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 ∙ – 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 32x

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 Find the difference: x 10⁴ x 10⁴

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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: … 0.75

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 # 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

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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 = 9 7 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

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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 # 1-9

Chapter 1 Lesson 7 Estimation

Rounding Whole Numbers 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 >> >> 1 – 3-1 = ∙ 9.25 – 10.5 >> >> 9 – 11 ∙ 9 = 99

Using Compatible Numbers Suppose you have $ About how many CDs can you buy for $7.95 – 50.25<< Set up the Quotient 7.95 – 48 << Choose compatible numbers 8 – 6<< 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  use compatible numbers Estimate ⅛ of ¼ of 884 then find 1/8 of that.

Lesson Practice Text p # 1-10 H.W. Chapter 1 Review – Text p # 1-16