COMPACTED MATHEMATICS
UNIT 1
OPERATIONS WITH POSITIVE RATIONAL NUMBERS
TOPICS COVERED:











Rational Numbers
Trip Across The USA Group Project
Place value of whole numbers
Place value of decimals
Adding and subtracting whole numbers
Multiplying and dividing whole numbers
Adding and subtracting decimals
Multiplying and dividing decimals
Rounding
Squares and Square Roots
Order of operations
Mathematics is the science of magnitude and number and related topics. It is derived from the Greek
“mathema” which means learning.
Arithmetic is the science of numbers and reasoning. It is derived from the Greek “arithmetike tekhne”
which means art of counting.
Activity 1-1
Interest Inventory
1.
My favorite subject(s)
2.
My hobbies
3.
My favorite sports
4.
The one song I will always remember from this
summer is…
5.
What I like about my friends
6.
What I like about myself
7.
Careers that might interest me
8.
When I have free time I enjoy…
9.
Books and magazines I enjoy
10. The three people I admire the most are…
11. If I were an animal I would be a…
12. My greatest talent is…
13. Where I'd like to live
14. My favorite cartoon character is…
15. A responsibility I handle well is…
16.
If I were principal of this school the one thing I
would change is…
17. Subjects I want to learn about
18. Things I want to improve
19. Major food preferences and favorite restaurant
20. My most valuable possessions
21. My most memorable events
22. Places I have traveled
23. What really gets on your nerves?
24. One of my earliest memories is…
25. The happiest day of my life was…
26. I was sad when I learned that…
27. The best opportunity I ever had was…
28. It was difficult to learn to…
NAME:
29.
If you were allowed to stop going to school, would
you?
30. An experience that embarrassed me was…
In five minutes you will be stranded on a desert
31. island. You may only take one realistic item with
you. That one item will be…
Think of your all-time favorite teacher. Why did you
32.
pick this teacher?
33. My favorite movie of all-time is….
34.
If you could be as talented as a friend of yours at one
thing, what would you choose?
35. The wildest and craziest thing I have ever done is…
If you were given $1,000 to help other people how
would you spend it?
The one activity I remember most from 5th grade
37.
math is…
36.
38. My fifth grade teachers would describe me as…
39. My parents would describe me as….
40. My best friend would describe me as…
If you had to pick an age to be for your entire life and
never grow older, what age would you pick?
If I had to pick one new nickname for everyone to
42.
call me, it would be…
What are you most proud of having accomplished in
43.
the past year?
41.
44. What is the hardest thing about growing up?
45.
46.
47.
48.
49.
What was the luckiest thing that ever happened to
you?
If you had to eat only one food for the entire next
week, what would it be?
You get to invite five famous people, dead or alive,
to come eat dinner with you. Who do you choose?
If you could grow up to be famous and successful,
what would you like to be known for?
If you could appear on any TV show (past or
present), what show would you pick?
Activity 1-2
NAME:
Newspaper Scavenger Hunt
On your poster board you must include the following:
1. The item number and the description of the item included on this page plus the newspaper cutout.
2. Box each item so that it is separate and easy to identify.
3. In the "Found" column, check the items you have included.
4. Your grade is the total points for all correctly identified items on your construction paper.
5. The maximum number of points you may earn is 110.
6. You may only include ONE of each item and one cut-out may not count for more than one item.
7. Turn this page into the tray after you have completed your work.
Place all on same side of construction paper
7 points
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A circle graph
An item with 2 different prices
A metric unit of weight
A metric unit of length
A percentage using a fraction
An octagon
A top 5 or 10 list
A ratio
A mixed number
A number written in words
A metric unit of volume
A hexagon
A temperature in Celsius
An address and phone number
A line graph
A real estate ad with prices
A percent using a decimal
A negative number
A decimal as money
A blueprint or floor plans of a building
Place all on the other side of construction paper
FOUND
4 points
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A pentagon
A baseball batting average
A baseball team's winning average (decimal)
Sale date (beginning and ending)
A bar graph
A date in numbers
A restaurant ad with prices
A number between 100 and 1000
A number greater than 10,000
A temperature in degrees
Time
A stock price with the company name or symbol
A coupon
A percent using a whole number
A decimal NOT as money
A fraction
A triangle
A circle
A rectangle
Picture of jewelry stating the total weight in carats
FOUND
Activity 1-3
Griswold Vacation Self-Evaluation
NAME:
1. Explain your main role for this project.
2. List three EDUCATIONAL, MATH RELATED things you learned from this project.
3. Your team is assigned 100 points. Divide up these points based on the amount of work each
person did, in your opinion.
4. Tell me any additional information you need to (you stayed late several times, someone
constantly goofed off, etc.)
Activity 1-4
Place Value: Find your partner!
NAME:
eight million,
eight thousand,
eight hundred
80 million,
800 thousand,
800
80,800,800
eighty million,
eighty thousand,
eight hundred
80,080,800
8,000,000
+
80,000
+
800
eight million,
80 thousand,
800
80 million,
80 thousand,
800
80,000,000
+
80,000
+
800
8 million,
8 thousand,
80
8,000,000
+
8,000
+
80
eighty million,
eight thousand,
eight hundred
80,008,800
eighty million,
eight hundred
thousand,
eighty
80,000,000
+
800,000
+
80
8,000,000
+
800,000
+
800
8 million,
800 thousand,
800
8,080,080
eight million,
eighty thousand,
eighty
8,800,080
eight million,
eight hundred
thousand,
eighty
80,000,000
+
8,000
+
80
80 million,
8 thousand,
80
800,008,080
eight hundred
million,
eight thousand,
eighty
800,080,800
eight hundred
million,
eighty thousand,
eight hundred
8,008,800
Activity 1-5
Write each rational number in the form
2. 2
1. 0.3
________________
5. 1
3
4
________________
NAME:
Rational Numbers
a
, where a and b are integers.
b
7
8
________________
6. 4.5
________________
3. 5
________________
7. 3
________________
4. 16
________________
8. 0.11
________________
Place each number in the correct place on the Venn diagram.
Then list all the sets of numbers to which each number belongs.
9. 13 ____________________________________________________________________________________
10.
1
_____________________________________________________________________________________
6
11. 0 ______________________________________________________________________________________
12. 0.99 ___________________________________________________________________________________
13. 6.7 ___________________________________________________________________________________
14. 34 _____________________________________________________________________________________
15. 14
1
_________________________________________________________________________________
2
Activity 1-6
Whole Numbers, Decimals, and Place Value
NAME:
Materials: Numbers 0-9 cut out separately, a dot on the desk to use as a decimal.
WHOLE NUMBERS
How many digits do you have?
Create an even number using all 10 digits. Ask the place value of the first and last digit. Put your
finger on the ten thousands digits. Make sure it is odd.
Where is the units place? What is a unit? What is another name for the units place?
Put your finger on the hundreds place. It must be a factor (or multiple) of 3 (or any number).
[Review other whole number place values].
WHOLE NUMBER PLACE VALUE CHALLENGES (one person)
1. Create the a. largest
b. 4-digit number
c. without consecutive digits next to each other
2. Create the a. smallest
b. 4-digit number
c. without consecutive digits next to each other
3. Create the a. largest
b. 8-digit
c. odd number
d. first three digits are not in descending order
e. product of the digits is 0
f. one-fourth of the digits are between 1 and 4
4. Create the a. largest
b. 10-digit number
c. odd number
d. multiple of 5
5. Create the a. smallest
b. 10-digit number
c. without consecutive digits next to each other
WHOLE NUMBER PLACE VALUE CHALLENGES (combine with a partner)
1. Create the a. largest
b. 4-digit number
c. without the digit 8
d. which would round to 8000 if rounded to the nearest thousand
2. Create the a. smallest
b. 4-digit number
c. even number
d. which would round to 1000 if rounded to the nearest thousand
3. Create the a. smallest
4.
5.
6.
7.
8.
9.
b. odd
c. 9-digit number
d. not a multiple of 5
e. only one-third of the digits are factors of 6
f. contains the largest even digit
Create the smallest 5-digit even number
Create the largest 6-digit odd number
Create the smallest 6-digit multiple of 10
Create the largest 7-digit multiple of 5
Create the closest number to half a million
Create the smallest 9-digit number with more than 50% of its digits odd
DECIMALS
Now use the dot on your desk as a decimal point.
Make a 10 digit number with 5 digits to the right of the decimal point and 5 digits to the left of the
decimal point. Place your finger on the tenths and make sure it is a factor of 2. Who at your table
has the largest number? Take away the 5 digits to the left of the decimal. Who at your table has the
largest decimal? (Go over the symbols <, >, =) [Review other decimal place values].
DECIMAL PLACE VALUE CHALLENGES (one person)
1. Create the a. smallest decimal using any number of digits you choose
2. Create the a. smallest decimal
b. using only the five odd digits
c. the hundredths place must contain a 9
3. Create the a. closest number to 400 that you can using all ten digits
4. Create the a. largest
b. 6 digit decimal
c. without consecutive digits next to each other
5. Create the a. closest decimal to 0.8
b. using the numbers 6-9
c. with 7 in the ten-thousandths place
NAME:
Place Value
Activity
The following chart demonstrates place value from the billions place down to the hundredthousandths place.
5
Billions
,
Whole Number Place Value
1
9 ,
, 3
8
4
6
Hundred
Millions
Ten
Millions
Millions
1
Ones
5
Tenths
Hundred
Thousands
Ten
Thousands
Decimal Place Value
3
7
2
Hundredths Thousandths
Thousands
2
0
8
Hundreds
Tens
Ones
8
TenHundredthousandths thousandths
How to read a number with a decimal in it:
Read the entire whole number part (without saying “and”). After the ones place, say “and.” Then,
read the number after the decimal as if it were a whole number. The last words are the place value
of the final digit.
Example: 82.0075
“Eighty-two AND seventy five ten-thousandths”
Activity 1-7
Distance from
Earth (miles)
1.
Sun
2.
Mercury
3.
Venus
4.
Moon
5.
Mars
6.
Jupiter
7.
Saturn
8.
Uranus
9.
Neptune
NAME:
Whole Numbers
Distance from Earth in words (miles)
Ninety-four million, four hundred eight thousand, twenty
158,241,250
One hundred sixteen million, seventy thousand, six hundred ninety-six
238,857
Two hundred thirty-five million, seven hundred sixty-two thousand, four
hundred forty
Five hundred sixty-five million, seven hundred thirty thousand, one
hundred sixty
Nine hundred thirty-five million, seven hundred seventy-six thousand,
three hundred twenty-three
1,826,710,650
Two billion, seven hundred forty million, two hundred fifty-three
thousand, seven hundred forty-two
Determine which object is further away. Below each object write its distance from Earth. Then fill in the
square with <, >, or = to make each sentence true.
10.
Moon
___________
12.
Neptune
___________
Sun
11.
___________
Pluto
___________
13.
Mars
Venus
___________
___________
Saturn
Jupiter
___________
___________
14.
Which planet is closest to Earth?
15.
Which planet is farthest from Earth?
16.
Which planets are more than one billion miles away from
Earth?
17.
Which planet is about half a billion miles from Earth?
Whole Number and Decimal Place Value
Activity 1-8
Start at…
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Finish at…
Charleston, West Virginia
Frankfort, Kentucky
Nashville, Tennessee
Raleigh, North Carolina
Columbia, South Carolina
Atlanta, Georgia
Tallahassee, Florida
Montgomery, Alabama
Jackson, Mississippi
Baton Rouge, Louisiana
Frankfort, Kentucky
Nashville, Tennessee
Raleigh, North Carolina
Columbia, South Carolina
Atlanta, Georgia
Tallahassee, Florida
Montgomery, Alabama
Jackson, Mississippi
Baton Rouge, Louisiana
Austin, Texas
NAME:
Gas used
(Gallons)
9.851
10.4
27.15
11.328
10.7
13.59
10.3605
12.25
8.006
21.4
Key
number
5
1
7
8
7
3
5
5
6
2
Find the key number in each amount of gasoline in the table. Write the place value of the digit (tenths,
hundredths, millions, etc.)
1. _________________
2. ___________________
3. _____________________
4. _________________
5. ___________________
6. _____________________
7. _________________
8. ___________________
9. _____________________
10. __________________
Gas used
(Gallons)
Gas used (Gallons) in words
Start at…
Finish at…
11.
Austin
Santa Fe
12.
Santa Fe
Denver
13.
Denver
Cheyenne
Five and five hundred forty-eight thousandths
14.
Cheyenne
Salt Lake City
Twenty-one and nine tenths
15.
Salt Lake City
Phoenix
35.47
16.
Phoenix
Carson City
36.8503
17.
Carson City
Sacramento
6.5
18.
Sacramento
Salem
26.751
19.
Salem
Olympia
Seven and two thousandths
20.
Olympia
Boise
Twenty-six and eighty-two hundredths
Thirty-seven and twenty-five hundredths
19.015
Activity 1-9
From New
York to…
Paris
London
Tokyo
Cairo
Sydney
Whole Number Addition and Subtraction
Round-trip
mileage
7,234
6,902
13,488
11,194
19,886
From New York
to…
Singapore
Toronto
Moscow
Buenos Aires
Hong Kong
Round-trip
mileage
19,054
708
9,326
10,586
16,106
NAME:
From New York
to…
Mexico City
Lima
Rio De Janeiro
Beijing
Round-trip
mileage
4,188
7,298
9,612
13,656
Note that the mileages listed are round-trip. Thus, they include traveling from New York to the city and then
back to New York. You decide to visit two cities during the summer – one in June and one in July. Calculate
your total round-trip miles from New York.
Two cities visited…
Total Mileage
1.
Paris and Toronto
2.
London and Cairo
3.
Mexico City and Toronto
4.
Beijing and Moscow
5.
Singapore and Rio De Janeiro
6.
Tokyo and Lima
7.
Hong Kong and Buenos Aires
8.
Paris and Singapore
9.
London and Moscow
Determine the difference in mileage between the following pairs of cities.
Two cities visited…
Difference in Mileage
10.
Paris and Sydney
11.
London and Cairo
12.
Mexico City and Toronto
13.
Beijing and Moscow
14.
Singapore and Rio De Janeiro
15.
Tokyo and Lima
16.
Hong Kong and Buenos Aires
17.
Mexico City and Lima
18.
Cairo and Hong Kong
19.
Which city is closest to New York City?
20.
Which city is about eight thousand miles from New York City?
Activity 1-10
NAME:
Whole Number Multiplication
Below are some distances between cities in the United States.
Total distance
Starting at…
Arriving at…
(miles)
Boston, Massachusetts
Providence, Rhode Island
49
Providence, Rhode Island
Hartford, Connecticut
86
Hartford, Connecticut
Trenton, New Jersey
176
Trenton, New Jersey
Dover, Delaware
111
Dover, Delaware
Annapolis, Maryland
67
Annapolis, Maryland
Richmond, Virginia
137
Richmond, Virginia
Charleston, West Virginia
314
Charleston, West Virginia
Frankfort, Kentucky
197
Frankfort, Kentucky
Nashville, Tennessee
208
Nashville, Tennessee
Raleigh, North Carolina
543
TOTAL ROUND TRIP USA DISTANCE (Austin to Austin)
14,165
Complete the table below using the information above.
Name of the Race
Number of cars
entered
1.
Dover-Annapolis Battle of the Buicks
8
2.
Hartford-Trenton Chase of the Chevys
3
3.
Nashville-Raleigh Pursuit of the Porshes
11
4.
Boston-Providence Contest of the Corollas
74
5.
Frankfort-Nashville Event of the Eclipses
30
6.
Richmond-Charleston Fight of the Ferraris
6
7.
Providence-Hartford Clash of the Camrys
5
8.
Trenton-Dover Brawl of the Beetles
20
9.
Austin-Austin War of the Winnebagos
12
10.
Annapolis-Richmond Drive of the Durangos
25
11.
Charleston-Frankfort Match of the Mustangs
10
12.
Dover-Annapolis Race of the Rams
16
13.
Hartford-Trenton Battle of the Buses
7
14.
Austin-Austin Lap of the Limousines
55
Total distance driven by
all cars (assuming they all
finish)
15.
In the total round trip (Austin-Austin) the number 4 represents what place value?
16.
The shortest race is between which two cities?
17. A race from Annapolis to Charleston via Richmond is exactly how many miles?
18.
Rounded to the nearest ten, how far is it from Hartford to Trenton?
19.
Rounded to the nearest thousand, how far is the Austin-Austin round trip?
Activity 1-11
NAME:
Whole Number Division
Mr. Underwood kept track on his gas mileage as he drove a wide variety of rental cars across the United
States. Complete the table by dividing. Write your answer as a whole number and a remainder (ex. 10 r6).
THIS SUMMER
Total
Average
Gallons of gas
Starting at…
Arriving at…
distance
miles per
used*
(miles)
gallon
1.
Austin, Texas
Santa Fe, New Mexico
745
22
2.
Cheyenne, Wyoming
Salt Lake City, Utah
439
8
3.
Salt Lake City, Utah
Phoenix, Arizona
708
34
4.
Carson City, Nevada
Helena, Montana
1911
9
5.
Denver, Colorado
Bismarck, North Dakota
4551
23
6.
Phoenix, Arizona
Pierre, South Dakota
3513
10
7.
Sacramento, California
Boise, Idaho
1230
5
8.
Austin, Texas
Austin, Texas
14,165
20
* Write your answer as a whole number and a remainder (ex. 10 r6) or as a decimal and round to the tenth
place.
9.
PROPOSAL WITH NEW CAR AND BETTER GAS MILEAGE
Total
Average
Starting at…
Arriving at…
distance
miles per
(miles)
gallon
Austin, Texas
Santa Fe, New Mexico
745
32
10.
Cheyenne, Wyoming
Salt Lake City, Utah
439
18
11.
Salt Lake City, Utah
Phoenix, Arizona
708
42
12.
Carson City, Nevada
Helena, Montana
1911
20
13.
Denver, Colorado
Bismarck, North Dakota
4551
30
14.
Phoenix, Arizona
Pierre, South Dakota
3513
26
15.
Sacramento, California
Boise, Idaho
1230
15
16.
Austin, Texas
Austin, Texas
14,165
35
Gallons of
gas used*
For the concluding exercise, use only the whole numbers from your answers above (forget about the
remainder!)
17. How many gallons could have been saved on the Austin-Santa Fe route?
18.
How many gallons could have been saved on the Carson City-Helena route?
19.
How many gallons could have been saved on the entire Austin-Austin route?
20.
Rounded to the nearest hundred, how far is it from Denver to Bismarck?
Is the Austin-Santa Fe trip or the Salt Lake City-Phoenix trip longer in
distance?
21.
NAME:
Decimal Addition
Activity 1-12
Your dad sat down to analyze the results of the recent road trip the family had made across America. Having
arrived at Walt Disney World too late to get on the rides, he needed to figure out how to make better time for
future travels. Dad concluded that the family had to make too many restroom stops along the way and that
kept slowing them down. Help your dad determine the sum of the drinks that the family had during various
parts of the trip.
Starting at…
Arriving at…
Pierre, South Dakota
Lincoln, Nebraska
Topeka, Kansas
Oklahoma City, Oklahoma
Little Rock, Arkansas
Jefferson City, Missouri
Des Moines, Iowa
St. Paul, Minnesota
Madison, Wisconsin
Springfield, Illinois
Lincoln, Nebraska
Topeka, Kansas
Oklahoma City, Oklahoma
Little Rock, Arkansas
Jefferson City, Missouri
Des Moines, Iowa
St. Paul, Minnesota
Madison, Wisconsin
Springfield, Illinois
Indianapolis, Indiana
Liters of Coke
consumed by
You
1.5
1.66
2.921
0.384
3.4
1
2.45
2.6
1.632
2.09
Route
Griswold family
members
1.
Lincoln-Topeka
Sister, Mom
2.
Pierre-Lincoln
You, Sister
3.
Oklahoma City-Little Rock
You, Mom
4.
Topeka-Oklahoma City
Sister, Mom
5.
Little Rock-Jefferson City
You, Sister
6.
Des Moines-St. Paul
You, Sister, Mom
7.
Jefferson City-Des Moines
Sister, Mom
8.
Madison-Springfield
You, Sister, Mom
9.
St. Paul-Madison
You, Sister
10.
Springfield-Indianapolis
You, Mom
11.
Lincoln-Topeka
You, Sister
12.
Pierre-Lincoln
Sister, Mom
13.
Oklahoma City-Little Rock
Sister, Mom
14.
Topeka-Oklahoma City
You, Sister, Mom
15. Who drank the most amount of Coke between Lincoln and Topeka?
16. Who drank the least amount of Coke between Des Moines and St. Paul?
Place the three family members in order from greatest to least based on
17.
the amount they drank on the Springfield to Indianapolis route.
Liters of Coke
consumed by
Sister
2.135
1.9
1.47
2
1.82
2.787
2.18
1.368
2
1.077
Liters of Coke
consumed by
Mom
3.82
1
2.4
1.688
2.333
1.5
2.21
3
0.3
1.44
Total amount of
Coke consumed
(liters)
NAME:
Decimal Subtraction
Activity 1-13
Mom and Dad love to eat Little Debbies after every meal. Their favorites are the Swiss Cake Rolls and the
Brownies. You and your sister also enjoy Little Debbies, however your favorites are the Nutty Bars and the
Donut Sticks. With so much time in the car to eat and not much exercise on the big trip, each family member
gained a little weight before the return to Austin. Use the following table to determine the differences in
weight.
When the family arrived
at….
Indianapolis, Indiana
Lansing, Michigan
Columbus, Ohio
Harrisburg, Pennsylvania
Albany, New York
Montpelier, Vermont
Augusta, Maine
Concord, New Hampshire
Boston, Massachusetts
Dad’s weight
(lbs.)
208.3
209.15
210.37
213
214.6
216.813
218
218.99
219.463
Your weight
(lbs.)
142
143.63
144.7
145.123
146
147.88
148.5
149
150.23
Sister’s
weight (lbs.)
98.27
99.458
100
100.7
101.562
102
103.11
103.8
104.63
1.
Indianapolis, Indiana
What is the difference in weight
between…
Dad, Mom
2.
Lansing, Michigan
Dad, You
3.
Columbus, Ohio
You, Mom
4.
Harrisburg. Pennsylvania
Mom, Sister
5.
Albany, New York
You, Sister
6.
Montpelier, Vermont
Dad, Mom
7.
Augusta, Maine
You, Mom
8.
Concord, New Hampshire
Dad, Sister
9.
Boston, Massachusetts
Sister, Mom
10.
Columbus, Ohio
Dad, Sister
11.
Harrisburg, Pennsylvania
Dad, You
12.
Albany, New York
Dad, Mom
13.
Montpelier, Vermont
You, Sister
At this city…
14.
15.
16.
17.
18.
19.
Augusta, Maine
Dad, Sister
On the trip from Concord to Boston which Griswold gained the most
weight?
On the trip from Indianapolis to Lansing which Griswold gained the
least weight?
List the Griswolds in order of weight from greatest to least.
Your dad’s goal when he leaves Boston is to get back to his weight in
Indianapolis. How many pounds does he need to lose?
Your sister’s goal when she leaves Boston is to get back to her weight
in Indianapolis. How many pounds does she need to lose?
Mom’s
weight (lbs.)
118
119.1
119.789
120.42
120.4
121
121.213
122.5
122.77
Weight Difference
(lbs.)
NAME:
Decimal Multiplication
Activity 1-14
One day Dad and Mom were going for a ride in Dad’s new car. Dad was trying to pull out of the driveway
when he accidentally put the car in drive instead of reverse. The car went straight into the tree in the
backyard. As the tree fell over, Dad watched in shock not only as his new car was totaled, but that oil seemed
to be spurting up from the ground! Immediately Dad thought finding new oil might lower gas prices
throughout the entire nation. Based on your Dad’s dream that gas prices could drop by a dollar a gallon,
below is revised trip information.
Start at…
Finish at…
Carson City, Nevada
Sacramento, California
Salem, Oregon
Olympia, Washington
Boise, Idaho
Helena, Montana
Bismarck, North Dakota
Concord, New Hampshire
Boston, Massachusetts
Providence, Rhode Island
Sacramento, California
Salem, Oregon
Olympia, Washington
Boise, Idaho
Helena, Montana
Bismarck, North Dakota
Pierre, South Dakota
Boston, Massachusetts
Providence, Rhode Island
Hartford, Connecticut
Gas used
(gallons)
6
27
8
26
28
33
11
3.4
2.5
4.3
Cost of Gas
($ per gallon)
$2.35
$2.20
$2.24
$2.50
$2.45
$2.25
$2.30
$2.40
$2.37
$2.28
Complete the table below based on the information above.
Start at…
Finish at…
1.
Carson City, Nevada
Sacramento, California
2.
Sacramento, California
Salem, Oregon
3.
Salem, Oregon
Olympia, Washington
4.
Olympia, Washington
Boise, Idaho
5.
Boise, Idaho
Helena, Montana
6.
Helena, Montana
Bismarck, North Dakota
7.
Bismarck, North Dakota
Pierre, South Dakota
8.
Concord, New Hampshire
Boston, Massachusetts
9.
Boston, Massachusetts
Providence, Rhode Island
10.
Providence, Rhode Island
Hartford, Connecticut
11.
Which segment of the trip had the most expensive gasoline per gallon?
12.
Which segment of the trip had the least expensive gasoline per gallon?
If six cars drove from Boise to Helena (for a total of 168 gallons of gas)
how much did they spend total on gas?
If 70 cars drove from Boston to Providence, how much gasoline would
be used?
For each trip segment list how much 100 gallons of gas would cost.
13.
14.
15.
Total cost of
gasoline
NAME:
Decimal Division
Activity 1-15
You were beginning to get bored now that you were back at home after the best vacation ever. You happen to
discover a sales receipt from a 7-11 that the family stopped at in Tallahassee, Florida. Although the prices of
the food and drinks are all over the place you wonder what the price is per serving. That way you could tell
how expensive things are on a relative basis. Although you do not have the boxes to say exactly how many
servings there were per container you make your best guess. Determine each price per serving.
Food/Drink Item
Store Price
1.
Swiss Cake Rolls
$1.20
Estimated
Servings
6
2.
Ranch Doritos
$3.00
12
3.
Honey Nut Cheerios
$3.80
10
4.
Milky Way Candy Bar
$0.90
2
5.
12 pack of A&W Root Beer
$2.46
12
6.
Ruffles Barbeque Potato Chips
$1.80
8
7.
Big Red Bubble Gum
$0.50
10
8.
Super Big Gulp
$0.99
6
9.
Tic Tac’s
$0.48
40
10.
Coca-Cola Slurpee
$0.79
2
11.
Large bag of peanuts
$5.04
14
12.
Cost per
serving
Skittles
$0.65
2
Place the 12 items above in order from least to greatest based on their STORE PRICE.
13.
Place the 12 items above in order from least to greatest based on their COST PER SERVING.
14.
If you were buying snacks for the car, which food item would you say is the best value? Why?
15.
Is the Super Big Gulp, Slurpee, or 12 pack of Root Beer a better deal? Why?
16.
NAME:
Dividing Decimals by Decimals
Activity 1-16
Find each quotient.
1. 9.5 142.5
2. 3 39.6
________________________
4. 10.5  1.5
3. 2 10.88
________________________
5. 9.75  1.3
________________________
_________________
6. 37.5  2.5
________________________
_________________
Estimate each quotient to the nearest whole number. Then, find the
actual quotient.
7. 2.5 36
8.
Estimate:
Exact Quotient:
____________
_________________
5.45  0.5
Estimate:
____________
Exact Quotient:
_________________
Compare using , , or  without calculating the quotient.
9. 0.35 0.78
 0.35 7.8
10. 1.2 34
 0.12 3.4
Solve.
11. A geologist noticed that land along a fault line moved 24.8 centimeters
over the past 175 years. On average, how much did the land move each
year?
________________________________________________________________________________________
Solve.
12. Acme Hardware is introducing a new product called Greener Cleaner.
Complete the table by finding the cost per milliliter for each size based on
the sales price. One liter is 1,000 milliliters.
Amount
of Liquid
Sale Price
Small
250 milliliters
$4.50
Medium
500 milliliters
$9.95
1 liter
$16.95
Size
Large
Price
per Milliliter
a. What is the least expensive and most expensive ways to buy 1,500 milliliters
of Green Cleaner? ____________________________________________
Activity 1-17
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Word Problems with Decimals
NAME:
Jeff had $120.73 in his bank account. He wrote a check for $78.32 for two
new tires. How much money is left in his account?
Subtract ninety-two and seven tenths from two hundred forty-eight and
forty-six thousandths.
If the US produced 1.824 million bushels of soybeans one year and 1.966
million bushels the following year. How much more did the US produce in
the second year?
Write the numbers six hundred eighty-three and twenty-three hundredths,
fifty-nine and one hundred eleven thousandths, two hundred fourteen and
seven tenths, and six thousand two. Find the sum.
Write the following sums of money in the form of decimals and find the
sum. $2 and 3 cents, $26 and 8 dimes, 26 cents, $15, and 7 cents.
The largest cockroach ordered from Roasted Cockroaches was 5.1 cm. long.
The shortest is 3.99 cm. long. What is their total length?
If buy a triple-decker burger, Roasted Roaches and a Cricket Cola separately
it cost $4.27. The Super Sac Meal Deal with these same items is only $3.99.
How much do you save by buying the Meal Deal?
When you fill your gas tank, the odometer read 2529.7. The next time you
filled the tank, the odometer read 2760.1. How many miles did you travel?
The cost of 12 gallons of gas is $14.28. How much would you pay per
gallon?
Your car travels an average of 19.7 miles per gallon in the city and 23.8
miles per gallon on the highway. On an 11-gallon tank of gas how much
farther can you travel on the highway than in the city?
A big company used 2.86 million sheets of paper for correspondence last
year and 3.1 million this year. By how many million sheets of paper did
their correspondence grow in one year?
A seed company sold 7.126 million packets of seeds last year and 8.4 million
packets this year. How many more packets did they sell this year?
Subtract eighty and five tenths from one hundred thirty and fifty-two
thousandths.
Find the sum of three thousand forty-two and seven tenths, three hundred
forty-two and seventeen hundredths, thirty-four and two hundred seventeen
thousandths, and three and four thousand two hundred seventeen tenthousandths.
Brian worked four days last week doing odd jobs. He earned $4.50, $5.75,
$6.50, and $6.10. How much did Brian earn last week?
Your dad spends $14.39 at McMealworms and your sister spends another
$4.99. What is their total cost?
You find once cockroach that weighs .321 grams and another that weighs .4
grams. What is the difference in their weights?
Your car gets about 19.8 miles to the gallon. If you buy 12 gallons of gas,
how many miles can you expect to drive?
You took a car trip that was exactly 496.8 miles. The trip took 9 hours.
What was your average speed per hour?
Rounding
Activity 1-18
Number
Ten
6.43
17.19
43.751
0.5059
6.6666
37.3274
354.9009
$7.752
30.07777
$99.909
$99.099
592.5
192.354009
7.98
15.20072
0.48649
0.00772
816.63451
$5.375
789
654
61.75
3.1736404
28.2525252
NAME:
Rounded to the nearest…
One/Unit
Tenth
Hundredth
Thousandth
Activity 1-19
Really Big Numbers!
NAME:
Everyone has heard of the website Google, right? Well, how did they come up with the name
“Google’?
Google is a play on the word googol, which was coined by Milton Sirotta, nephew of American
mathematician Edward Kasner, and was popularized in the book, "Mathematics and the
Imagination" by Kasner and James Newman. It refers to the number represented by the numeral 1
followed by 100 zeros. Google's use of the term reflects the company's mission to organize the
immense, seemingly infinite amount of information available on the web.
So a googol is:
10000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000
So what about a googolplex? A googolplex is much bigger than a googol, much bigger than a
googol times a googol. A googol times a googol would be 1 with 200 zeros, but a googolplex is 1
with a googol of zeros. Can you imagine how big that is? Think you can write it down? If you
wrote 1 zero every inch there would not be enough room to write this number if you went to the
farthest star in the universe. Your homework tonight is to start writing a googolplex. 
So what are some other large numbers?
Thousand
1 with 3 zeros
Million
1 with 6 zeros
Billion
1 with 9 zeros
Trillion
1 with 12 zeros
Quadrillion, then Quintillion, Sextillion, Septillion, Octillion, Nontillion, Decillion, Undecillion,
and a Duodecillion would be 1 with 39 zeros
Continuing
Tredecillion
Quattuordecillion
Quidecillion
Sexdecillion
Septendecillion
Octadecillion
Novemdecillion
Vigintillion
Unvigintillion
Duovigintillion
Trevigintillion
Quattuorvigintillion
42 zeros
45 zeros
48 zeros
51 zeros
54 zeros
57 zeros
60 zeros
63 zeros
66 zeros
69 zeros
72 zeros
75 zeros
Q: On what day will you celebrate having been alive for one billion seconds? How old will you be?
Activity
NAME:
Squares and Square Roots
Using centimeter cubes create the following squares. Then count the number of cubes necessary to
create each square.
Square
1 by 1
2 by 2
3 by 3
4 by 4
5 by 5
6 by 6
7 by 7
8 by 8
9 by 9
10 by 10
11 by 11
12 by 12
x by x
Number of cubes
3 by 3 = 3 x 3 = 3  3 = 32 = 9
exponent
Three squared equals 9.
9 3
This is a radical sign. It represents a square root. Square root is the opposite operation of square.
What number times what same number equals nine? Three. Thus, the square root of 9 is 3.
NAME:
Squares and Square Roots
Activity 1-20
You are finding the square of a number when you multiply a number by itself.
Examples
4  4 = 42 = 16
6  6 = 62 = 36
If a2 = b, then a is the square root of b. The symbol,
called a radical sign, is used to represent
a square root. Read 16 as “the square root of 16.”
Examples
a. Find 9
Since 32 = 9,
9 = 3.
b. Find
Find the square of each number.
1.
92
2.
302
64 Since 82 = 64,
3.
42
4.
102
5.
152
6.
402
7.
82
8.
112
9.
1002
10.
242
Find each square root.
11.
4
12.
169
13.
196
14.
64
15.
16.
225
17.
16
18.
1
36
19.
2500
20.
121
21.
3600
22.
144
23.
400
24.
100
Solve.
25.
52
30.
26.
27.
17
900
31.
32.
28.
1024
222
33.
1225
452
576
312
34.
729
29.
2
64 = 8.
Activity
Order of Operations
NAME:
Mathematical operations follow a logical order. This order is not always from left to right, but
instead is based on giving importance to certain operations. The following displays the correct order
of operations:
P
E
MD
AS
parentheses
exponents
multiplication/division – whichever comes first
addition/subtraction – whichever comes first
PEMDAS is frequently remembered using the phrase, “Please excuse my dear aunt, Sally.”
The order of operations can be used to solve problems one-step at a time by creating a funnel.
(8 + 9)  4 + 12 - 82
17  4 + 12 - 82
17  4 + 12 – 64
68 + 12 – 64
80 – 64
16
(12 + 15)  3 – 4 + 52
27  3 – 4 + 52
27  3 – 4 + 25
9 – 4 + 25
5 + 25
30
Activity 1-21
NAME:
Order of Operations
Fill in the blanks.
According to the order of operations, all operations that appear within ________________
1.
should be performed first.
2.
According to the order of operations, all ______________ should be solved second.
3.
Third, divide and ____________ from left to right.
4.
Fourth, add and ____________ from left to right.
In an expression that involves a division operation and an addition operation, the
____________ operation should be performed first.
In an expression that involves a subtraction operation and a multiplication operation, the
____________ operation should be performed first.
5.
6.
True or false.
7. Always add before you subtract.
8. Always start with parentheses.
9. Always multiply before you divide.
10. Always go left to right.
Circle the operation that should be performed first in each expression.
11.
(9 + 3)  7
12.
98 – 5  7
13.
5  (9 – 1)
14.
(15  3) + (4 + 5)
5 42
15.
5(5 – 3)  2
16.
Evaluate each expression.
17. 2  9 + 5  3
18.
(9 – 4)  5
19.
10 – 4 + 1
20.
15 – 18  9 + 3
21.
30  (12 – 6) + 4
22.
(72 – 12)  2
23.
2(16 – 9) – (5 + 1)
24.
(43 – 23) – 2  5
25.
90 – 45 – 24  2
26.
81  (13 – 4)
27.
7  8–2  8
28.
71 + (34 – 34)
29.
5 + 42  3 - 32
30.
8  3 + 22 – 1
31.
8  32 + 72 – 2
Insert parentheses to make each statement true.
32. 32 + 8  3  4 = 30
33. 15 – 3  1  6 = 2
34. 88  22 + 8  3 = 4
35. 18  3 + 3 – 2 = 1
36. 16 – 8  4 + 10 = 12
37. 5  5 + 5 – 5 = 45
38. 6 + 6  6  6 = 42
39. 200 – 90 + 80 + 20 = 10
Change one of the operational symbols in the expression below so that the value of the expression is
multiplied by 4.
81-12-13-14-15-17
NAME:
Order of Operations
Activity 1-22
Circle the operation that should be performed first in each expression.
1.
5+4  7
2.
13(6 + 3)
3.
(4 – 2) + 6
(6  8)  4
4.
5.
32  4  2
9(4 + 2)  3
6.
Evaluate each expression.
7. 8  7 + 8  3
8. (12 – 3)  3 2
9. 8 – 6 + 3
10. 18  3  6
11. (34 + 46)  20 + 20
12. 9  3 + 8  4
13. 10 2  3 + 1
14. 23 – 45  9 + 5
15. 10 + 9 2  3 – 4
17. 1 + 3  4 + 5 - 32
18. 42  3 + 3  2
20. (12 – 9)  (6 + 1)
21. 85 – 5  42
16.
52 – 12 + 84  3
19. 7  (8 + 6)
Compare. Use, <, >, or = to make each statement true.
22. 5 – 3  1
24. 3  (8 – 2)
26. 4 + (20  4)
(5 – 3)  1
23. (4 + 8)  3
4+8  3
3  8–2
25. (7 + 2)  4
7+2  4
(4 + 20)  4
28. (9 – 2)  3
9–2+3
Solve.
30. 132
31. 262
27. 42 – (35 + 4)
32.
42 – 35 + 4
29. 55 + 10 – 7
55 + (10 -7)
961
529
33.
Place parentheses to make each statement true.
34. 12  3  2 = 2
35. 6  8 + 3  2 = 33
36. 7 + 8  2 = 23
37. 5  8 – 4  2 = 38
38. 11 + 5  2  2 = 4
39. 30  5 + 1  3 = 15
40. 24  4  6  12 = 3
41. 5 + 5  5 – 28  4  7 = 1
42. Using parentheses and any operations you wish (+, - ,  ,  ), make equations that equal 0
through 11.
8
4
2
1 =0
8
4
2
1 =1
8
4
2
1 =2
8
4
2
1 =3
8
4
2
1 =4
8
4
2
1 =5
8
4
2
1 =6
8
4
2
1 =7
8
4
2
1 =8
8
4
2
1 =9
8
4
2 1 = 10
8
4
2
1 = 11
Activity 1-23
Order of Operations
NAME:
For each PEMDAS story below, write the correct mathematical expression. Include parentheses as
needed in order to follow the order of operations.
1. Mr. Underwood’s IQ – What is Mr.
Underwood’s IQ now?
One day Mr. Underwood found out that his IQ was
only 20. That made him feel sad. He went to the
library and studied for a few hours and raised his IQ
by 12 points. As he was walking out library aliens
abducted him and stole half of his brain and then they
put him back on Earth (so he only knew half the stuff
he knew before). Then he babysat for his little niece
and learned a lot from the baby lowering his IQ by 6
points. Next he went to a math convention where 3
speakers each raised his IQ by 3 points.
3. The Toilet Weepers –
How many total people are at Dairy Queen?
Thirty people worked at the plumber service.
Twelve of them were laid off so there were eighteen
employees left. They got a phone call from 1980
Maple Street were the toilet had flooded. In the
office, their boss said to split up into two equal
groups – one to go to the house while the other group
could go to Dairy Queen. In the Dairy Queen group,
two employees left because they were mad. When
the rest of the group arrived at Dairy Queen, they
saw five tables each with five people sitting at them.
5. Sour Chocolate Camp – How many licorice bags
did they have when they woke up?
There were eight M&M people at Chocolate Camp.
There were nine Sour Skittle people at Sour Camp.
The two camps joined together and called the camp
Sour Chocolate Camp. Each person had four bags of
Black Licorice. The camp counselor had twelve
extra bags of Black Licorice. Eight lollipop people
came to Sour Chocolate Camp while everyone was
sleeping and stole eight bags each. When all of the
people woke up they were very mad so they turned
into pink Leprechauns and swam into the rainbow
until next summer.
7. Apples – How many apples were left?
There were nine apples and Hillbilly Bob ate eight of
them. There was only one apple left. Bob ran into a
apple tree and knocked off tons of apples. In fact,
Bob realized he now had forty times as many apples.
Bob’s son, Bob Jr., then ran into the same tree and
seventeen more apples fell. Next, six more of Bob’s
relatives arrived and they each ate six apples.
2. Mr. Monkey’s Teeth – How many monkeys
were in the room?
One day Monkey Mel went to the dentist. There
were 35 more monkeys in the waiting room that
needed to get their teeth cleaned. The dentist split
the monkeys into two even groups. In Mel’s
group, three groups of three monkeys got their
teeth cleaned and left. The dentist found that Mel
had a big cavity so he called 72 more monkeys to
help out. One of the monkeys got scared from the
size of cavity that she ran away. If you happen to
see Monkey Mel call 1-800-ISAWMEL.
4. Ants at the Picnic –
How many ants are left at the picnic?
Shelby and Emily were at a picnic. All of a
sudden, they saw a hundred ants. They got so
scared that they stepped on twenty of the ants.
The ants then got so scared that they scattered into
five equal groups of which only one stayed at the
picnic. Then their friend Kristen ran up to us and
accidentally stepped on seven of the ants. Since
ants have a good sense of smell, three groups of
three ants each then came to join the ones that
were left at the picnic.
6. Fruit Football Players –
How many players are on the Seeds?
There were nine grapefruits that went grocery
shopping. They decided to get nineteen bananas.
When they got home, they found out there were
twenty-eight fruits in all. They split into two even
teams to play football, the Seeds and the Peels.
On the Seeds one banana got split and died so he
was off the team. Two kiwis came over and got
cloned by the angry Seeds who were now losing
the game. Since there were now four kiwis they
decided to join the Seeds football team. In the
end the Seeds won and they were all very happy.
8. SpongeBob –
How many cooked patties are there?
SpongeBob made forty patties and twelve of them
were eaten. He then divided the remaining patties
into two groups and cooked one of the groups.
With the cooked patties, SpongeBob gave six to
Patrick. Then six friends came by and each of
them brought six cooked patties.
Problems #9-#16 on the back
9. The Skydiving Massacre –
How many skydivers were there in the end?
There were two planes. One plane had 10 people.
The other plane has 12 people. The groups of
skydivers jumped out of the planes and formed one
big group. They formed a circle by holding hands.
One of the people’s hands slipped and as a result
one-half of the skydivers went flying away from the
group. Birds starting pecking at the remaining
skydivers and eight more people went flying away
from the group. Soon four more groups of 4
skydivers joined the remaining few to make one big
group.
11. The Hiccup Birthday Party –
How many kids are at the movies without the
hiccups?
Once there was a little boy named Mr. Underwood.
He and eleven little friends were celebrating Mr.
Underwood’s birthday! Then fifteen more little
friends showed up for the party. The kids were split
into three cars Mr. Underwood’s group drove to the
movies while the others went home. In Mr.
Underwood’s car, four of the kids got the hiccups.
When his car got to the movies there were five
groups of five kids waiting to celebrate with him.
13. Mr. Underwood’s Cats –
How many cats are at Daisy’s bowl of food?
Mr. Underwood had eleven cats. He decided to
adopt thirteen more cats because he loved them so
much. His favorite cat in the whole wide world was
Daisy. With six bowls of cat food, the cats divided
up evenly to eat dinner. At Daisy’s bowl one of the
cats ran away and Mr. Underwood was so sad. Mr.
Underwood looked everywhere for the missing cat
and while he was looking seven groups of seven cats
each all tried to join in at Daisy’s bowl of food.
15. The High and the Odd –
How many animals are in group A?
There once was a group of 32 flying cows. They
soon met 16 flying pigs. Then the group of 48 odd
flying animals divided into 12 equal groups for a
flying obstacle course. Now there are 4 animals in a
group. In group A, sadly one of the flying cows got
airsick. Surprisingly, four groups of four flying
monkeys came to join team A so that they could
increase their total of very odd flying animals.
10. Dem Bones –
How many bones did the puppies have?
Four puppies were playing hide and go seek.
Nine more puppies came to play with them. Each
puppy was carrying four delicious bones. Some
of the puppies were goofing off when they found
twenty more bones that were hidden in the
ground. The puppies were now very happy. Then
three mean dogs came by and took three bones
each. That didn’t bother the puppies too much
though and then spent the rest of the day playing
with their bones.
12. The Race –
How many horses are in Race #1?
There are seven horses in the race. Fourteen more
horses came to join the race. Since there were so
many, the horses divided into three equal groups
to run three races. In race #1, a horse named
Dodger hurt his leg so he was not able to
participate in the race. At the last moment, two
owners entered two horses each in race #1.
14. The Baked Cookies –
How many cookies were left in the end?
Mallory baked two cookies. Then she cooked
three more cookies. She decided she needed more
so she ended up with ten times her original total of
cookies. Mallory’s friend, Jennifer, then brought
over 25 more cookies. Mallory and Jennifer
invited over six friends and each friend ate six of
the cookies.
16. The Mudball Team –
How many mudballs were left?
Five small pigs were going to play Mudball.
Twelve other pigs saw them playing and joined in.
Now there were 17 pigs. Each pig had 5
mudballs. Mrs. Pig showed up and brought
eleven more mudballs. Then, mean Mr. Pig and
his seven friends showed up and each took away
eight mudballs. With the remaining mudballs, the
pigs jumped in the mud and played until dark.
Activity 1-24
WRITING A PEMDAS STORY
NAME:
Work either individually or in pairs
1. The expression below has been created using the following elements:
 Addition
 Subtraction
 Multiplication
 Division
 A set of parenthesis
 An exponent
___________________________________________________________
2. Simplify your expression on a separate sheet of paper. Show in order all of the steps that you
used to simplify.
3. Write your PEMDAS story. Your story MUST follow the order of operations as it applies to
your expression. You will translate each operation into a real-world situation. Make your story
as creative and fun as possible while following all mathematical rules.
SAMPLE PEMDAS STORY
(4 + 2)  2  4
Four friends were playing ball in the park. They were having a great day because it was the
weekend. Later, 2 more of their friends from their neighborhood joined them. Now there were 6
friends playing in the park. Another group of 6 kids saw the group of 6 playing and asked if they
could join to make 2 teams. Everyone agreed and now there were twice as many people playing;
this made the game more competitive. Everyone was out to win. The group stayed in the park long
after the game was over, just talking about their favorite topic.
As it was getting later, everyone was getting tire and hungry. When they were ready to go home, the
large group of 12 friends divided into 4 groups. Each group had the same number of people. This
way, 4 groups of 3 kids walked each other home.
Type your finished story on the computer. Copy your original problem below your story and solve
using the order of operations (tornado method).