COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS 2013

COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS

2013

COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS

Purpose: Mathematics Review for 7th Grade (Can be used as enrichment or remediation for most middle school levels)

Contents: Concept explanations & practice problems.

Sources: PA Standards-PDE website.

Additional Reinforcement:www.studyisland.com www.ixl.com (links provided throughout)

www.mathmaster.org (links provided throughout)

and PSSA Coach workbook

Created by: Jessie Minor

IN ORDER TO CALCULATE EXPERIMENTAL PROBABILITY OF AN EVENT USE THE FOLLOWING DEFINITION:

P(Event)=

3Coach Lesson 30

Number of times the event occurredNumber of total trials

EXPERIMENTAL PROBABILITY!

Example:

A student flipped a coin 50 times. The coin landed on heads 28 times.

Find the experimental probability of having the coin land on heads.

P(heads) = 28 = .56 = 56% 50

It is experimental because the outcome will change every time we flip the coin.

EXPERIMENTAL PROBABILITY!

Experimental Probability IXL

4

5

PRACTICE EXPERIMENTAL PROBABILITY!

A spinner is divided into five equal sections numbered 1 through 5. Predict how many times out of 240 spins the spinner is most likely to stop on an odd number.

F. 80G. 96H. 144I. 192

Marilyn has a bag of coins. The bag contains 25 wheat pennies, 15 Canadian pennies, 5 steel pennies, and 5 Lincoln pennies. She picks a coin at random from the bag. What is the probability that she picked a wheat penny?

F. 10%G. 25%H. 30%I. 50%

Coach Lesson 296

THEORETICAL PROBABILITY!

The outcome is exact!When we roll a die, the total possible

outcomes are 1, 2, 3, 4, 5, and 6. The set of possible outcomes is known as the sample space.

Find the prime numbers of the sample space above– since 2, 3, and 5 are the only prime numbers in the same space…

P(prime numbers)= 3/5 = ______%

PRACTICE THEORETICAL PROBABILITY!

60

RATE: comparison of two numbers Example: 40 feet per second or 40 ft/ 1 sec

UNIT PRICE: price divided by the unitsExample: 10 apples for $4.50

Unit price: $4.50 ÷ 10 = $0.45 per apple

SALES TAX: change sales tax from a percent to a decimal, then multiply it by the dollar amount; add that amount to the total to find the total price

Example 1: $1,200 at 6% sales tax = 6 ÷ 100 = 0.06 x 1,200 = 72

1200 + 72 $1272

COACH LESSON 4Unit Prices IXL

7

RATE/ UNIT PRICE/ SALES TAX!

$7.99 x 3 = $23.97

$23.97 x 0.06 = $1.4382

Sales Tax = $1.44

8

Example 2: Rachel bought 3 DVDs. Using the 6% sales tax rate, calculate the amount of tax she paid if each DVD costs $7.99?

PRACTICE SALES TAX!

Distance formula: distance = rate x timeOR

D = rt

Example 1: A car travels at 40 miles per hour for 4 hours. How far did it travel?

d=rtd=40 miles /hr x 4 hrsd = 160 miles.

We can also use this formula to find time and rate. We just have to manipulate the equation.

Example 2: A car travels 160 miles for 4 hours. How fast was it going?

d = rt160 miles = r (4 hours)160 miles ÷ 4 hrs = r40 miles/hr = r

COACH LESSON 239

DISTANCE FORMULA!

DISTANCE = RATE X TIME

WITH THIS FORMULA WE CAN FIND ANY OF THE THREE QUANTITIES, RATE, TIME, OR DISTANCE, IF AT LEAST TWO OF THE QUANTITIES ARE GIVEN.

If the time and rate are given, we can find the distance:

EXAMPLE: How far did Ed travel in 7 hours if he was going 60 miles per/hour?

d = rtd = 60miles/hr x 7 hrsd = 420 miles

Or if the distance and rate are given, we can find the time:

d = rt420miles = 60 miles/hr x t(420 miles ÷ 60 miles/hr) = 7 hours

10

PRACTICE THE DISTANCE FORMULA!

Michael enters a 120-mile bicycle race. He bikes 24 miles an hour. What is Michael's finishing time, in hours, for the race?d = rt

A 2B 5C 0.2D 0.5

11

PRACTICE USING THE DISTANCE FORMULA!

Gilda’s family goes on a vacation. They travel 125 miles in the first 2.5 hours. If Gilda’s family continues to travel at this rate, how may miles will they travel in 6 hours?Distance = rate x time

300 miles

Ratio: comparison of two numbers.

Example: Johnny scored 8 baskets in 4 games. The ratio is 8 = 2 4 1

Proportion: 2 ratios separated by an equal sign .

If Johnny score 8 baskets in 4 games how many baskets will he score in 12 games?

1. Set up the proportion

8 baskets = x baskets4 games 12 games

2. Cross multiply & Divide4x = 8 ( 12 )4x = 96x = 96

4x= 24 baskets

COACH LESSON 7

Ratios Word Problems IXL12

RATIOS & PROPORTIONS!

ADDING AND SUBTRACTION – FIND COMMON DENOMINATORS! Use factor trees, find prime factors , circle ones that are the

same, circle the ones by themselves. Multiply the circled numbers.

EXAMPLE: 5 + 812 9

12 9

2 6 3 3 12: 2 2 3 2 3 9: 3 3

3 x 3 x 2 x 2 = 36Common denominator = 36

3 x 5 = 4 x 8 = 15 + 32 = 47 36 36 36 36 36

COACH LESSON 1Least Common Denominator IXL13

FRACTIONS!

14

PRACTICE FRACTIONS!

Multiplying fractions : cross cancel and multiply straight across

¹ 4 X ¹ 5 = 1 ¹ 5 ² 8 2

Dividing fractions : change the sign to multiply, then reciprocate the 2nd fraction

3 ÷ 54 8 =

3 X 8 = 24 REDUCE!!!4 5 20

COACH LESSON 2

Multiplying Fractions IXLDividing Mixed Numbers IXL

15

MULTIPLYING & DIVIDING FRACTIONS!

1 1/5

3 X 54 6

1 X

7

49 135 X 49 5

16

PRACTICE MULTIPLYING FRACTIONS!

58

191

49

When multiplying or dividing mixed numbers, always change them to improper fractions, then multiply.

Example 1: 1 ¾ x 1 ½ = 7 x 3 = 214 2 8

Example 2: 12 x 2 ½ = 12 x 5 = 60 = 1 2 2

17Dividing Mixed Numbers IXL

Multiplying & Dividing Mixed Numbers!

2 5 8

30

When dividing any form of a fraction, change the division to multiplication, then reciprocate the 2nd fraction.

Example: 1 ¾ ÷ 1 ½ =

7 ÷ 34 2

7 x 2 = 14 = 4 3 12

Dividing Fractions IXL18

Dividing Mixed Numbers!

11/6

LCM : Least Common Multiple : the smallest number that 2 or more numbers will divide into

Example: Find the LCM of 24 and 32

You can multiply each number by 1,2,3,4… until you find a common multiple which is 96.

Or you can use a factor tree: 24 32

2 12 2 16

2 2 6 2 2 8

2 2 2 3 2 2 2 4

24: 2 2 2 2 2 32:

22

22

22

32 2 2x2x2x3x2x2 = 96

19

LEAST COMMON MULTIPLE!

GCF~ GREATEST COMMON FACTOR : The Largest factor that will divide two or more numbers. In this case we would multiply the factors that are the same.

24: 32:

Example: 2x2x2 = 8, so 8 is the GCF of 24 and 32.

20

22

22

22

32 2

GREATEST COMMON FACTOR!

21

PRACTICE LCM AND GCF!

What is the least common multiple of 3, 6, and 27?

A 3B 27C 54D 81

What is the greatest common factor of 12, 16, and 20?

A 2B 4C 6D 12

What is the greatest common factor (GCF) of 108 and 420 ?

A     6B     9C    12D     18

What is the least common multiple (LCM) of 8, 12, and 18 ?

A      24B      36C      48D      72

22

PRACTICE LCM AND GCF!

ABSOLUTE VALUE: the number itself without the sign; a number’s distance from zero

The symbol for this is | |

Example:

The absolute value of |-5| is 5

The absolute value of |5| is 5

Absolute Value IXL23

ABSOLUTE VALUE!

24

PRACTICE ABSOLUTE VALUE!

If x=-24 and y=6, what is the value of the expression |x + y|?

A 18B 30C -18D -30

DISTRIBUTIVE PROPERTY!

A(B + C) = AB + AC (We distributed A to B and then A to C)

Solving 2 step equations: 4(x + 2) = 244x + 8 = 24

subtract 8 4x = 16divide by 4 x = 4

•Remember when solving 2 step equations do addition and subtraction first then do multiplication and division.

•This is opposite of (please excuse my dear aunt sally,) which we use on math expressions that don’t have variables.

COACH LESSON 20Distributive Property IXL25

Always has parentheses

A ( B X C) = B (C X A) FOR MULTIPLICATION

A + (B + C) = B + (C + A) FOR ADDITION

A X B = B X A FOR MULTIPLICATION

A + B = B + A FOR ADDITION

26

Associative Commutative

Properties for Multiplication IXL

Commutative Property for Addition IXL

Associative & Commutative Property!

We use stem and leaf plots to organize scores or large groups of numbers.

To arrange the numbers into a stem and leaf plot, the tens place goes in the stem column and the ones place goes in the leaf column.

Example: We will arrange the following numbers in a stem & leaf plot: 40, 30, 43, 48, 26, 50, 55, 40, 34, 42, 47, 47, 52, 25, 32, 38, 41, 36, 32, 21, 35, 43, 51, 58, 26, 30, 41, 45, 23, 36, 41, 51, 53, 39, 28 Stem

2345

Leaf1 3 5 6 6 80 0 2 2 4 5 6 6 8 90 0 1 1 1 2 3 3 5 7 7 8 0 1 1 2 3 5 8

27

Stem and Leaf Plots, Box – and – Whisker Plots

Stem-and-Leaf-Plots IXL

COACH LESSON 24

MODE—The number that occurs the most often—The mode of these scores– is 41.

RANGE—The difference between the least and greatest number—is 37.

MEDIAN—The middle number of the set when the numbers are arranged in order—it is 40.

MEAN– Another name for average is mean.

FIRST QUARTILE OR LOWER QUARTILE —The middle number of the lower half of scores—is 32.

THIRD QUARTILE OR UPPER QUARTILE—The middle number of the upper half of scores—is 47.

COACH LESSON 27, 2528

Leaf1 3 5 6 6 80 0 2 2 4 5 6 6 8 90 0 1 1 1 2 3 3 5 7 7 8 0 1 1 2 3 5 8

Lower quartile- 32

Upper quartile- 47

Stem2345

Box-and-Whisker Plot!

Lower extreme

First quartile or lower quartile

Second quartile or median

Third quartile or upper quartile

Upper extreme

Inter quartile

Range

29

Make a stem and leaf plot from the following numbers. Then make a box and whiskers diagram.

25, 27, 27, 40, 45, 27, 29, 30, 26, 23, 31, 35, 39

30

PRACTICE STEM & LEAF/ BOX & WHISKERS!

Stem234

Leaf3 5 6 7 7 7 90 1 5 90 5

Below are the number of points John has scored while playing the last 14 basketball games. Finish arranging John’s points in the stem and leaf plot and then find the range, mode, and median.

Points: 5, 14, 21, 16, 19, 14, 9, 16, 14, 22, 22, 31, 30, 31

Stem Leaf

0

1

2

3

Range:

Mode:

Median:

31

PRACTICE STEM & LEAF/ BOX & WHISKERS!

5 9

4 4 4 6 6 9

1 2 2

0 1 1

26

14

17.5

Note that there are not any variables in the statement.

This is why we use order of operation instead of the Distributive Property.

3 ( 4 + 4 )

÷ 3 - 2

3 ( 8 ) ÷ 3 - 2

24 ÷ 3 - 2

8 - 2

=6

COACH LESSON 532

Order of Operations!

More Practice!1.) 3 + 2(4 x 3) 2.) 12 - 15 - 3

3.) (22 + 14) – 6 4.) 64 – 8 + 8

33

PRACTICE ORDER OF OPERATIONS!Karen is solving this problem: (3² + 4²)² = ?

Which step is correct in the process of solving the problem?A (3² + 4⁴) B (9² + 16²)² C (7²)² D (9 + 16)²

3 + 2(12)3+ 24

27

-3 -3-6

36 – 630

56 + 864

Order of Operations Math Masters

Order of Operations IXL34

PRACTICE ORDER OF OPERATIONS!

Simplify the expression below.

(6² - 2⁴) · √16A 16B 64C 80D 108

1.) 2³ = 2 x 2 x 2 =

2.) 3⁴ = 3 x 3 x 3 x 3 =

3.) 4² = 4 x 4 =

5.) √64 =

4.) √144 = 8

81

16

12

8

FINDING THE MISSING ANGLE OF A TRIANGLE!

65°

50°

a

b c

Finding b: Since the sum of the degrees of a triangle is 180 degrees, we subtract the sum of 65 + 50 = 115 from 180 180 - 115 = 65…so Angle b = 65°

Finding c:If b = 65 to find c we know that a straight line is 180 degrees so if we subtract 180 – 65 = 115° …so Angle c = 115°

Finding a:To find a we do the same thing.

180 – 50 = 130 …so Angle a = 130°

Measuring Angles IXL35

Practice finding the measure of <A in the triangle ABC below!

m<A + 90 + 30 = 180

m<A =

36

A

BC

30°

60 °

A square has 4 angles which each measure 90 degrees.

45

45 4

5

45

D A

C B

37

What is the total measure of the interior angles of a square?

360 °

Hypotenuse

Height = 6 in

Base = 8 inches

C² = A² + B²C² = (6)² in + (8)² inC² = 36 in² + 64 in²C² = 100 in²

√C²= √100 in²

C = 10 in²

Pythagorean Theorem MathMasters

38

Pythagorean Theorem!To find the missing hypotenuse of a right

triangle, we use the formula…

A² + B² = C²

Height= 8 in

Base= 10 in

Area = base x height 2

A = 10in x 8 in 2

A = 80 in² 2

A = 40 in²

Area of Triangles & Trapezoids IXLCOACH LESSON 1239

AREA OF A TRIANGLE!

A = base x height 2

Definition of height is a line from the opposite vertex perpendicular to the base.

AREA = ½ (BASE X HEIGHT)A = ½ bh

Height= 4 ft

Base= 2 ft

Area = ½ bhA = ½ (2ft)(4ft)A = ½ 8ft

A =4 ft²

40

PRACTICE FINDING THE AREA OF A TRIANGLE!

hb

Area = b x h

41

FINDING THE AREA OF A PARALLELOGRAM!

Area of a RECTANGLE = Length x WidthArea of a SQUARE = Side x Side

A = l x w

4ft

2ft

A = 4ft x 2ft

A = 8ft²

2ft2f

t

Area of Rectangles Parallelograms IXL42

AREA OF A RECTANGLE & A SQUARE!

Example:

A = s x s

A = 2ft x 2ft

A = 4ft²4ft²8ft²

PERIMETER IS THE OUTER DISTANCE AROUND A FIGURE. 9

FT3FT

P = a + b + c + …P = 9FT + 9FT + 3FT + 3FT P = ____ FT

43

CALCULATING PERIMETER!

27

To find the area of a compound figure, we simply have to find the area of both figures, then add them together.

6FT AREA = LENGTH X WIDTHA = 2FT X 6FTA = 12FT²

AREA = LENGTH X WIDTHA = 3FT X 5FTA = 15 FT²

44

CALCULATING PERIMETER AND AREA OF COMPOUND FIGURES!

7FT3FT

2FT

TOTAL AREA = 12FT² + 15FT² = 27FT²

CONGRUENT ANGLES & CONGRUENT SIDES!

Congruent angles and sides mean that they have the same measure. Use symbols to show this!

Complementary Supplementary Vertical & Adjacent Angles IXL

45

Complementary angles : angles whose sum equals 90 degrees

Supplementary angles: angles whose sum equals 180 degrees

Right angle: angle measures 90 degrees ---symbolAcute angle: angle less than 90

Obtuse angle: angle greater than 90 degrees

Congruent: when two figures are exactly the sameSimilar: when two figures are the same shape but not the same sizeRegular: when a figure has all equal sides

Line of symmetry: when a line can cut a figure in two symmetrical sides

COACH LESSON 1746

Parallel lines: lines that never touch--- symbol

Perpendicular lines: lines that intersect---symbol

Skew lines: lines in different planes that never intersect

Plane: a flat, 2-Dimensional surface, formed by many pointsA point (0-Dimension); A line (1-D); A plane (2-D); A solid (3-D)

Vertical angles: angles that share a point and are equal

Adjacent angles: are angles that are 180 degrees and share a side

COACH LESSON 1847

Adjacent Angles: Angles that share a common side.

14

3

2

In the figure below:

ANGLES 3 AND 4 ARE ADJACENT ANGLES.

ANGLES 2 AND 3 ARE ALSO ADJACENT ANGLES.

What are some other adjacent angles?

Complementary Supplementary Vertical Adjacent Angles IXL48

RECOGNIZING ADJACENT ANGLES!

REVIEW: CLASSIFYING LINES!

Supplementary angles: sum is 180 degrees

Complementary angles: sum is 90 degrees

Straight angle: equal to 180 degrees

49

Complementary Supplementary Vertical & Adjacent Angles IXL

What is the total number of lines of symmetry that can be drawn on the trapezoid below?

Circle One:

A .)    4 B .)    3

C .)    2 D .)    1

Which figure below correctly shows all the possible lines of symmetry for a square?

Circle One:A.)     Figure 1

B.)     Figure 2

C.)     Figure 3

D.)     Figure 4

Symmetry IXL50

PRACTICE GEOMETRY!

Calculating Volume of a Quadrilateral!

4 ft

5 ft3 ft

Volume IXL51

V = 5ft x 3ft x 4ft = 60ft³

[Volume= units³ or cubed units]

Volume = l x w x h

Two figures are similar if they have exactly the same shape, but may or may not have the same size.

The symbol is ≈

52

Identifying Similar Figures!

A

B C

X

Y Z

For example: ∆ ABC ≈ ∆ XYZ

Which angle is similar to angle B?

Angle: _______Y

Diameter: distance across the center of the circle (double radius)

Radius: the distance half way across the circle ( ½ diameter)

Chord: line that cuts the circle and does not go through the center of the circle

Sector: a pie-shaped part of a circle made by two radii

Segment: the area of a circle in which a chord creates

Circumference: distance around the outside of the circle

COACH LESSON 15

53

Arc: a connected section of the circumference of a circle

Inscribed angles: angles on the inside of the circle formed by two chords

Central angles: angles in the center of the circle formed by two radii

COACH LESSON 15

54

55

PRACTICE FINDING THE CIRCUMFERENCE OF A CIRCLE!

If the circumference of a circle s 16Π, what is the radius?Hint: C= 2Πr

A 4B 8C 16D 32

56

PRACTICE FINDING THE AREA OF A CIRCLE!

If the diameter of a car tire is 30 cm, what is the area of that circle? Round your answer.Hint: Area = Π x r² *USE ∏= 3.14

A     30.14 cm² B     314 cm² C     7,070 cm² D     707 cm²

A duck swims from the edge of a circular pond to a fountain in the center of the pond. Its path is represented by the dotted line in the diagram below.What term describes the duck's path?

A    chordB     radiusC     diameterD     central angle

57

MORE PRACTICE!

Rules:

Negative + Negative = Negative

-4 + -3 = -7

Positive + Positive = Positive

4 + 3 = 7

Negative + Positive = ? (Keep the sign of the larger integer & subtract)

-4 + 3 = -1

Add & Subtract Integers IXL

58

Adding Negative Numbers!

Rules:

Negative x Negative = Positive Negative ÷ Negative = Positive

-4 x -2 = 8 -4 ÷ -2 = 2

Positive + Positive = Positive Positive ÷ Positive = Positive

4 x 2 = 8 4 ÷ 2 = 2

Negative x Positive = Negative Negative ÷ Positive = Negative

-4 x 2 = -8 -4 ÷ 2 = -2

59

Multiplying & Dividing Negative Numbers!

Multiplying & Dividing Integers IXL

Negative integers further to the left of zero have less value.

Positive integers further to the right of zero have greater value.

Example: -3 IS GREATER THAN -6

COACH LESSON 360

Comparing & Ordering Integers!

NEGATIVE POSITIVE

Use the following symbols for inequality number sentences:

< less than -4 < 2

≤ less than or equal to 3 ≤ 4

> greater than 6 > 3

≥ greater than or equal to -5 ≥ -6

One-step Linear Inequalities IXL

61

Inequalities!

To solve for a variable in an equation, the variable must be alone on one side of the equals sign.

Use a model or an inverse operation to solve a one step equation.

Example: 3x = 24

Step 1: Divide by 3 3x = 24on both sides 3 3of the equation

x = 8

COACH LESSON 21

Two-step Linear Equations IXL62

Solving One-Step Equations!

We can translate math sentences to numbers and symbols only

Examples:

Translate: “five more than” (5 + n)

Translate: “three times a number” (3 x n, or 3n)

When you combine both: “five more than three times a number”

5 + 3n or 3n +5

COACH LESSON 2263

Modeling Mathematical Situations!

Functions: inserting a value in for x to find y or f(x)

Example: f(x) = 2x + 4 If x = 2

Then f(x) = 2 (2) + 4 f( x) = 4 + 4 f(x) = 8

So y = 8

A function is when we put a value in and get an answer out.

COACH LESSON 20

Evaluating Functions IXL64

Functions!

Scientific notation -- 4.057 x 10⁶(This means to move the decimal six places to the right.)

4.057 x 10⁶ becomes 4,057,000

Expanded notation --- numbers written using powers of 10

Example: 4,234 = (4 x 10³) + (2 x 10²) + (3 x 10¹) + (4 x 10⁰)

4000 + 200 + 30 + 4 = 4,234

Any number raised to the zero power equals 1. 10 ⁰ = 1

Any number raised to the 1st power equals that number. 8¹ = 8

65

Scientific Notation!

METRIC SYSTEM & CONVERSTION!

START at the unit you currently have, then move the decimal to the unit you’re looking for.

Example 1: 4 kilometers = 4000 meters

Example 2: 36 millimeters = 3.6 centimeters

COACH LESSON 11

66

KiloHect

o

Deka

MeterLiterGram Deci

Centi Milli

67

PRACTICE UNIT CONVERSIONS!The students in a math class measured and recorded their heights on a chart in the classroom. Keith’s height was 1.62 meters. Which is another way to show Keith’s height?

A    0.162 cmB     16.20 cmC     162 cmD     1,620 cm

A drawing of the Greensburg Airport uses a scale of 1 centimeter = 300 meters. Runway A is drawn 12 centimeters long. How many meters is the actual length of the runway?

F 300G 360H 3,000J 3,600

Weight Unit Conversions!

Use the chart and move the decimal point.

Gram = weightMeter = distanceLiter = volume

For U.S. Customary measurement, conversions are on PSSA charts provided during testing time.

68

The flower box in front of the city library weighs 124 ounces. What does the flower box weigh in pounds?*Hint: 1 pound = 16 ounces

A 7 ½ B 7 ¾ C 868D 1984

69

PRACTICE WEIGHT UNIT CONVERSIONS!Which of the following is a metric unit for measuring mass?

A    meterB     literC     poundD     gram

70

PRACTICE MORE UNIT CONVERSIONS!

A scientist measures the mass of a rock and finds that it is 0.16 kilogram. What is the mass of the rock in grams?

A    1.6 gramsB     16 gramsC     160 gramsD     1,600 grams

1. Always list the conversion.2. Identify the correct multiplier.3. Set up the multiplication problem with units being opposite

(top & bottom)4. Multiply & Simplify

For example: Change 240 feet to yardsa) First list the conversions: 3 feet OR 1 yard

1 yard 3 feet

b) Since we want yards multiply by 1 yard 3 feet

c) So 240 feet x 1 yard1 3 feet

d) Then 240 feet = 80 yards

COACH LESSON 971

Unit Multipliers!

A ratio is a comparison between two numbers.

Two ratios separated by an equals sign is called a proportion.

COACH LESSON 7

Ratios IXL72

Ratios & Proportions:

To solve a proportion, we cross multiply and divide.

Example: 4 = 25 = x

4x = 10 x = 104 4 4

x = 2 ½

73

Rational & Irrational NumbersAn Irrational Number is a real number that cannot be

written as a simple fraction.

A Rational Number can be written as a simple fraction.Irrational means not Rational.

Example: 7 is rational, because it can be written as the ratio 7/1Example 0.333... (3 repeating) is also rational, because it can

be written as the ratio 1/3

Practice Irrational Numbers!

74

Which of these is an irrational number?

A    -2B     √56C     √64D     3.14

Which of these is an irrational number?

A    √3

B    -13.5

C     7 11D     1 √9

Fraction Decimal Percent

Place number over its place

value and reduce

Divide by 100 Multiply by 100

75 = 3100 4 0.75 0.75 x 100 =

75%

125 = 11000 8 0.125 0.125 x 100 =

12.5%

150 = 3 = 1 ½ 100 2 1.50 1.50 x 100 =

150%

Converting Rational Numbers!

COACH LESSON 475

Points on a Coordinate Grid!

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

COACH LESSON 16

Ordered pair:[3, 2] 3 is x value and 2 is y value

Point of Origin [0, 0]

76

A scale is the ratio of the measurements of a drawing, a model, a map or a floor plan, to the actual size of the objects or distances.Example:

An architect’s floor plan for a museum exhibit uses a scale of 0.5 inch = 2 feet. On this drawing, a passageway between exhibits is represented by a rectangle 3.75 inches long. What is the actual length of the passageway?

To find an actual length from a scale drawing, identify and solve a proportion.

Drawing = DrawingActual Actual

Let p = the actual length in feet of the passagewayUse cross

products to solve the proportion

0.5 = 3.752 p

0.5 x p = 2 x 3.75 0.5 p = 7.5 p = 15

COACH LESSON 14

Scale & Indirect Measurement MathMaster77

Scaling!

SOLVING PROBLEMS USING PATTERNS!Example: Erin is collecting plastic bottles. On Monday she has 7 bottles, on Tuesday she has 14 bottles, on Wednesday she has 21 bottles, and on Thursday she has 28 bottles. If the pattern continues, how many bottles will she have on Friday?

1) Notice the pattern: 7, 14, 21, 28

2) Write the different operations that you can perform on 7 to get 14.

a) 7 + 7 = 14b) 7 x 2 = 14

3) Check these operations with the next term in the pattern.c) 14 + 7 = 21 d) 14 x 2 = 28

4) Find the next term in the pattern to determine how many bottles Erin will have on Friday.

5) 28 + 7 = 35

COACH LESSON 19

78

Estimation!

Estimating involves finding compatible numbers that will make the numbers easier to operate.

Leo’s yearly salary is $51,950. Estimate how much money Leo makes in one week.

$51,950 is about $52,000.

Divide the compatible numbers.

$52,000 divided by 52 = $1,000

COACH LESSON 1079

Histogram is a bar graph without the spaces between the bars.

Bar graphs have spaces to show differences in data.

COACH LESSON 26

Interpret Histograms IXL

80

0

1

2

3

a b c0

1

2

3

4

Double and Triple Bar & Line Graphs are used to show two sets of related data.

Categ

ory

1

Categ

ory

2

Categ

ory

3

Categ

ory

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1

2

3

4

5

6

Series 1Series 2Series 3

COACH LESSON 25

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Category 1

Category 2

Category 3

Category 4

0

1

2

3

4

5

6

Series 1Series 2Series 3

We can use trends or patterns seen in graphs to make predictions.

COACH LESSON 31

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Making Predictions!

Continue Studying & Good Luck!!!

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