Transcript - St. Patrick School (Bay Shore)

ADDITION, SUBTRACTION,
MULTIPLICATION, DIVISION
Integers
CHAPTER 1: MODULE 1 AND 2
BY: OLIVIA BURWELL, BROOKE
BOWERS, EMMA CAREY
MODULE 1 VOCABULARY
Additive inverse: the opposite of any number
Absolute value: the distance from zero on a number line; shown by l l.
Expression: a mathematical phrase that contains operations, numbers, and/or
variables.
1.1 ADDING INTEGERS WITH THE SAME
SIGN
Essential Question and rule:
How do you add integers with the same sign?
To add integers with the same sign, add the absolute value of the integers
and use the integers for the sum.
1.1 REVIEW QUESTIONS
1. -2 + -7 =
345=
2.-50 + -175 + -
3. A football team loses 3 yards on one play and 6 yards on another play. Write a sum of
negative ingeters to represent this situation.
1.2 ADDING INTEGERS WITH DIFFERENT
SIGNS
Essential Question and rule:
How to add integers with different signs?
Subtract the lesser absolute value from the greater absolute value. Use the
signs of the integers with the greater absolute value for a sum.
1.2 REVIEW QUESTIONS
1. 3 + (-4) =
79 =
2. -79 +
3. A soccer team is having a car wash. The team spent $55 on supplies. They
earned $ 275, including tips. The teams profit is the amount the team made
after paying for supplies. Write a sum of integers that represent the teams
profit.
1.3 SUBTRACTING INTEGERS
Essential Question and rule:
How do you subtract integers?
To subtract integers, you keep the first number, change the subtraction sign
into an addition sign, and do the opposite of the second number. Then use
the rule for adding integers.
1.3 REVIEW QUESTIONS
1. 15-21=
25=
2. 4-
3. Theo had a balance of -$4 dollars in his savings account. After making a
deposit, he has $25 in his account. What is the overall change to his account?
1.4 APPLYING ADDITION AND
SUBTRACTION OF INTEGERS
Essential Question:
How do you solve multistep problems involving addition and subtraction of
integers?
To solve multistep problems, you follow the rule of adding and subtracting
integers.
1.4 REVIEW QUESTIONS
-6+15+15=
2. 2.-35-14+45+31=
1.
3. Herman is standing on a ladder that is partly in a hole. He starts out at a
rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet.
What is Herman’s final position, relative to the ground?
2.1 MULTIPLYING INTEGERS
Essential Question and rule:
How do you multiply integers?
The product of two integers with opposite signs is negative. The product of
two integers with the same sign is positive.
2.1 REVIEW QUESTIONS
1. (-2)(50)= 2. -15(9)=
3. Adam is scuba diving. He descends 5 feet below sea level. He descends
the same distance four more times. What is Adam’s final elevation?
2.2 DIVIDING INTEGERS
Essential Question and rule:
How do you divide integers?
If the signs of the integers are the same, the answer is positive. If the signs of
the integers are different, the answer is negative. Then divide the integers.
2.2 REVIEW QUESTIONS
1. -14/2=
2. -500/-25=
3. Clark made four of his truck payments late and was fined four late fees. The
total change to his savings from late fees was -$40. How much was one late
fee?
2.3 APPLYING INTEGER OPERATION
Essential Question:
How can you use integer operations to solve real world problems?
The order of operation applies to integer operations as well as positive
number operations. Perform multiplication and division first, and then addition
and subtraction. Work from left to right in the expression. These equations can
be used to represent descent, gains, and loses.
2.3 REVIEW QUESTIONS
1. -6(-5)+12= 2. 4(13)+20=
3. Bella pays seven payments of $5 each to a game store. She returns one
game and receives $20 back. What is the change to the amount of money
she has?
ANSWER KEY
1.1:
1.3:
2.1:
2.3:
1.
-9
1. -6
1. -100
1. 42
2.
-570
2. -21
2. -135
2. -32
3. -9
3. increased by $29
3. -25
less
1.2:
2.2:
1.
-1
1.4:
1. -7
2.
0
1. 24
2. 20
3.
$220
2. 27
3. $10
3. 3 feet under ground
3. $15
Module 5: Proportions
and Percents
BY: JULIA MAIORINO, ALEXIS KERR, AND SARAH MORAN
Vocabulary Section 1
Percent Increase- describes how much a quantity increases in comparison to
the original amount.
Percent Decrease- describes how much a quantity decreases in comparision
to the original amount
Vocabulary Section 3
Simple Interest- a fixed percent of the principal
Principal- original amount of money deposited or borrowed
Formulas for Section 1
Percent of Change = amount of change
original amount
Amount of Change = greater value – lesser value
New Amount= original amount + amount of change
Formulas for Section 2
Retail price= original cost + markup
Sale price = original price - markdown
Formulas for Section 3
Simple Interest = principal x rate x time
Essential Questions
Section 1: What process do you use to find the percent change of a
quantity?
Given an original amount and a percent increase or decrease, you can use
the percent change to find the new amount.
Section 2: How can you determine the sale price if you are given the regular
price and percent of markdown?
You can turn the percent into a decimal and multiply the decimal by the
regular price. Then you subtract that answer from the regular price.
Section 3: How can you determine the total cost of an item including tax if
you know the price of the item and the tax rate?
You can turn the tax rate to a decimal then multiply it to the cost then add
what you got to the original price.
Section 1 Review Question
From $5 to $8 = 8-5 = 3
5
= 60% increase
5
From $80 to $64 = 80-64 = 16 = 20% decrease
80
80
Over the summer, Jackie played video games 3 hours per day. When school
began, she was only allowed to play video games for half and hour each
day. What is the percent decrease? Round to the nearest percent.
180-30 = 150
180
180
= 83% decrease
Section 2 Review Questions
Original Price: $18; markup:15%
18(0.15 +1)
18(1.15)
$2.70
Original Price: $45; markdown: 22%
45(1-0.22)
45(0.78)
$35.10
Dana buys dress shirts from a clothing manufacturer for x dollars each and then
sells the dress shirts in her retail clothing store at a 35% markup. What is the retail
price of a dress shirt that Dana purchased for $32.
32(0.35+1)
32(1.35)
$43.20
Section 3 Questions
5% of $30
0.05(30)
$1.50
150% of $22
1.5(22)
$33
Teresa's restaurant bill comes to $29.99 before tax. If the sales tax is 6.25% and
she tips the waiter %20. What is the total cost of the meal?
29.99(0.2) = $6 tip
29.99(0.0625) = $1.87 tax
29.99 + 6 + 1.87 = $37.86 total cost
Module 9
CIRCUMFERENCE, AREA, AND VOLUME
9.1 Circumference
Essential Question- How do you find and use the circumference of a circle?
Answer to Essential Question- To find the circumference of a circle use one of
the two equivalent formulas for circumference are c=πd and c=2πr. To use
the circumference of a circle, you can use the appropriate circumference
formula to find the radius or the diameter of the circle. You can use that
information to solve problems.
Formulasc=πd
c=2πr
9.1 Circumference
Vocabulary
A radius is a line segment with one endpoint at the center of the circle and
the other endpoint on the circle. The length of a radius is called the radius of
the circle.
A diameter of a circle is a line segment that passes through the center of the
circle and whose endpoints lie on the circle. The length of diameter is twice
the length of the radius. The length of a diameter is called the diameter of
the circle.
The circumference of a circle is the distance around the circle.
9.1 Circumference
Computational Questions- Round to the nearest hundredth. Use π for π.
1.
c=πd
c=24π
c=75.40 inches
2. c=2πr
c=2π8
c=50.27
9.1 Circumference
Word Problem-
A circular pool has a circumference of 72 meters.
Sophia is swimming a straight line along a diameter at a
rate of a half a meter per second. How many seconds
will it take her to swim across the whole pool?
Answer- About 46 seconds
9.2 Area of Circles
Essential Question- How do you find the area of a circle?
Answer to Essential Question- The formula for the area of a circle is 𝐴 = 𝜋𝑟 2
where a is area and r is radius.
FormulasThe area of a circle is equal to 𝜋 times the radius squared. 𝐴 = 𝜋𝑟 2 is the
equation. Area is given in square units.
9.2 Area of Circles
Computational Questions-Find the area of the circle. Use 𝜋 for 𝜋. Round to
the nearest tenth.
1.
𝐴 = 𝜋41.52 cm
A = 5410.6 cm
2.
𝐴 = 𝜋242 yd
A= 1809.6 yd
9.2 Area of Circles
Word Problem-
Grace bought a circular mirror that measures
1 and a half feet across. What is the area of
her mirror rounded to the nearest inch?
Answer- about 2 feet
9.3 Area of Composite Figures
Essential Question- How do you find the area of composite figures?
Answer to Essential Question- To find the area of a composite figures divide it into
simple, nonoverlapping figures. Find the area of each simpler figure, and then
add the areas together to find the total area of the composite figure.
FormulasTriangle is A=⅟2bh
Square is A=bxh or side squared
Rectangle A= lxw
Parallelogram A= bxh
Trapezoid A= ⅟2 h(b₁+b₂)
9.3 Area of Composite Figures
Computational Questions- Find the area of each figure. Use 𝜋 for 𝜋.
1.
Answer- 21 feet
2.
Answer- c
9.3 Area of Composite Figures
Word ProblemA bookmark is shaped like a rectangle with a semicircle attached at both
ends. The rectangle is 12 cm long and 4 cm wide. The diameter of each
semicircle is the width of the rectangle. What is the area of the bookmark?
Use 3.14 for 𝜋.
60.56 cm squared
Answer-
9.4 Solving Surface Area Problems
Essential Question- How can you find the surface area of a figure made up of
cubes and prisms?
Answer to Essential Question- Given a prism’s dimensions, you can use a
formula to find the surface area. The surface area S of a prism with base
perimeter P, height h, and base area B is S = Ph+ 2B.
FormulasThe surface area S of a prism with base perimeter P, height h, and base area
B is S = Ph+ 2B.
9.4 Solving Surface Area Problems
Computational Questions- Find the surface area of each solid figure. Round
to the nearest meter.
1.
39 meters
Answer-
2.
Answer- 74 meters
9.4 Solving Surface Areas Problems
Word Problem- Timmy wants to cover the box shown with paper without any
overlap. How many square meters will be covered with paper?
meters of paper
Answer- 220 square
9.5 Solving Volume Problems
Essential Question- How do you find the volume of a figure made of cubes
and prisms?
Answer to Essential Question- The formula for the volume of a rectangular
prism can be used for any prism. The volume V of a prism is the area of its
base B times its height h. V= Bh.
FormulasThe volume V of a prism is the area of its base B times its height h. V= Bh.
9.5 Solving Volume Problems

Computational Problems- Find the volume of the triangular prism. Round to the
nearest unit.
1. (a) Calculate the volume of the prism if / = 5 cm
Answer-50 cm cubed



2.
Answer- 96 cm cubed
9.5 Solving Volume Problems

Word Problem-
A trap for insects in the shape of a triangular prism. The
area of the base is 3.5 inches squared and the height of
the prism is 5 inches. What is the volume of this trap?

Answer- 17.5 inches cubed.
By Adia and Victoria
MODULE 10
ANALYZING AND COMPARING DATA
Ms. Corazza
MODULE 10 VOCABULARY
Data- Factual information used as a basis for reasoning, discussion, or calculation.
Interquartile range- The difference between the upper and lower quartiles in a box-and-whisker
plot.
Mean- The sum of the items in a set of data divided by the number of items in the set; also called
average.
Measure of speed- A measure used to describe how much a data set varies; the range, IQR, and
mean absolute deviation are measures of spread.
Median- The middle number or the mean (average) of the two middle numbers, in an ordered
set of data.
Survey-to look over and examine closely.
Box plot- a graph that shows how data is distributed by using the median, quartiles, least value,
and greatest value; also called a pox plot.
Dot plot- display data using a number line.
Mean absolute deviation- The mean distance between each data value and the mean of the
data set.
10.1 COMPARING DATA DISPLAYED IN DOT PLOTS
ESSENTIAL QUESTION
Essential Question: How do you compare two sets of data displayed in dot plots?
Answer:
You can compare dot plots visually using various characteristics,
such as center, spread, and shape. You can also compare the
shape, center, spread of two dot plots numerically by calculating
values related to the center and spread.
10.1 COMPARING DATA DISPLAYED IN DOT PLOTS
REVIEW QUESTIONS
0
2 4
6
8 10 12 14
1. Describe the shape of the box
Answer: The dots have a relatively even spread, with a peak at 8 letters.
2. Describe the center of the dot plot
Answer: 6 and 7 letters.
3. Describe the spread of the dot plot
Answer: The dots spread from 3 to 9 letters.
10.1 COMPARING DATA DISPLAYED IN DOT PLOTS
Two Computational
28 29 30 31 32 33 34 35
Are the dots evenly distributed or grouped on one side?
Answer: The dots seem to be evenly distributed.
Calculate the mean and median of data in the dot plot?
Answer: Mean:31.6 Median: 31¾
1 Word Problem
How do you calculate the mean, median, and mode of a dot plot?
Answer:
To find the mean:
Add all the items of the data, then divided the sum by the number of items on the dot
plot.
To find the median:
Order the data from least to greatest, then find the middle or average number.
To find the mode:
Find the number that appears most in the data
10.2 COMPARING DATA DISPLAYED IN BOX PLOTS
ESSENTIAL QUESTION
Essential Question: How do you compare two sets of data displayed in dot plots?
Answer:
You can compare two dot plots numerically according to their
centers, or medians, and their spreads, or variability, range and
interquartile range (IQR) are both measures of spreads. Box plots
with similar variability should have similar boxes and whiskers. You
can compare box plots box plots with greater variability, where
there is less overlap of the median and interquartile range.
10.2 COMPARING DATA DISPLAYED IN BOX PLOTS
REVIEW QUESTIONS
1. How can you compare two box plots?
Answer: You can compare two box plots numerically according to
their centers, or medians and their spreads or variability.
2. Do box plots with similar variability have similar boxes and whiskers?
Answer: They should have similar boxes and whiskers.
10.2 COMPARING DATA DISPLAYED IN BOX PLOTS
Volleyball players
Two Computational
Hockey players
1 2 3 4 5 6 7 8 9 10 1112 13
Which group has a bigger median height?
Answer: The volleyball players
Which group has the shortest players?
Answer: The hockey players
1 Word Problem
What information can you use to compare two box plots?
Answer: Hockey players are shorter than volleyball players.
10.3 STATISTICAL MEASURES TO COMPARE
POPULATIONS
ESSENTIAL QUESTION
Essential Question: How can you use statistical measures to compare population. ?
Answer:
Many different random samples are possible for any given
population, and their measures of center can vary. Using multiple
samples can give us an idea of how reliable any inferences or
predictions we make are.
10.3 USING STATISTICAL MEASURES TO COMPARE
POPULATIONS REVIEW QUESTIONS
1. How is using multiple are samples helpful?
Answer: Using multiple samples can give us an idea of how reliable any
inferences or predictions we make are.
2. How many random samples are possible for any given population?
Answer: Many different random samples are possible for any given
population and their measures of center can vary.
10.3USING STATISTICAL MEASURES TO COMPARE
POPULATIONS
Two Computational
Average Monthly temperatures for Atlanta City in Fahrenheit:
23,38,39,48,55,56,71,86,57,53,43,31
Average monthly temperatures for New York City in Fahrenheit:
8,23,24,33,40,41,56,71,42,38,28,16
1. For city 1, what is the mean of the average monthly temperatures?
Answer: Mean=50 degrees Fahrenheit
2. What is the mean absolute deviation of the average monthly temperatures?
Answer: Mean Absolute Deviation=13 degrees Fahrenheit.
1 Word Problem
1. What do you think the mean of the average monthly temperatures for New York City is? What do you
think the Mean Absolute Deviation of the average monthly temperatures for New York City is?
Answer- The mean of the average monthly temperatures for New York City is 35◦F. The mean for New York
City must be 15◦F less than the mean for Atlanta City and the Mean Absolute Deviation must be the same. The
Mean Absolute Deviation of the average monthly temperatures for New York City is 13◦F.
Darius Abdulhaqq and
Christian Aponte
Module 14: Real
Numbers
By: Cristian Espinosa and Sebastian Bonhomme
14.1 Vocabulary

Rational number- any number that can be written as a ratio in the form a/b,
where a and b are integers and b is not 0.

Terminating decimal- a decimal number whose repeating digit is 0.

Repeating decimal- a decimal in which one or more digits repeats infinitely.

Square root- a number that is multiplied by itself to form a product is called a
square root of that number.

Principle square root- the nonnegative square root of a number.
Perfect square- a square of a whole number.
 Cube root- a number, written as 3 x


Perfect cube- A cube of a whole number

Irrational Number- Numbers that are not rational
14.2 Vocabulary

Real Numbers-A rational or irrational number
14.1 Formulas

Square Root

Principle Square Root- 25 = 5

Perfect square- 52 =25

Perfect cube- 23 =8

Cube root-
3
16=4 because 42 = 4x4 = 16
8 2𝑋2𝑋2 = 8
14.2 Formulas
Rational Numbers-
𝐼𝑟𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟𝑠 −
𝟏𝟕
𝟐
− 𝟏𝟏
𝜋
27
4
Integers- -3, -2, -1
0.3
Whole Numbers67, 75,
21
−6
7
14.3 Formulas
3+5 O 3+ 5
1.7+5 O 3 +2.2
6.7>5.2

14.1 Review Questions

Write each decimal as a fraction:
1.
0.675=

Solve for x:
27
40
2. 𝑥 2 =196 x=4

A heartbeat takes 0.8 second. How many seconds is this written as a fraction?
4
5
14.2 Review Questions

Write all the names that apply to each number
1.
7
8
2.
3.
Rational and Real
81
9
Whole, Integer, Rational, Real
2
A baseball pitcher has pitched 123 Innings. Rational, Real
14.3 Review Questions

Compare:

3+2 O 3+3= 3+2 < 3+3

17+3 O 3 + 11= 17+3 > 3 + 11

Give A real number between 13 and 14: 3.65
Essential Questions

14.1: How do you rewrite rational numbers and decimals, take square roots
and cube roots, and approximate irrational numbers?

To rewrite rational numbers, turn it into a fraction or decimal. To take square
roots and cube roots you add an exponent to the number.

14.2: How can you describe relationships between sets of real numbers?

Using terms such as whole, integer, rational, irrational, and real.

14.3: How do you order a set of real numbers?

To make ordering easier, convert all the numbers to decimals. Then, plot
those decimals on a number line and compare them.