irrationalamybushhms.weebly.com/uploads/5/6/8/5/56851301/7th_grade... · 2019-10-03 · 7.ns.1....

Irrational

7NS1 Apply and extend previous understandings of addition and subtraction to add and subtract rational num-bers represent addition and subtraction on a horizontal or vertical number line diagram

a Describe situations in which opposite quantities combine to make 0 For example a hydrogen atom has 0 charge because its two constituents are oppositely charged

b Understand p + q as the number located a distance |q| from p in the positive or negative direction depending on whether q is positive or negative Show that a number and its opposite have a sum of 0 (are additive inverses) Inter-pret sums of rational numbers by describing real-world contexts

c Understand subtraction of rational numbers as adding the additive inverse p ndash q = p + (ndashq) Show that the dis-tance between two rational numbers on the number line is the absolute value of their difference and apply this prin-ciple in real-world contexts

d Apply properties of operations as strategies to add and subtract rational numbers

7NS2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers

a Understand that multiplication is extended from fractions to rational numbers by requiring that operations con-tinue to satisfy the properties of operations particularly the distributive property leading to products such as (ndash1)(ndash1) = 1 and the rules for multiplying signed numbers Interpret products of rational numbers by describing real-world contexts

b Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with non-zero divisor) is a rational number If p and q are integers then ndash(pq) = (ndashp)q = p(ndashq) Interpret quotients of rational numbers by describing real-world contexts

c Apply properties of operations as strategies to multiply and divide rational numbers

d Convert a rational number to a decimal using long division know that the decimal form of a rational number ter-minates in 0s or eventually repeats

7NS3 Solve real-world and mathematical problems involving the four operations with rational numbers (Computations with rational numbers extend the rules for manipulating fractions to complex fractions)

Divide Rational Numbers Rational Number Any number that can be written as

a fraction and that the denom-inator does not equal to zero

1

Unit 1 Vocabulary

Additive Inverse Two numbers whose sum is 0 are additive inverses of one another

Example and ndash are additive inverses of one another because + (ndash ) =

( ndash ) + = 0

Multiplicative Inverse Two numbers whose product is 1 are multiplicative inverses of

one another

Example and are multiplicative inverses of one another because x =

x = 1

bull Absolute Value The distance between a number and zero on the number line The

symbol for absolute value is shown in this equation

bull Integers A number expressible in the form a or ndasha for some whole number a The set

of whole numbers and their opposites hellip-3 -2 -1 0 1 2 3hellip

bull Natural Numbers The set of numbers 1 2 3 4hellip Natural numbers can also be called

counting numbers

bull Negative Numbers The set of numbers less than zero

bull Opposite Numbers Two different numbers that have the same absolute value Exam-

ple 4 and -4 are opposite numbers because both have an absolute value of 4

bull Positive Numbers The set of numbers greater than zero

bull Rational Numbers The set of numbers that can be written in the form ab where a and

b are integers and b 0

bull Repeating Decimal A decimal number in which a digit or group of digits repeats with-

out end

bull Terminating Decimal A decimal that contains a finite number of digits

bull Zero Pair Pair of numbers whose sum is zero

|7| = 7

2

5 - 085

3

C1mdashC6

YOU MUST HAVE A COMMON DENOMINATOR FOR ADDING AND SUBTRACTING FRACTIONS

USING A RATIO TABLE

Write both fractions in a table

Continue listing the multiples of

the denominators until you find a

common denominator

FOR EXAMPLE

1

4 8 12 16 20

3

5 10 15 20

Fill in the numerators on the

table to find your fractions with

a common denominator

EXAMPLE CONTINUED

1 2 3 4 5

4 8 12 16 20

3 6 9 12

5 10 15 20

Addsubtract

fractions

EXAMPLE CONTINUED

5

20

12

+ 20

17

So 20 is the

common

denominator for

4

G1mdashG4

divide =

KEEP the first fraction

CHANGE FLIP the second

fraction

X =

Write mixed numbers as

improper fractions

Put whole numbers over

one


CHANGE divide to multi-

ply FLIP the second

fraction (reciprocal)

Multiply the numerators

Multiply the denomina-

1 2 divide = 4 1

5 9 divide

5 2 10 x =

5

1 3

5 8

1 8 8

5 3 15

5

G7mdashG13

6

Integer Whole numbers and their opposites

Example hellip -2 -1 0 1 2 hellip

Positive Number A number greater than zero

Example 1 2 3 hellip

Negative Number A number less than zero

Example hellip -3 -2 -1

Zero is neither negative nor positive

ldquoSame signs add and keep different signs subtract

Take the sign of the larger number then yoursquoll be exactrdquo

4+(-3)=1

=

= 19

Different

Signs

Same Signs Subtraction

You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =

AddSubtract Fruit Splat

D1 D2 D3 D4 D5

E1 E2 E3 E4 H1

Adding integers Video Subtracting integers video

+ +

+ + +

7

You can make ANY subtraction

problem an addition problem by

using the rule ldquokeep change

change Then follow the rules from

the song

FOUND AT httpwwwsw-georgiaresak12gausinteger20rulespdf

Keep Change Change

Same Sign Add and keep the sign

2 + 2 = 4

Positive + Positive = Positive

(-2) + (-2) = (-4)

Negative + Negative = Negative

Different Signs Subtract and keep the sign

of the larger value (from zero)

Subtracting a negative is like ADDING A POSITIVE

-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4

Subtracting a positive IS subtracting

or like ADDING A NEGATIVE

Positive x Positive = Positive Negative x Negative = Positive Negative x Positive = Negative Positive x Negative = Negative Division (same pattern)

8

E6mdashE8

Plug it in and use order of operations to solve

(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )

8 + 48 Multiply (3bull16)

56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right

Definition A numberrsquos distance from zero

on a number line Hint Always make the number positive

| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =

Same Sign = Positive

7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3

Different Signs = Negative

-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6

What must you do to the number to

make it equal to zero

Creating Neutral Fields

-14 +14=0

-4 -4

X = 2 Additive Inverse

Rags to Riches Rational Numbers

H2 H7 E9

You Try

X +4 =6

9

7EE1 Apply properties of operations as strategies to add subtract factor and expand linear expressions with rational coefficients

7EE2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related For example a + 005a = 105a means that ldquoincrease by 5rdquo is the same as ldquomultiply by 105rdquo

7EE3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers fractions and decimals) using tools strategically Apply properties of operations to calculate with numbers in any form convert between forms as appropriate and assess the reasonableness of answers using mental computation and estimation strategies For example If a woman making $25 an hour gets a 10 raise she will make an additional 110 of her salary an hour or $250 for a new salary of $2750 If you want to place a towel bar 9 34 inches long in the center of a door that is 27 12 inches wide you will need to place the bar about 9 inches from each edge this estimate can be used as a check on the exact computation

7EE4 Use variables to represent quantities in a real-world or mathematical problem and construct sim-ple equations and inequalities to solve problems by reasoning about the quantities

a Solve word problems leading to equations of the form px + q = r and p(x + q) = r where p q and r are specific rational numbers Solve equations of these forms fluently Compare an algebraic solution to an arithmetic solution identifying the sequence of the operations used in each approach For example the perimeter of a rectangle is 54 cm Its length is 6 cm What is its width

b Solve word problems leading to inequalities of the form px + q gt r or px + q lt r where p q and r are spe-cific rational numbers Graph the solution set of the inequality and interpret it in the context of the prob-lem For example As a salesperson you are paid $50 per week plus $3 per sale This week you want your pay to be at least $100 Write an inequality for the number of sales you need to make and describe the solutions

EVALUATING EXPRESSIONS

You evaluate an expression by replacing the variable

with the given number and performing the indicated

Examples Evaluate 10a if a = 15

1990 Glade Commercial

10

Unit 2 Vocabulary

Algebraic expression An expression consisting of at least one varia-

ble and also consist of numbers and operations

Coefficient The number part of a term that includes a variable For

example 3 is the coefficient of the term 3x

Constant A quantity having a fixed value that does not change or

vary such as a number For example 5 is the constant of x + 5

Equation A mathematical sentence formed by setting two expres-

sions equal

Inequality A mathematical sentence formed by placing inequality

symbol between two expressions

Term A number a variable or a product and a number and variable

Numerical expression An expression consisting of numbers and op-

erations

Variable A symbol usually a letter which is used to represent one or

more numbers

11

Multiply the number touching the

outside of the parenthesis with

each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6

AddSubtract each like term (numbers with

the same variable raised to the same exponent)

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10

Associative Property

The sum or product of a set of numbers is the same no matter

how the numbers are grouped

(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)

Commutative Property

The sum or product of a group of numbers is the same regardless

of the order in which the numbers are arranged

5 + 3 = 3 + 5 4 X 7 = 7 X 4

Perimeter Add up all of the sides

Area of a rectangle A=lw

Area 4(3x) = 12x

Perimeter 3x + 3x + 4+ 4

6x + 8

3x

4

A B A(B) (A)(B) A X B

Combining Like Terms

Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS

ORDER OF OPERATIONS EXAMPLES

(PE)(MD)(AS)

1 (PE)

Do parentheses and exponents FIRST

2 (MD)

Solve all multiplying and dividing from

left to right (It may be divide first)

EXPRESSION EVALUATION OPERATION

50 - 12 divide 3 6= 50 - 12 divide 3 6= Division

50 - 4 6= Multiplication

50 - 24= Subtraction

26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)

22 - 14 + 20= Subtraction

8 + 20= Addition

28

EXPONENTS

Exponents tell how many

times to multiply a number

by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION

8 more than a number 8 + n

7 less than a number n - 7

The product of a number and 11 11n

The quotient of 6 and a number 6

A number decreased by 12 n - 12

13

n

U1

Two-step equations are exactly like what they sound like equations that take TWO STEPS to solve

You have to use INVERSE OPERATIONS to solve each equation

The goal is to get the variable by itself on one side of the equal sign You need to do the inverse

operation of what is furthest from the variable without crossing an equal sign

Below are examples of 2-step equations and how to solve using algebraic notation

2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt

If there is a line under the greater

than or less than sign it means the

variable can be equal to the value

In this case donrsquot forget to fill in your

circle on the number line to represent

the equal to sign

Each month Chucks phone company charges a flat

fee of $12 plus $005 per minute His bill for last

month was $18 How many minutes did Chuck talk

on the phone last month

05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15

Susan sold 5 times as many raffle tickets as Jill If Susan sold 40 raffle tickets in all what equation can be

used to find x if x is the number of tickets Jill sold

5x = 40

A Large bag of sand weighs 70 pounds The bag weighs 4 pounds less than the weight of 5 small boxes

of sand Which equation can be used to find the weight w in pounds of each small box of sand

5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine

3) Solve (when there is an

equal sign)

7RP1 Compute unit rates associated with ratios of fractions including ratios of lengths areas and other quanti-ties measured in like or different units For example if a person walks 12 mile in each 14 hour compute the unit rate as the complex fraction 1214 miles per hour equivalently 2 miles per hour

7RP2 Recognize and represent proportional relationships between quantities

a Decide whether two quantities are in a proportional relationship eg by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin

b Identify the constant of proportionality (unit rate) in tables graphs equations diagrams and verbal descriptions of proportional relationships

c Represent proportional relationships by equations For example if total cost t is proportional to the number n of items purchased at a constant price p the relationship between the total cost and the number of items can be ex-pressed as t = pn

d Explain what a point (x y) on the graph of a proportional relationship means in terms of the situation with spe-cial attention to the points (0 0) and (1 r) where r is the unit rate

7RP3 Use proportional relationships to solve multistep ratio and percent problems Examples simple interest tax markups and markdowns gratuities and commissions fees percent increase and decrease percent error

7G1 Solve problems involving scale drawings of geometric figures including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale

J1mdash5 L 2mdash4

16

Unit 3 Vocabulary

Constant of Proportionality Constant value of the ratio of proportional quantities

x and y Written as y = kx k is the constant of proportionality when the graph passes

through the origin Constant of proportionality can never be zero

Equivalent Fractions Two fractions that have the same value but have different numer-

ators and denominators Equivalent fractions simplify to the same fraction

Fraction A number expressed in the form ab where a is a whole number and b is a pos-

itive whole number

Multiplicative inverse Two numbers whose product is 1 Example (34) and (43)

are multiplicative inverses of one another because 34 times (43) = (43) times 34 = 1

Percent rate of change A rate of change expressed as a percent Example if a popula-

tion grows from 50 to 55 in a year it grows by 550 = 10 per year

Proportion An equation stating that two ratios are equivalent

Ratio A comparison of two numbers using division The ratio of a to b (where b ne 0) can

be written as a to b as or as a b

Similar Figures Figures that have the same shape but the sizes are proportional

Unit Rate Ratio in which the second term or denominator is 1

Scale factor A ratio between two sets of measurements

17

18

In Georgia we have a 6 sales tax

You want to buy a shirt that costs

$1200 How much does the shirt

cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION

Cinthia earns 20 commission on her

sales In February she sold $380 in

merchandise How much did Cinthia make

in commission in February

$380 x 020 = $7600

She earned $76 in commission

INTEREST

Albertorsquos savings account earns 3 inter-

est ever month If Alberto puts $4500

in his bank account at the beginning of

L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual

The weather person predict-

ed it would snow 4 inches It

actually snowed 7 12 inches

What is his percent error

Find the percent change and state

whether increase or decrease

from 12 to 16 from 60 to 45

From 12 to 16 From 60 to 45

333 Increase 333 Decrease

Simple Interest The amount paid or earned for the use of

money

Principal The amount of money deposited or

borrowed

Rate The percent you earn or owe on the

principal

Dustin paid for a new skateboard

with his credit card The skate-

board cost $290 and has 125

interest If it takes him 6 months

to pay of the credit card how

much interest did he pay

290 X 125 X 6 = $21750

L6mdashL8

Use the formula to

find the interest by

multiplying

22

7SP1 Understand that statistics can be used to gain information about a population by examining a sample of the population generalizations about a population from a sample are valid only if the sample is representative of that population Understand that random sampling tends to produce representative samples and support valid infer-ences

7SP2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions For example estimate the mean word length in a book by randomly sampling words from the book pre-dict the winner of a school election based on randomly sampled survey data Gauge how far off the estimate or pre-diction might be

7SP3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities measuring the difference between the centers by expressing it as a multiple of a measure of variability For exam-ple the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soc-cer team about twice the variability (mean absolute deviation) on either team on a dot plot the separation be-tween the two distributions of heights is noticeable

7SP4 Use measures of center and measures of variability for numerical data from random samples to draw infor-mal comparative inferences about two populations For example decide whether the words in a chapter of a sev-enth-grade science book are generally longer than the words in a chapter of a fourth-grade science book

A way to organize data to Shows the distribution of data

Shows each value and how

they are distributed

Skewed Right

Mean is greater than the median

Median is the best measure of center

because the median is not affected

by very large data values

Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left

Mean is less than the median

Median is the best measure of

center because the median is

not affected by very small data

values

AA1 AA2 AA4 AA5 O14O15

23

Unit 4 Vocabulary

Box and Whisker Plot A diagram that summarizes data using the median the upper and lowers quartiles and

the extreme values (minimum and maximum) Box and whisker plots are also known as box plots It is construct-

ed from the five-number summary of the data Minimum Q1 (lower quartile) Q2 (median) Q3 (upper quartile)

Maximum

Frequency The number of times an item number or event occurs in a set of data

Grouped Frequency Table The organization of raw data in table form with classes and frequencies

Histogram A way of displaying numeric data using horizontal or vertical bars so that the height or length of the

bars indicates frequency

Inter-Quartile Range (IQR) The distance between the first and third quartiles of the data set (sometimes called

upper and lower quartiles)

Maximum value The largest value in a set of data

Mean Absolute Deviation The average distance of each data value from the mean ( ) The MAD is a gauge of

ldquoon averagerdquo how different the data values are form the mean value

= ℎ

Mean A measure of center in a set of numerical data computed by adding the values in a list and then dividing

by the number of values in the list Example For the data set 1 3 6 7 10 12 14 15 22 120 the mean is 21

Measures of Center The mean and the median are both ways to measure the center for a set of data

Measures of Spread The range and the mean absolute deviation are both common ways to measure the spread

for a set of data

Median The middle number

Minimum value The smallest value in a set of data

Mode The number that occurs the most often in a list There can more than one mode or no mode

Mutually Exclusive two events are mutually exclusive if they cannot occur at the same time (ie they have not

outcomes in common)

Outlier A value that is very far away from most of the values in a data set

Range A measure of spread for a set of data To find the range subtract the smallest value from the largest value

in a set of data

Sample A part of the population that we actually examine in order to gather information

Simple Random Sampling Consists of individuals from the population chosen in such a way that every set of

individuals has an equal chance to be a part of the sample actually selected Poor sampling methods that are not

random and do not represent the population well can lead to misleading conclusions

Stem and Leaf Plot A graphical method used to represent ordered numerical data Once the data are ordered the

stem and leaves are determined Typically the stem is all but the last digit of each data point and the leaf is that

last digit

24

25

WORD DEFINITION IN YOUR WORDS EXAMPLE

Measures of

Center

A measurement that

summarizes a data set

with a single number

Johnrsquos quiz scores

75 80 85 90 85

Median of scores_____

Mean of scores ______

Mode of scores ______

Mean The sum of the values

in a data set divided by

the number of values in

the set

MEAN of Johnrsquos scores

Median The middle value in a

data set when it is in

numerical order

MEDIAN of Johnrsquos scores

Mode The value that appears

most often in a data

set There can be one

or none

MODE of Johnrsquos scores

Remember

Shows how values are distributed

9 8 2 4 8 5 6 7

Put rsquos in order from least to greatest

2 4 5 6 7 8 8 9

Minimum 2 Upper Quartile 8

Maximum 9 Lower Quartile 45

Median 65

Range Difference between biggest and

smallest number

Median Middle number

Upper Quartile Median of upper half of data

Lower Quartile Median of lower half of data

Inner Quartile Range Subtract the lower

quartile from the upper quartile

Absolute Deviation The __distance__ of each data value from the __mean_____

Mean Absolute Deviation The __mean_ of the absolute deviations

MAD is another way to describe the __spread__ of a data set

AA1

26

1 Find the IQR of Class A ______

2 Find the IQR of Class B_____

3 Which class has a greater median attendance How much greater is it ________

4 Which class has an attendance of less than 14 people 75 of the time ______

5 Which class appears to have a more predictable attendance ________

6 What percent of the time does Class B have an attendance greater than 16 ______

7 Which class has an attendance of more than 14 people 50 of the time ______

___ of the data falls above the median

___ of the data falls below the median

___ of the data falls above Q1


Each quartile of a set of data represents 25 of the data You can use the shape of the box plot to

tell if the data is consistent or spread out

O14 27 Answers

50 1 14-4=10 50 2 16-12=4 75 3 Class B by 8 25 4 Class A 5 Class B 6 25 7 Class B

You Try

1) Find the mean of the data set 11+11+6+26+6+12=72 726=12

2) Find the distance between each data value and the mean

(Subtract the mean from each data value)

3) Find the average of those differences

(Add up all the absolute deviations and divide by how many)

Determine the mean absolute deviation for Indyah by finding the mean abso-

lute deviation and mean absolute deviation Points

Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_

Overall are the data values close to the mean or far away from the mean

Population and Samples

Population The entire group

EX East Hall Middle School

Sample Part of a whole

EX Ms Slaymakerrsquos class

Bias Unfair preference

Biased Sample

The first 5 people leaving a movie theater at a

sneak preview were asked how they liked the

movie

Biased Survey Question

Do you think Jones is a good mayor in spite of

his questionable character

28

Learnzillion

Mean Absolute Deviation

Mean the average

You add and divide

Median line lsquoem up

find whatrsquos inside

Measures of center -

They help you to know

If the middle is high or the middle is low

If you need to check out the variation

You use mean absolute deviation

You get mean you subtract and then you get MAD

Itrsquos a whole lot of math

But it isnrsquot that bad

You could maybe use the IQR--

To see if theyrsquore close or If they are far

You have to subtract Q3 and Q1

Yoursquoll get IQR and then you are DONE

I Unbiased Sample is selected so that it accurately represents the entire

population

Simple Random Sample Each item or person in the population is as likely to be chosen as any other

Example Each students name is written on a piece of paper The names are placed in a bowl and

names are picked without looking

Systematic Random Sample The items or people are selected according to a specific time or item intraval

Example Every 20th person is chosen from an alphabetical list of all students attending a school

II Biased Sample one or more parts of the population are favored over others

1 Convenience Sample consists of members of a population that are easily

accessed

Example To represent all the students attending a school the principal surveys the students in one math class

2 Voluntary Response Sample involves only those who want to participate in

the sampling

Example Students at a school who wish to express their opinions complete an online survey

AA5

29

7G2 Draw (freehand with ruler and protractor and with technology) geometric shapes with given conditions Focus on constructing triangles from three measures of angles or sides noticing when the conditions determine a unique triangle more than one triangle or no triangle

7G3 Describe the two-dimensional figures that result from slicing three-dimensional figures as in plane sections of right rectangular prisms and right rectangular pyramids

7G4 Know the formulas for the area and circumference of a circle and use them to solve problems give an informal derivation of the relationship between the circumference and area of a circle

7G5 Use facts about supplementary complementary vertical and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure

7G6 Solve real-world and mathematical problems involving area volume and surface area of two- and three-dimensional objects composed of triangles quadrilaterals polygons cubes and right prisms

Triangle Inequality Tool

The sum of the lengths of any two sides of

a triangle is greater than the length of the

third side

The sum of measures of the interior

angles of a triangle is 180 degrees

X+Y+Z= 180

Triangle Sum Tool

Vertical Angles are the angles opposite each other when two

lines cross

Supplementary Angles Two or more angles that add up to

180 degrees

Complementary Angles Two or more angles that add up to

90 degrees (A right angle)

Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary

Adjacent Angle Angles in the same plane that have a common vertex and a common

side but no common interior points

Circumference The distance around a circle

Complementary Angle Two angles whose sum is 90 degrees

Congruent Having the same size shape and measure lt A cong lt B denotes that lt A is

congruent to lt B

Cross- section A plane figure obtained by slicing a solid with a plane

Irregular Polygon A polygon with sides not equal andor angles not equal

Parallel Lines Two lines are parallel if they lie in the same plane and they do not inter-

sect

Pi The relationship of the circlersquos circumference to its diameter when used in calcula-

tions pi is typically approximated as 314 the relationship between the circumference

(C) and diameter (d) or cd

Regular Polygon A polygon with all sides equal (equilateral) and all angles equal

(equiangular)

Supplementary Angle Two angles whose sum is 180 degrees

Vertical Angles Two nonadjacent angles formed by intersecting lines or segments Also

called opposite angles

31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces

Pyramids have one base

Pyramids have mostly

triangular faces

NAMING SOLID FIGURES

The base of a pyramid or prism gives the shape its ldquofirst namerdquo

The ldquolast namerdquo is either prism or pyramid and is based on triangular or rectangular

faces

EXAMPLE At right is a Hexago-

Face

Base

Edge

Vertex

Parallel lines two lines that are in the same plane and do not intersect

Perpendicular lines two lines that intersect to form right angles

Plane a flat surface that goes on forever in all directions

Cross Section The intersection of a solid and a plane

Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26

Below are formulas you may find useful as you work the problems However some of the formulas

may not be used You may refer to this page as you take the test

The formula above for finding the area of a rec-

tangle is A = bh An alternate formula for area

of a rectangle is

when A represents area l represents

length and w

represents

width

EXAMPLE

Perimeter distance

around a plane figure

EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34

Circle All points same distance from center point

Radius line segment from the center to the side of the circle

Diameter line segment from side to side of the circle passing

through the center

Circumference distance around the circle

Pi (П) ratio of the circumference to the diameter

3141592hellip

The radius is 12 of the diameter

35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one

Irsquom going to find the volume

Find out how much goes inside it

Multiply length times the width times the height

And Irsquove found the prismrsquos volume thatrsquos right

Verse two

Now Irsquove got a cylinder

What goes in for Big B I wonder

Pi times the radius squared Donrsquot blunder

Multiply by the height Now wersquore done here

Verse three

What about pyramids in Egypt

Find out how much sand goes in it

Area of the base times the height and then what

Divide by 3 and then yoursquove got it

Verse four

How much in a volcano

Pi times the radius squared and then go

Times the height take one third and then know

Thatrsquos how much of the lava can flow

P21mdashP23 P31 P32

7SP5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the like-lihood of the event occurring Larger numbers indicate greater likelihood A probability near 0 indicates an un-likely event a probability around 12 indicates an event that is neither unlikely nor likely and a probability near 1 indicates a likely event

7SP6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency and predict the approximate relative frequency given the prob-ability For example when rolling a number cube 600 times predict that a 3 or 6 would be rolled roughly 200 times but probably not exactly 200 times

7SP7 Develop a probability model and use it to find probabilities of events Compare probabilities from a model to observed frequencies if the agreement is not good explain possible sources of the discrepancy

a Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events For example if a student is selected at random from a class find the proba-bility that Jane will be selected and the probability that a girl will be selected

b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process For example find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down Do the outcomes for the spinning penny appear to be equally like-ly based on the observed frequencies

7SP8 Find probabilities of compound events using organized lists tables tree diagrams and simulation

a Understand that just as with simple events the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs

b Represent sample spaces for compound events using methods such as organized lists tables and tree dia-grams For an event described in everyday language (eg ldquorolling double sixesrdquo) identify the outcomes in the sample space which compose the event

c Design and use a simulation to generate frequencies for compound events For example use random digits as a simulation tool to approximate the answer to the question If 40 of donors have type A blood what is the probability that it will take at least 4 donors to find one with type A blood

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary

Chance Process The repeated observations of random outcomes of a given event

Compound Event Any event which consists of more than one outcome

Empirical A probability model based upon observed data generated by the process Also referred to as

the experimental probability

Event Any possible outcome of an experiment in probability Any collection of outcomes of an experi-

ment Formally an event is any subset of the sample space

Experimental Probability The ratio of the number of times an outcome occurs to the total amount of

trials performed

=The number of times an event occurs

The total number of trials

Independent events Two events are independent if the occurrence of one of the events gives us no infor-

mation about whether or not the other event will occur that is the events have no influence on each other

Probability It can be listed as a number between 0 and 1

Probability Model It provides a probability for each possible non-overlapping outcome for a change pro-

cess so that the total probability over all such outcomes is unity This can be either theoretical or experi-

mental

Relative Frequency of Outcomes Also Experimental Probability

Sample space All possible outcomes of a given experiment

Simple Event Any event which consists of a single outcome in the sample space A simple event can be

represented by a single branch of a tree diagram

Simulation A technique used for answering real-world questions or making decisions in complex situa-

tions where an element of chance is involved

Theoretical Probability The mathematical calculation that an event will happen in theory It is based on

the structure of the processes and its outcomes

Tree diagram A tree-shaped diagram that illustrates sequentially the possible outcomes of a given event

37

Probability- is the measure of how likely an event is to occur

Probabilities are written as fractions or decimals from 0 to 1 or as a percent from 0 to 100

The higher an events probability the more likely an event will happen

Experimental probability- probability found

as a result of an experiment

A bag contains 10 red marbles 8 blue marbles and 2 yellow

marbles Find the experimental probability of receiving a blue

marble

Solution

Step 1 Take a marble from the bag

Step 2 Record the color and return the marble

Step 3 Repeat a few times (maybe 10 times)

Step 4 Count the number of times a blue marble was

pick (Suppose it is 6)

Step 5 The experimental probability of receiving a

blue marble from the bag is 610 =35

EXAMPLES

Sam rolled a number cube 50 times A 3 ap-

peared 10 times Then the experimental prob-

ability of rolling a 3 is 10 out of 50 or 20

A coin is tossed 60 times Amanda lands on

heads 27 times The experimental probability

of landing on heads is 27 out of 60 or 920

COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN

WHITE Gregory spun the spinner at left 20 times and rec-

orded his result in a frequency table

1) What is the theoretical probability of spinning

white 18 or 125 because on the SPINNER

one out of eight sections are white

2) What is the experimental probability of spinning

GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6

Using the spinner above Write your answer

in a fraction decimal and percent Decide if

it impossible unlikely even likely certain

What is the probability of spinning grey

____________________________

What is the probability of spinning red and

white_____________________________

Using the probability model what is the probability of an outcome that is an even number

Probability model a list of each possible outcome along with its probability

Uniform Probability Model occurs when all the probabilities are equally likely to occur

Non-Uniform Probability Model occurs when all the probabilities are NOT equally likely to occur

Construct a probability model for a spin on a spinner with 8 numbered sections of equal size

39

Blue Green Yellow Purple Orange Red Black White

Simple Event an event consisting of one outcome exWhat is the probability of tossing heads on a coin

Compound Event consists of two or more simple events ExhellipWhat is the probability of tossing heads on a coin

and then rolling a 4 on a six-sided dice

Systematic Method organizing information in some way so that no outcomes are missed

Fundamental Counting Principal

MULTIPLY TO FIND OUT HOW MANY OUTCOMES

So if you roll a six-sided die and spin an 8 sided spinner Use the fundamental counting to find the number of possi-

ble outcomes 8 x 2 = 16

Independent Events The first event does not affect the outcome of the second event P(A and B) = P(A) P(B)

Dependent Events The outcome of the first event affects the outcome of the second event P(A and B) = P(A) P

(B following A)

1) Caroline wants to wear

either green blue or pink

pants with a white or black

top Show the combinations

using a list

List-

Gw Gb

Bw Bb

Pw Pb

2) Jackrsquos Snackrsquos makes flavored

sodarsquos Cola sprout or rain drop

with a splash of cherry orange

grape lime or blue raspberry

Make a tale showing the possible

outcomes

Table

Casey wants to see all the different pos-

sibilities for her outfit for hat day If she

wears black white or red sneakers and

a red blue black or tan cap

Tree Diagram

Ch Or Gr LI Br

Co CoCh CoOr CoGr CoLi CoBr

Sp SpCh SpOr SpGr SpLi SpBr

RD RdCh RdOr RdGr RdLi RdBr

What is the probability of tossing heads on a coin AND

then rolling a 4 on a six-sided dice

P(Heads)= 12 P(4)=16 12 X 16 = 112

Cards labeled 5 6 7 8 and 9 are in a stack A card is

drawn and not replaced Then a second card is drawn at

random Find the probability of drawing two even num-

bers

P(Even) = 25 NOT REPLACED

P(Even)= 14

25 X 14 =

220=110

WHEN FIRST EVENT IS NOT REPLACED

There are 4 oranges and 7 bananas in a fruit basket

Bobby selects a piece of fruit and then Susan selects a

piece of fruit What is the probability that two bananas

were chosen

YOU TRY

First Outcome Second Outcome Probability

40

Z 5mdash7

You can flip a coin to

represent the same

probability that a boy

will be born versus a

girl

What are different types of simulations

Random number generator

Spinner Flip A Coin Roll A Dice Pick A Marble From A Bag

Use A Random Number Generator Draw A Card

41

7NS1 Apply and extend previous understandings of addition and subtraction to add and subtract rational num-bers represent addition and subtraction on a horizontal or vertical number line diagram

a Describe situations in which opposite quantities combine to make 0 For example a hydrogen atom has 0 charge because its two constituents are oppositely charged

b Understand p + q as the number located a distance |q| from p in the positive or negative direction depending on whether q is positive or negative Show that a number and its opposite have a sum of 0 (are additive inverses) Inter-pret sums of rational numbers by describing real-world contexts

c Understand subtraction of rational numbers as adding the additive inverse p ndash q = p + (ndashq) Show that the dis-tance between two rational numbers on the number line is the absolute value of their difference and apply this prin-ciple in real-world contexts

d Apply properties of operations as strategies to add and subtract rational numbers

7NS2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers

a Understand that multiplication is extended from fractions to rational numbers by requiring that operations con-tinue to satisfy the properties of operations particularly the distributive property leading to products such as (ndash1)(ndash1) = 1 and the rules for multiplying signed numbers Interpret products of rational numbers by describing real-world contexts

b Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with non-zero divisor) is a rational number If p and q are integers then ndash(pq) = (ndashp)q = p(ndashq) Interpret quotients of rational numbers by describing real-world contexts

c Apply properties of operations as strategies to multiply and divide rational numbers

d Convert a rational number to a decimal using long division know that the decimal form of a rational number ter-minates in 0s or eventually repeats

7NS3 Solve real-world and mathematical problems involving the four operations with rational numbers (Computations with rational numbers extend the rules for manipulating fractions to complex fractions)

Divide Rational Numbers Rational Number Any number that can be written as

a fraction and that the denom-inator does not equal to zero

1

Unit 1 Vocabulary



( ndash ) + = 0


one another


x = 1






counting numbers








out end



|7| = 7

2

5 - 085

3

C1mdashC6


USING A RATIO TABLE




common denominator

FOR EXAMPLE

1

4 8 12 16 20

3

5 10 15 20




EXAMPLE CONTINUED

1 2 3 4 5

4 8 12 16 20

3 6 9 12

5 10 15 20

Addsubtract

fractions

EXAMPLE CONTINUED

5

20

12

+ 20

17

So 20 is the

common

denominator for

4

G1mdashG4

divide =



fraction

X =


improper fractions


one



ply FLIP the second




1 2 divide = 4 1

5 9 divide

5 2 10 x =

5

1 3

5 8

1 8 8

5 3 15

5

G7mdashG13

6










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Unit 1 Vocabulary



( ndash ) + = 0


one another


x = 1






counting numbers








out end



|7| = 7

2

5 - 085

3

C1mdashC6


USING A RATIO TABLE




common denominator

FOR EXAMPLE

1

4 8 12 16 20

3

5 10 15 20




EXAMPLE CONTINUED

1 2 3 4 5

4 8 12 16 20

3 6 9 12

5 10 15 20

Addsubtract

fractions

EXAMPLE CONTINUED

5

20

12

+ 20

17

So 20 is the

common

denominator for

4

G1mdashG4

divide =



fraction

X =


improper fractions


one



ply FLIP the second




1 2 divide = 4 1

5 9 divide

5 2 10 x =

5

1 3

5 8

1 8 8

5 3 15

5

G7mdashG13

6










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

5 - 085

3

C1mdashC6


USING A RATIO TABLE




common denominator

FOR EXAMPLE

1

4 8 12 16 20

3

5 10 15 20




EXAMPLE CONTINUED

1 2 3 4 5

4 8 12 16 20

3 6 9 12

5 10 15 20

Addsubtract

fractions

EXAMPLE CONTINUED

5

20

12

+ 20

17

So 20 is the

common

denominator for

4

G1mdashG4

divide =



fraction

X =


improper fractions


one



ply FLIP the second




1 2 divide = 4 1

5 9 divide

5 2 10 x =

5

1 3

5 8

1 8 8

5 3 15

5

G7mdashG13

6










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41


USING A RATIO TABLE




common denominator

FOR EXAMPLE

1

4 8 12 16 20

3

5 10 15 20




EXAMPLE CONTINUED

1 2 3 4 5

4 8 12 16 20

3 6 9 12

5 10 15 20

Addsubtract

fractions

EXAMPLE CONTINUED

5

20

12

+ 20

17

So 20 is the

common

denominator for

4

G1mdashG4

divide =



fraction

X =


improper fractions


one



ply FLIP the second




1 2 divide = 4 1

5 9 divide

5 2 10 x =

5

1 3

5 8

1 8 8

5 3 15

5

G7mdashG13

6










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

divide =



fraction

X =


improper fractions


one



ply FLIP the second




1 2 divide = 4 1

5 9 divide

5 2 10 x =

5

1 3

5 8

1 8 8

5 3 15

5

G7mdashG13

6










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

6










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41










4+(-3)=1

=

= 19

Different

Signs


You try

A 2+-3= B 10mdash -4 = C ndash1+-8 =


D1 D2 D3 D4 D5

E1 E2 E3 E4 H1


+ +

+ + +

7





the song


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41


Keep Change Change


2 + 2 = 4


(-2) + (-2) = (-4)





-8 - 4 =

-8 + (-4) = - 12

Keep the Change

minus

Chang

Keep the Change

minus

Chang

2 - ( -2) =

2 + +2 = 4




8

E6mdashE8


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41


(12 - 4) + 3(4)2

(12 - 4) + 3(16) Exponents (42 = 4bull4)

8 + 3(16) Parenthesis (12 - 4 )


56 Add (8 + 48)

P arenthesis

E xponents

M ultilication

D ivision

A ddition

S ubtraction

From left

to right

From left

to right



| -3 | = 3 | -8 | = 8 - | 4 | = -4

| 5 | = | 8 - 5 | = - | -2 | =


7 bull 8 = 56 -56 divide (-8) = 7

5 x 2 = 10 -10 (-2) = 5

3(9) = 27 -27 = 9

-3


-2 bull 8 = -16 16 divide (-8) = -2

7 x (-9) = -63 -639 = -7

-6(4) = -24 -24 = -4

6




-14 +14=0

-4 -4



H2 H7 E9

You Try

X +4 =6

9












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41












10

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Unit 2 Vocabulary








sions equal





erations


more numbers

11



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41



each term inside

3(2x + 6) 2(3x - 4x2 + 3)

3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)

6x + 18 6x - 8x2 + 6



3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3x3 + 9x + 2 - 4x2 - 7x - x3 + 8

3 - 1 -4 9 - 7 2 + 8

2x3 - 4x2 + 2x + 10




(4+3)+2 = 4+(3+2) (5X7)X3=5X(7X3)




5 + 3 = 3 + 5 4 X 7 = 7 X 4



Area 4(3x) = 12x


6x + 8

3x

4



Practi

ce

12

Y1-4 U1-4 U6

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

WRITING EXPRESSIONS


(PE)(MD)(AS)

1 (PE)


2 (MD)







26

22 - (8 + 6) + 20= 22 - (8 + 6) + 20= Parentheses

(Add)


8 + 20= Addition

28

EXPONENTS



by itself

(-3)2=(- 3) (-3) = 9

-43= -4 4 4 = -64

PHRASE EXPRESSION






13

n

U1






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41






2x - 5 = 9

+ 5 +5

2x = 14

2 2

x = 7

add 5 to undo

subtraction

Divide by 2 to

undo multiplica-

tion

18 = - 8

+8 +8

26 =

bull2 bull2

52 = x

Add 8 to undo

subtraction

Multiply by 2 to

undo division

X

2

X

2

3(x - 2) = 18

3 3

x - 2 = 6

+ 2 +2

x = 8

Divide by 3 to

undo multiplica-

tion

Add 2 to undo

subtraction

x + 8

4

bull4 bull4

x + 8 = 36

- 8 - 8

x = 28

Subtract 8 to

undo addition

= 9

Multiply by 4 to

-8 + 3x = -26

+8 +8

3x = -18

3 3

x = -6

Add 8 to undo

adding (-8)

Divide by 3 to

undo multiplica-

tion

-18 = -2x - (-9)

-9 -9

-27 = -2x

-2 -2

135 = x

Divide by ndash2 to

undo multiplying

by ndash2

Subtract 9 to

14

V1mdashV4

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

W1 W3 W4 W5 W6

ge le gt lt






the equal to sign





05x + 12 = $1800

-12 -12

05x = 6

05 05

X= $12000

15



5x = 40



5w-4 = 70

2(x + 4) + 3 4(x ndash 3) ndash 2x

(2x + 8) +3 4x-12-2x

2x +11 2x-12

1) Distribute

2) Combine


equal sign)









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41









J1mdash5 L 2mdash4

16

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Unit 3 Vocabulary







itive whole number











17

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

18




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41




cost after taxes

STEP 1 Find TAX

6 = 006 1200

x

006

Turn the percent

There are

four decimal

places in

your problem

so the tax is

COMMISSION





$380 x 020 = $7600


INTEREST




L6 L7 L8 L9 L10 L11 L12

19

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

L6mdash12

20

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

J13

21

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Change

Original

Change

Actual











money


borrowed


principal







290 X 125 X 6 = $21750

L6mdashL8

Use the formula to


multiplying

22








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41








Skewed Right





Symmetric

Mean and median are

equal

Mean is the best

measure of center

Skewed Left





values


23

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Unit 4 Vocabulary




Maximum










= ℎ





for a set of data





outcomes in common)



in a set of data







last digit

24

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

25


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41


Measures of

Center

A measurement that




75 80 85 90 85







the set




numerical order





or none


Remember


9 8 2 4 8 5 6 7


2 4 5 6 7 8 8 9



Median 65


smallest number









AA1

26














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41














O14 27 Answers


You Try








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41








Scored

Absolute

Deviation

11 12-11=1

11 12-11=1

6 12-6=6

26 26-12=14

6 12-6=6

12 12-12=0 __1__ + __1__ + __6__ + __14__ + __6__ + _0___ = _28___

__28__ divide __6__ = _467_








Biased Sample



movie




28

Learnzillion


Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Mean the average

You add and divide
















population








accessed



the sampling


AA5

29









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41









third side



X+Y+Z= 180

Triangle Sum Tool


lines cross


180 degrees



Rem

emb

er straw in

qu

iry lab

Vertical

Complementary

Supplementary

P4 P5

30

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Unit 5 Vocabulary






congruent to lt B




sect





(equiangular)




31

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

PRISMS PYRAMIDS

Rectangular

Prism

Triangular

Prism

Triangular

Rectangular

Prisms have 2 bases

Prisms have mostly

rectangular faces



triangular faces




faces


Face

Base

Edge

Vertex





Creates a

Triangle

Creates a Rectangle

Creates a

Rectangle

32

P26





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41





of a rectangle is


length and w

represents

width

EXAMPLE

Perimeter distance


EXAMPLE

15 ft

6 ft

A = l x w

6 x 15

90

15 ft

6 ft

What do

these

variables stand

for

B = area

of the

base

h = height

r = radius

P = 15 + 15 + 6 + 6 P = 15 feet

33

P17mdash18

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

P28 P29 P33 P34

34




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41




through the center



3141592hellip


35

Chorus

Area of the base

Area of the base

Area of the base

Times the height

Big B

Big B

Big B

Times the height

Verse one





Verse two





Verse three





Verse four





P21mdashP23 P31 P32










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41










A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

36

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Unit 6 Vocabulary








trials performed








mental










37








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41








marble

Solution








EXAMPLES







COLOR FREQUENCY

Red IIII

Blue IIII I

White II

Grey IIII II

GREY

RED

GREEN







GREY

RED

GREEN

GREY

38

Z1mdashZ4

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41

Z3mdashZ6





____________________________


white_____________________________






39












(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41











(B following A)





using a list

List-

Gw Gb

Bw Bb

Pw Pb






outcomes

Table





Tree Diagram

Ch Or Gr LI Br






P(Heads)= 12 P(4)=16 12 X 16 = 112




bers


P(Even)= 14

25 X 14 =

220=110





were chosen

YOU TRY


40

Z 5mdash7


represent the same



girl





41


represent the same



girl





41

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