅚
=
⅔
?
Example 3: Solve Proportions
• Solve for x.
3
7
=
9
x
Example 4: Find the perimeter of a larger similar
Rectangle to the one below with a ratio of 5 :2
45 mm
25 mm
Lesson Practice
• Text P. 67-68 # 1-8
Chapter 1 Lesson 6
Percent Problems
Solving Percent Problems
• Finding the Part, Whole, or the Percent
 Percent Proportion
Part = %
Whole
100
 Percent Equation
 What: variable
 Is : = sign
 Of: Multiplication
Find the Part
• What is 82% of 145
Find the Whole
• 50 is 25% of what number?
Find the percent
• A 3-D T.V. on sale for $450 was originally $600. What
percent is the sale price.
Lesson Practice
• P. 76-77 # 1-9
Chapter 1 Lesson 7
Estimation
Rounding Whole Numbers
• 3,528
• 3,528
– 2 is less than 5
• 3,500
• Look at the number to the
direct right of the underlined
letter
– If the number is 5 or bigger
make the underlined
number 1 higher
– If the number is less than 5
the underlined number will
remain the same
• After the underlined number is
assigned all number after it will
become zeros
Estimating a Sum, Difference, Product, or
Quotient
• Round to the nearest whole number
• 3.27 – 0.88
– 3.27 >> 3 0.88 >> 1
– 3-1 = 2
• 10.5 ∙ 9.25
– 10.5 >> 11 9.25>> 9
– 11 ∙ 9 = 99
Using Compatible Numbers
• Suppose you have $50.25. About how many
CDs can you buy for $7.95
– 50.25
7.95
– 48
8
– 6
<< Set up the Quotient
<< Choose compatible numbers
<< Simplify (Divide)
Using Benchmarks
• When estimating a fraction, one of the most important
concepts is the ability to determine whether a fraction is
larger than or smaller than one-fourth, one-third, one-half,
two-thirds, or three-fourths. This ability allows you to "round"
a fraction to the closest "common" fraction -- 1/4, 1/2, 3/4, or
1.
Example 1: Estimate the value of the
fraction: 4/5
• Solution: First, think of a diagram
of the fraction 4/5
• Now, think of the diagram
benchmarks and compare it to
the diagrams above to determine
the "common" fraction above
that has almost the same amount
of area covered as the fraction
4/5.
• The fraction that is closest to 4/5
is 3/4
Find 1/5 of $ 985
• Find 1/5 of $ 985
 use compatible numbers
• Estimate ⅛ of ¼ of 884 then find 1/8 of that.
Lesson Practice
• Text p. 86 -88 # 1-10
• H.W. Chapter 1 Review
– Text p. 89-93 # 1-16