2013

COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS

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

3 EXPERIMENTAL PROBABILITY!

IN ORDER TO CALCULATE EXPERIMENTAL PROBABILITY OF AN EVENT USE THE FOLLOWING DEFINITION: P(Event)=

Number of times the event occurred Number of total trials Coach Lesson 30

4 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 IXL

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. 80 G. 96 H. 144 I. 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%

6 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.

PRACTICE THEORETICAL PROBABILITY!

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

60

Coach Lesson 29

RATE/ UNIT PRICE/ SALES TAX!

RATE: comparison of two numbers Example: 40 feet per second or 40 ft/ 1 sec 7 UNIT PRICE: price divided by the units Example: 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 Unit Prices IXL COACH LESSON 4

8 PRACTICE SALES TAX!

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?

$7.99 x 3 = $23.97

$23.97 x 0.06 = $1.4382

Sales Tax = $1.44

Distance formula: DISTANCE FORMULA!

distance = rate x time OR D = rt Example 1: A car travels at 40 miles per hour for 4 hours. How far did it travel?

d=rt d=40 miles /hr x 4 hrs d = 160 miles.

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

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

d = rt 160 miles = r (4 hours) 160 miles ÷ 4 hrs = r 40 miles/hr = r COACH LESSON 23

10 PRACTICE THE 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 = rt d = 60miles/hr x 7 hrs d = 420 miles Or if the distance and rate are given, we can find the time: d = rt 420miles = 60 miles/hr x t (420 miles ÷ 60 miles/hr) = 7 hours

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 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 B C D 2 5 0.2

0.5

RATIOS & PROPORTIONS!

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 baskets 4 games 12 games 2. Cross multiply & Divide 4x = 8 ( 12 ) 4x = 96 x = 96 4 x= 24 baskets 12 Ratios Word Problems IXL COACH LESSON 7

FRACTIONS!

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 12 + 8 9 12 9 2 6 3 3 12: 2 2 3 2 3 9: 3 3 3 x 3 x 2 x 2 = 36 Common denominator = 36 3 x 5 = 4 x 8 = 15 + 32 = 47 36 36 36 36 36 13 Least Common Denominator IXL COACH LESSON 1

14 PRACTICE FRACTIONS!

MULTIPLYING & DIVIDING FRACTIONS!

Multiplying fractions : cross cancel and multiply straight across ¹ 4 X ¹ 5 ¹ 5 ² 8 = 1 2 15 Dividing fractions : change the sign to multiply, then reciprocate the 2 nd fraction 3 ÷ 5 4 8 = 3 X 8 = 24 4 5 20  REDUCE!!!

1 1/5 Multiplying Fractions IXL Dividing Mixed Numbers IXL COACH LESSON 2

16 PRACTICE MULTIPLYING FRACTIONS!

3 4 X 5 6 5 8 1 X 7 49 13 1 91 5 X 4 9 5 4 9

17 Multiplying & Dividing Mixed Numbers!

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

Example 1: 7 1 ¾ x 1 ½ = x 3 = 21 4 2 8 2 5 8 Example 2: 12 x 2 ½ = 1 2 2 Dividing Mixed Numbers IXL

18 Dividing Mixed Numbers!

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

Example: 1 ¾ ÷ 1 ½ = 7 4 7 4 ÷ 3 2 3 12 1 1/6 Dividing Fractions IXL

19 LEAST COMMON MULTIPLE!

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 24: 32: 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 4 2 2 2 2 2 2x2x2x3x2x2 = 96

20 GREATEST COMMON FACTOR!

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: 2 2 2 2 2 2 3 2 2 Example: 2x2x2 = 8, so 8 is the GCF of 24 and 32.

21 PRACTICE LCM AND GCF!

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

A B C D 3 27 54 81 What is the greatest common factor of 12, 16, and 20?

A B C D 2 4 6 12

22 PRACTICE LCM AND GCF!

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

A B D 6 9 C 12 18 What is the least common multiple (LCM) of 8, 12, and 18 ?

A B C D 24 36 48 72

23 ABSOLUTE VALUE!

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 IXL

24 PRACTICE ABSOLUTE VALUE!

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

A B C D 18 30 -18 -30

25 DISTRIBUTIVE PROPERTY!

A(B + C) = AB + AC (We distributed A to B and then A to C) Solving 2 step equations: subtract 8 divide by 4 4(x + 2) = 24 4x + 8 = 24 4x = 16 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.

Distributive Property IXL COACH LESSON 20

26 Associative & Commutative Property!



Associative

 Always has parentheses   A ( B X C) = B (C X A) FOR MULTIPLICATION   A + (B + C) = B + (C + A) FOR ADDITION 

Commutative

  A X B = B X A FOR MULTIPLICATION   A + B = B + A FOR ADDITION Properties for Multiplication IXL Commutative Property for Addition IXL

27 Stem and Leaf Plots, Box – and – Whisker Plots 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 2 3 4 5 Leaf 1 3 5 6 6 8 0 0 2 2 4 5 6 6 8 9 0 0 1 1 1 2 3 3 5 7 7 8 0 1 1 2 3 5 8 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 scores—is 32.

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

— The middle number of the upper half Stem 2 3 4 5 Leaf 1 3 5 6 6 8 0 0 2 2 4 5 6 6 8 9 0 0 1 1 1 2 3 3 5 7 7 8 0 1 1 2 3 5 8 Upper quartile- 47 Lower quartile- 32 28 COACH LESSON 27, 25

29 Lower extreme Box-and-Whisker Plot!

First quartile or lower quartile Second quartile or median Third quartile or upper quartile Upper extreme Inter quartile Range

30 PRACTICE STEM & LEAF/ BOX & WHISKERS!

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 Stem 2 3 4 Leaf 3 5 6 7 7 7 9 0 1 5 9 0 5

31 PRACTICE STEM & LEAF/ BOX & WHISKERS!

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 0 1 2 3 Leaf 5 9 4 4 4 6 6 9 1 2 2 0 1 1 Range: 26 Mode: 14 Median: 17.5

32 Order of Operations!

3 ( 4 + 4 ) ÷ 3 - 2 3 ( 8 ) 24 ÷ ÷ 3 - 2 3 - 2 8 =6 2 Note that there are not any variables in the statement. This is why we use order of operation instead of the Distributive Property.

COACH LESSON 5

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 C D (9² + 16²)² (7²)² (9 + 16)² More Practice!

1.) 3 + 2(4 x 3) 3 + 2(12) 3+ 24 27 2.) 12 - 15 - 3 -3 -3 -6 3.) (22 + 14) – 6 36 – 6 30 4.) 64 – 8 + 8 56 + 8 64

PRACTICE ORDER OF OPERATIONS!

Simplify the expression below.

(6² - 2⁴) · √16 A 16 B C D 64 80 108 1.) 2³ = 2 x 2 x 2 = 8 Order of Operations Math Masters 4.) √144 = 12 2.) 3⁴ = 3 x 3 x 3 x 3 = 3.) 4² = 4 x 4 = 16 81 5.) √64 = 8 34 Order of Operations IXL

35 FINDING THE MISSING ANGLE OF A TRIANGLE!

a 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° 50° 65° b c 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 IXL

Practice finding the measure of

A 36 C m

37 A square has 4 angles which each measure 90 degrees.

D C 45 45 45 45 B A

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

360 °

Pythagorean Theorem!

To find the missing hypotenuse of a right triangle, we use the formula… Height = 6 in Base = 8 inches C² = A² + B² C² = (6)² in + (8)² in C² = 36 in² + 64 in² C² = 100 in² √C²= √100 in² C = 10 in² 38 Pythagorean Theorem MathMasters

AREA OF A TRIANGLE!

Height= 8 in Area = base x height 2 A = 10in x 8 in 2 A = 80 in² 2 Base= 10 in A = 40 in² Definition of height is a line from the opposite vertex perpendicular to the base.

39 Area of Triangles & Trapezoids IXL COACH LESSON 12

40 PRACTICE FINDING THE AREA OF A TRIANGLE!

Base= 2 ft

Area = ½ bh A = ½ (2ft)(4ft) A = ½ 8ft

Height= 4 ft

A =4 ft²

41 FINDING THE AREA OF A PARALLELOGRAM!

b h

42 AREA OF A RECTANGLE & A SQUARE!

Area of a RECTANGLE = Length x Width Area of a SQUARE = Side x Side Example: 4ft

A = l x w

2ft

A = 4ft x 2ft

2ft 2ft

A = s x s A = 2ft x 2ft

Area of Rectangles Parallelograms IXL

43 CALCULATING PERIMETER!

PERIMETER IS THE OUTER DISTANCE AROUND A FIGURE.

9 FT 3FT

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

44 CALCULATING PERIMETER AND AREA OF COMPOUND FIGURES!

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

6FT 2FT 3FT 7FT

AREA = LENGTH X WIDTH A = 2FT X 6FT A = 12FT² AREA = LENGTH X WIDTH A = 3FT X 5FT A = 15 FT² 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!

45 Complementary Supplementary Vertical & Adjacent Angles IXL

Complementary angles : angles whose sum equals 90 degrees Supplementary angles: angles whose sum equals 180 degrees Right angle: angle measures 90 degrees ---symbol  Acute angle: angle less than 90 Obtuse angle: angle greater than 90 degrees Congruent: when two figures are exactly the same Similar: when two figures are the same shape but not the same size Regular: when a figure has all equal sides Line of symmetry: when a line can cut a figure in two symmetrical sides 46 COACH LESSON 17

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 points A 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 47 COACH LESSON 18

48 RECOGNIZING ADJACENT ANGLES!

Adjacent Angles: Angles that share a common side.

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?

2 3 1 4 Complementary Supplementary Vertical Adjacent Angles IXL

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

PRACTICE GEOMETRY!

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

Circle One: A .) 4 C .) 2 B .) 3 D .) 1 Which figure below correctly shows all the possible lines of symmetry for a square? Circle One: A.) Figure 1 B.) C.) D.) Figure 2 Figure 3 Figure 4 50 Symmetry IXL

Calculating Volume of a Quadrilateral!

51 [Volume= units³ or cubed units]

4 ft 3 ft 5 ft V = 5ft x 3ft x 4ft = 60ft³

Volume IXL

52 Identifying Similar Figures!

Two figures are similar if they have exactly the same shape, but may or may not have the same size. The symbol is ≈ For example: ∆ ABC ≈ ∆ XYZ Which angle is similar to angle B?

X A B C Y Z

Chord: line that cuts the circle and does not of the circle go through the center Diameter: across the center of the circle distance (double radius) Radius: the distance half way across the circle ( ½ diameter) Segment: the area of a circle in which a chord creates Sector: a pie-shaped part of a circle made by two radii Circumference: distance around outside of the circle the Arc: section a circumference circle connected of of the a 53 COACH LESSON 15

54

Central angles: angles in the center of the circle formed by two radii Inscribed angles: angles on the inside of the circle formed by two chords

COACH LESSON 15

PRACTICE FINDING THE CIRCUMFERENCE OF A CIRCLE!

If the circumference of a circle s 16Π, what is the radius?

Hint: C= 2Πr A B C D 4 8 16 32 55

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 B C D

30.14 cm² 314 cm² 7,070 cm² 707 cm² 56

MORE PRACTICE!

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 chord B radius C D diameter central angle

57

58 Adding Negative Numbers!

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

59 Multiplying & Dividing Negative Numbers!

Rules: Negative x Negative = Positive -4 x -2 = 8 Positive + Positive = Positive 4 x 2 = 8 Negative x Positive = Negative -4 x 2 = -8 Negative ÷ Negative = Positive -4 ÷ -2 = 2 Positive ÷ Positive = Positive 4 ÷ 2 = 2 Negative ÷ Positive = Negative -4 ÷ 2 = -2 Multiplying & Dividing Integers IXL

Comparing & Ordering Integers!

NEGATIVE POSITIVE 60 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 3

61 Inequalities!

Use the following symbols for inequality number sentences: < less than -4 < 2 ≤ less than or equal to 3 ≤ 4 > greater than ≥ greater than or equal to -5 ≥ -6 6 > 3 One-step Linear Inequalities IXL

62 Solving One-Step Equations!

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: Step 1: Divide by 3 on both sides of the equation 3x = 24 3x = 24 3 3 x = 8 Two-step Linear Equations IXL COACH LESSON 21

63 Modeling Mathematical Situations!

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 22

64 Functions!

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.

Evaluating Functions IXL COACH LESSON 20

65 Scientific Notation!

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 1 st power equals that number. 8 ¹ = 8

METRIC SYSTEM & CONVERSTION!

Kilo Hecto Deka Meter Liter Gram Deci Centi Milli 66 START at the unit you currently have, then move the decimal to the unit you’re looking for.

Example 1: Example 2: 4 kilometers = 4000 meters 36 millimeters = 3.6 centimeters COACH LESSON 11

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 cm B 16.20 cm C 162 cm D 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 G H J 300 360 3,000 3,600

67

68 Weight Unit Conversions!

Use the chart and move the decimal point.

Gram = weight Meter = distance Liter = volume For U.S. Customary measurement, conversions are on PSSA charts provided during testing time.

PRACTICE WEIGHT UNIT CONVERSIONS!

Which of the following is a metric unit for measuring mass?

A meter B liter C D pound gram A B C D

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 7 ½ 7 ¾ 868 1984

69

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 grams B 16 grams C D 160 grams 1,600 grams

70

71

Unit Multipliers!

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 yards a) 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 yard 1 3 feet d) Then 240 feet = 80 yards COACH LESSON 9

Ratios & Proportions:

A ratio is a comparison between two numbers.

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

72 To solve a proportion, we cross multiply and divide.

Example: 4 = 2 5 = x 4x = 10 4 4 x = 10 4 x = 2 ½ Ratios IXL COACH LESSON 7

Rational & Irrational Numbers

An 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.

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

74 Practice Irrational Numbers!

Which of these is an irrational number?

A -2 B C √56 √64 D 3.14

Which of these is an irrational number?

A √3 B -13.5

C D 7 11 1 √9

75 Converting Rational Numbers!

Fraction Place number over its place value and reduce 75 = 3 100 4 Decimal Divide by 100 0.75

Percent Multiply by 100 0.75 x 100 = 75% 125 = 1 1000 8 150 = 3 = 1 ½ 100 2 0.125

1.50

0.125 x 100 = 12.5% 1.50 x 100 = 150% COACH LESSON 4

Points on a Coordinate Grid!

Point of Origin [0, 0]

Quadrant II Quadrant III Quadrant I Ordered pair: [3, 2] 3 is x value and 2 is y value Quadrant IV 76 COACH LESSON 16

Scaling!

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?

77 To find an actual length from a scale drawing, identify and solve a proportion. Drawing = Drawing Actual Actual Let p = the actual length in feet of the passageway Use cross products to  solve the proportion 0.5 = 3.75

2 p 0.5 x p = 2 x 3.75

0.5 p = 7.5 p = 15 Scale & Indirect Measurement MathMaster COACH LESSON 14

78 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 = 14 b) 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

79 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 10

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

4 2 0 Bar graphs have spaces to show differences in data.

4 2 0 a b c Interpret Histograms IXL COACH LESSON 26

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

3 2 1 0 6 5 4 Category Category Category Category 1 2 3 4 Series 1 Series 2 Series 3 COACH LESSON 25

82

Making Predictions!

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

6 3 2 5 4 1 0 Category 1Category 2Category 3Category 4 Series 1 Series 2 Series 3 COACH LESSON 31

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