COMPREHENSIVE REVIEW FOR MIDDLE SCHOOL MATHEMATICS 2013.
-
Upload
gavin-verne -
Category
Documents
-
view
240 -
download
13
Transcript of 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
40
1
2
3
4
5
6
Series 1Series 2Series 3
COACH LESSON 25
81
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
82
Making Predictions!
Continue Studying & Good Luck!!!
83