2015-2016 7th Grade Math Supplemental Notes

Irrational

1

 7.NS.1. 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. Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which oppo-
site quantities combine to make 0. For example, your bank account balance is -$25.00. You deposit $25.00 into
your account. The net balance is $0.00.

 b. Understand p + q as the number located a distance from p, in the positive or negative direction depending on
whether q is positive or negative. Interpret sums of rational numbers by describing real world contexts.

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

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

 7.NS.2. 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
continue to satisfy the properties of operations, particularly the distributive property, leading to products such as
(–1)(–1) = 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 –(p/q) = (–p)/q = p/(–q). Interpret quo-
tients 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
terminates in 0s or eventually repeats.

 7.NS.3. 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

inanaRfutraomatrcibtodieonornaetlshaNnanutodmtctaehbnqaeutbra:tehlAwetnorydizteteneronom.as-

2

Unit 1 Vocabulary

 Additive Inverse: Two numbers whose sum is 0 are additive inverses of one another.
Example: and – are additive inverses of one another because + (– ) =

( – ) + = 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.

• Absolute Value: The distance between a number and zero on the number line. The

symbol for absolute value is shown in this equation: |7| = 7

• Integers: A number expressible in the form a or –a for some whole number a. The set
of whole numbers and their opposites {…-3, -2, -1, 0, 1, 2, 3…}

• Natural Numbers: The set of numbers {1, 2, 3, 4,…}. Natural numbers can also be called
counting numbers.

• Negative Numbers: The set of numbers less than zero.

• 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.

• Positive Numbers: The set of numbers greater than zero.

• Rational Numbers: The set of numbers that can be written in the form a/b where a and
b are integers and b 0.

• Repeating Decimal: A decimal number in which a digit or group of digits repeats with-
out end.

• Terminating Decimal: A decimal that contains a finite number of digits.

• Zero Pair: Pair of numbers whose sum is zero.

3

5 - 0.85

C1—C6

4

YOU MUST HAVE A COMMON DENOMINATOR FOR ADDING AND SUBTRACTING FRACTIONS.
USING A RATIO TABLE

 Write both fractions in a table.  Fill in the numerators on the  Add/subtract
table to find your fractions with fractions.
 Continue listing the multiples of a common denominator.
the denominators until you find a EXAMPLE CONTINUED:
common denominator. EXAMPLE CONTINUED:
5
1 So, 20 is the 12345 20
4 8 12 16 20 common 4 8 12 16 20
3 12
5 10 15 20 denominator for 3 6 9 12 + 20
5 10 15 20
17
20

G1—G4

5

 Write mixed numbers as 123 ÷ 4 1
improper fractions. 2

 Put whole numbers over 5 ÷ 9
one. 3 2

 KEEP the first fraction, 5 x 2 = 10
CHANGE divide to multi- 3 9 18
ply, FLIP the second
fraction (reciprocal) 5
9
 Multiply the numerators.

 Multiply the denomina-
tors.

1 3

5 ÷=

first fKraEcEtiPonthe 8

1 CHANGE FLIP the fraction
second
5
88
X 3 = 15

G7—G13

6

7

Integer: Whole numbers and their opposites
Example: …, -2, -1, 0, 1, 2, …

Positive Number: A number greater than zero
Example: 1, 2, 3, …..

Negative Number: A number less than zero
Example: …, -3, -2, -1

Zero is neither negative nor positive.

4+(-3)=1 ++ DOUBLE NEGATIVE SIGNS??
Make it a PLUS SIGN,
now you are adding!

+ ++

“Same signs, add and keep, different signs subtract,
Take the sign of the larger number, then you’ll be exact!”

= ?? D.1, D.2, D.3, D.4, D.5
E.1, E.2, E.3, E.4, H.1

= 19 Adding integers Video Subtracting integers video

You can make ANY subtraction You try!
problem an addition problem by
using the rule “keep, change,
change. Then, follow the rules
from the song.

A. 2+-3= B. 10— -4 = C. –1+-8 =

Different Subtraction Same Signs
Signs

Add/Subtract Fruit Splat

8

E6—E8

Keep Change Change

FOUND AT http://www.sw-georgia.resa.k12.ga.us/integer%20rules.pdf

Same Sign: Add and keep the sign Subtracting a negative is like ADDING A POSITIVE
2+2=4 2 - ( -2) =
Positive + Positive = Positive
(-2) + (-2) = (-4) 2 + +2 = 4
Negative + Negative = Negative
fiKrestepsigthne Change Chansgigen
Different Signs: Subtract and keep the sign minus
of the larger value (from zero)
Subtracting a positive IS subtracting
Positive x Positive = Positive or like ADDING A NEGATIVE
Negative x Negative = Positive
Negative x Positive = Negative -8 - 4 =
Positive x Negative = Negative
-8 + (-4) = - 12
Division (same pattern)
firKsteesipgnthe Change Chansgigen
minus to
plus

9

Plug it in and use order of operations to solve. P arenthesis
E xponents
(12 - 4) + 3(4)2 M ultilication
D ivision
(12 - 4) + 3(16) Exponents (42 = 4•4) A ddition
S ubtraction
8 + 3(16) Parenthesis (12 - 4 ) From left
to right
8 + 48 Multiply (3•16)
From left
56 Add (8 + 48) to right

Same Sign = Positive Definition: A number’s distance from zero
on a number line.
7 • 8 = 56 -56 ÷ (-8) = 7
Hint: Always make the number positive.

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

3(9) = 27 -27 = 9
-3

Different Signs = Negative

-2 • 8 = -16 16 ÷ (-8) = -2 | -3 | = 3 | -8 | = 8 - | 4 | = -4

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

-6(4) = -24 -24 = -4 |5|= | 8 - 5 | = - | -2 | =
6

H.2, H.7, E.9

What must you do to the number to Rags to Riches Rational Numbers
make it equal to zero.?
You Try!
-14 +14=0

Creating Neutral Fields X +4 =6
Additive Inverse
-4 -4

X=2

10

 7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions
with rational coefficients.

 7.EE.2. Understand that rewriting an expression in different forms in a problem context can clarify the
problem and how the quantities in it are related. For example a + 0.05a = 1.05a means that adding a 5%
tax to a total is the same as multiplying the total by 1.05.

 7.EE.3. Solve multistep real-life and mathematical problems posed with positive and negative rational
numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as
strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasona-
bleness 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 1/10 of her salary an hour, or $2.50, for a new
salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2
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.

 7.EE.4. 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 > r or px + q < 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

11

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.

12

Associative Property Multiply the number touching the
outside of the parenthesis with each
The sum or product of a set of numbers is the same no matter
how the numbers are grouped. (Hint: It’s a conversation, speaker changes) term inside

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

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

The sum or product of a group of numbers is the same regardless 3(2x) + 3(6) 2(3x) - 2(4x2) + 2(3)
of the order in which the numbers are arranged.
6x + 18 6x - 8x2 + 6
(Hint: Order changes, but they are still neighbors.)

5+3=3+5 4X7=7X4

Add/Subtract each like term (numbers with A B A(B) (A)(B) A X B
the same variable raised to the same exponent)

MAKE SURE YOU TAKE THE SIGN
IN FRONT OF THE TERM!!!

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

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

33x –13x -42x 9x – 7x 2 + 8

2x3 - 4x2 + 2x + 10 Y1-4, U1-4, U6

3x Area: 4(3x) = 12x Practice

Perimeter: 3x + 3x + 4+ 4
4 = 6x + 8

Combining Like Terms

Perimeter: Add up all of the sides
Area of a rectangle: A=lw

13

ORDER OF OPERATIONS EXAMPLES:

(PE)(MD)(AS) EXPRESSION EVALUATION OPERATION

1. (PE) Do parentheses and exponents 50 - 12 ÷ 3 · 6= 50 - 12 ÷ 3 · 6= Division
FIRST 50 - 4 · 6= Multiplication

2. (MD) Solve all multiplying and dividing 22 - (8 + 6) + 20= 50 - 24= Subtraction
from left to right. 26
22 - (8 + 6) + 20= Parentheses
(It may be divide first) Subtraction
22 - 14 + 20= Addition
3. (AS) 8 + 20=
28
Solve all adding and subtracting from
left to right. (It may be subtract first).

EXPONENTS WRITING EXPRESSIONS

Exponents tell how many PHRASE EXPRESSION
times to multiply a
by itself. 8 more than a number 8+n
(-3)2=(- 3) · (-3) = 9
-43= -4 · 4 · 4 = -64 number 7 less than a number n-7

The product of a number and 11 11n

The quotient of 6 and a number 6
n

A number decreased by 12 n - 12

U1

14

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

solve.

You have to use IN- VERSE OPERATIONS to

solve each equation.

he 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.

(Hint: Move what is not attached to the variable FIRST!!)

V1—V4

Below are examples of 2-step equations and how to solve using algebraic no-

2x - 5 = 9 add 5 to undo 18 = X - 8 Add 8 to undo
subtraction, mak- +8 2 +8 subtraction, mak-
+ 5 +5 ing the 8 zero
2x = 14 ing the 5 zero 2 26 = X 2
22 Multiply by 2 to
Divide by 2 to 2 undo division,
x= 7 undo multiplica- which leaves
tion, which 52 = x you with 1

leaves you with1

3(x - 2) = 18 Divide by 3 to 4 x+8 =9 4 Multiply by 4 to
33 undo multiplica- 4 undo division,
tion, which which leaves 1
x-2 = 6 leaves 1 x + 8 = 36
+ 2 +2 Subtract 8 to
Add 2 to undo -8 -8 undo addition,
x =8 subtraction, making the 8 a
making the 2 x = 28 zero
-8 + 3x = -26 zero
+8 +8
Add 8 to undo -8, -18 = -2x - (-9) Subtract 9 to un-
3x = -18 making –8 zero -9 -9 do -(-9) or +9,
33 making 9 zero
x = -6 Divide by 3 to -27 = -2x
undo multiplica- -2 -2 Divide by –2 to
tion, leaving 1 undo multiplying
13.5 = x by –2, which
leaves 1

15

5 steps process:
1. Name your variable in words.
2. Put equal sign and total to the right of
the = sign
3. Write the left side of the equation using
word clues from your problem.
4. Solve for the variable
5. Check your answer

EXAMPLE:

Each month Chuck's phone company charges a flat ≥≤ > <

fee of $12 plus $0.05 per minute. His bill for last If there is a line under the greater
than or less than sign, it means the
month was $18. How many minutes did Chuck talk variable can be equal to the value.
In this case, don’t forget to fill in your
on the phone last month? Step 1: x= number of circle on the number line to represent
the equal to sign.
minutes Chuck talked

.05x + 12 = $18.00 last month
-12 -12

.05x = 6 Steps 2-4
.05 .05 Step 5: Check
X= $120.00

W1, W3, W4, W5, W6 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

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 – 3) – 2x 1) Distribute
2x + 8 +3 4x -12 - 2x
2) Combine
2x +11 2x-12
3) Solve (when there is an

equal sign)

16

J1—5, L 2—4

 7.RP.1. 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 1/2 mile in each 1/4 hour, compute the unit
rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

 7.RP.2. Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., 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.
 7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest,
tax, markups and markdowns, gratuities and commissions, and fees.
 7.G.1. 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.

17

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 a/b where a is a whole number and b is a pos-
itive whole number.

 Multiplicative inverse: Two numbers whose product is 1. Example: (3/4) and (4/3)
are multiplicative inverses of one another because 3/4 × (4/3) = (4/3) × 3/4 = 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 5/50 = 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 ≠ 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.

18

19

In Georgia, we have a 6% sales tax. COMMISSION:
You want to buy a shirt that costs
$12.00. How much does the shirt Cinthia earns 20% commission on her
cost after taxes? sales. In February, she sold $380 in
merchandise. How much did Cinthia make
STEP 1: Find TAX in commission in February?

6% = 0.06 12.00 There are $380 x 0.20 = $76.00
x four decimal She earned $76 in commission.
Turn the percent
places in
0.06 your prob-
lem, so the

INTEREST:

Alberto’s savings account earns 3% inter-
est ever month. If Alberto puts $45.00
in his bank account at the beginning of

L6, L7, L8, L9, L10, L11, L12

20

L6—12

21
J13

22

Change Find the percent of change and state
Original whether it is a mark up or mark
down.
From 12 to 16
From 60 to 45

33.3% Mark up 33.3% Mark down

Simple Interest: The amount paid or earned for the use of Dustin paid for a new skateboard
money. with his credit card. The skate-
board cost $290 and has 12.5%
Principal: The amount of money deposited or Use the formula to interest. If it takes him 6 months
borrowed find the interest by to pay of the credit card, how
multiplying. much interest did he pay?
Rate: The percent you earn or owe on the
principal 290 X .125 X 6 = $217.50

L6—L8

23

 7.SP.1. 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.

 7.SP.2. 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;
predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or
prediction might be.

 7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities,
measuring the difference between the medians by expressing it as a multiple of the interquartile range.

 7.SP.4. 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

AA.1, AA.2,

AA.4, AA.5,

Skewed Right Symmetric Skewed Left O.14,O.15

 Mean is greater than the median  Mean and median are  Mean is less than the median

 Median is the best measure of center equal  Median is the best measure

because the median is not affected  Mean is the best of center because the median is
not affected by very small data
by very large data values measure of center values

24

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
“on average” 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 (i.e., 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.

25

Remember??? 26
EXAMPLE
WORD DEFINITION IN YOUR WORDS
Measures of John’s quiz scores:
A measurement that 75, 80, 85, 90, 85
Center summarizes a data set
with a single number. Median of scores:_____
Mean of scores: ______
Mean The sum of the values MEAN of John’s scores
Median in a data set divided by
the number of values in MEDIAN of John’s scores

the set. MODE of John’s scores

The middle value in a
data set when it is in

Mode The value that appears
most often in a data
set. There can be one
or none.

Range: Difference between biggest and Shows how values are distributed
smallest number
9, 8, 2, 4, 8, 5, 6, 7
Median: Middle number
Put #’s in order from least to greatest
Upper Quartile: Median of upper half of data
2, 4, 5, 6, 7, 8, 8, 9
Lower Quartile: Median of lower half of data
Minimum: 2 Upper Quartile: 8
Inner Quartile Range: Subtract the low-
er Maximum: 9 Lower Quartile: 4.5

Median: 6.5

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

27 O14
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.

You Try!

___% of the data falls above the median.
___% of the data falls below the median.
___% of the data falls above Q1.
___% of the data falls above Q3.

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? ______

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

Answers

28

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 student's 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

Mean the average,
You add and divide.
Median line ‘em up
find what’s 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.
It’s a whole lot of math,
But it isn’t that bad.
You could maybe use the IQR--
To see if they’re close or If they are far.
You have to subtract Q3 and Q1
You’ll get IQR and then you are DONE!

29

 7.G.2. Explore various geometric shapes with given conditions. Focus on creating triangles from three
measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than
one triangle, or no triangle.

 7.G.3. Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional
figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders,
and spheres.

 7.G.4. Given the formulas for the area and circumference of a circle, use them to solve problems; give
an informal derivation of the relationship between the circumference and area of a circle.

 7.G.5. 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.

 7.G.6. 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.

Vertical Angles are the angles opposite each other when two Complementary
Supplementary
lines cross.
Vertical
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)

The sum of measures of the interior P4, P5 The sum of the lengths of any two sides of Remember straw inquiry lab
angles of a triangle is 180 degrees. a triangle is greater than the length of the
third side.
X+Y+Z= 180

Triangle Sum Tool Triangle Inequality Tool

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. < A ≅ < B denotes that < A is
congruent to < B.

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

 Irregular Polygon: A polygon with sides not equal and/or 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 circle’s circumference to its diameter, when used in calcula-
tions, pi is typically approximated as 3.14; the relationship between the circumference
(C) and diameter (d), or c/d.

 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 PYRAMIDS

PRISMS Triangular

Rectangular
Prism

Rectangular

Triangular

Prism

 Prisms have 2 bases.  Pyramids have one base.

 Prisms have mostly  Pyramids have mostly

rectangular faces. triangular faces.

NAMING SOLID FIGURES
 The base of a pyramid or prism gives the shape its “first name”
 The “last name” is either prism or pyramid and is based on triangular or rectangular

faces.
EXAMPLE: At right is a Hexago-

P26

Face Edge Parallel lines: two lines that are in the same plane and do not intersect.

Perpendicular lines: two lines that intersect to form right angles.

Base Vertex

Creates a Cross Section: The intersection of a solid and a plane.
Triangle Plane: a flat surface that goes on forever in all directions

Creates a Rectangle

Creates a
Rectangle

32

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. P17—18

Perimeter: distance What do
around a plane figure these

The formula above for finding the area of a variables stand
rectangle is A = bh. An alternate formula for for?
area of a rectangle is:
B = area
6 ft of the
base
when A represents area, l represents length, 1.5 ft
and w represents width. 6 ft h = height

1.5 ft r = radius

EXAMPLE: A=lxw EXAMPLE:
6 x 1.5 P = 1.5 + 1.5 + 6 + 6
9.0 P = 15 feet

33
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; 3.141592…..

The radius is 1/2 of the diameter.

Chorus

Area of the base

Area of the base

Area of the base

Times the height P21—P23, P31, P32
Big B

Big B

Big B

Times the height

Verse one

I’m going to find the volume

Find out how much goes inside it

Multiply length times the width times the height

And I’ve found the prism’s volume that’s right.

Verse two

Now I’ve got a cylinder

What goes in for Big B I wonder

Pi times the radius squared. Don’t blunder.

Multiply by the height. Now we’re 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 you’ve 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

That’s how much of the lava can flow.

35

 7.SP.5. 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 1/2 indicates an event that is neither unlikely nor likely, and a probability
near 1 indicates a likely event.

 7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces
it and observing its long-run relative frequency. Predict the approximate relative frequency given the probabil-
ity. 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.

 7.SP.7. Develop a probability model and use it to find probabilities of events. Compare experimental and theo-
retical probabilities of events. If the probabilities are not close, 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?

 7.SP.8. 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 (e.g., “rolling double sixes”), identify the outcomes in the
sample space which compose the event.

 c. Explain ways to set up a simulation and use the simulation to generate frequencies for compound events.
For example, if 40% of donors have type A blood, create a simulation to predict the probability that it will take
at least 4 donors to find one with type A blood?

A2 3 456 7 89 10 J Q K

A2 3 456 7 89 10 J Q K

A2 3 456 7 89 10 J Q K

A2 3 456 7 89 10 J Q K

Unit 6 Vocabulary: 36

 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 in-
formation 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
process so that the total probability over all such outcomes is unity. This can be either theoretical or ex-
perimental.

 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.