COMPACTED MATHEMATICS: CHAPTER 3

INTEGERS IN SPORTS

TOPICS COVERED:

Introduction to integers

Opposite of a number and absolute value

Adding integers

Subtracting integers

Multiplying and dividing integers

Integer Labs

Survival Guide to Integers Project

Activity 3-1: Introduction to Integers Name:

The number line can be used to represent the set of integers. Look carefully at the number line

below and the definitions that follow.

Definitions

The number line goes on forever in both directions. This is indicated by the arrows.

Whole numbers greater than zero are called positive

integers. These numbers are to the right of zero on the

number line.

Whole numbers less than zero are called negative

integers. These numbers are to the left of zero on the

number line.

The integer zero is neutral. It is neither positive nor

negative.

The sign of an integer is either positive (+) or negative (-),

except zero, which has no sign.

Two integers are opposites if they are each the same

distance away from zero, but on opposite sides of the

number line. One will have a positive sign, the other a

negative sign. In the number line above, +3 and

-3 are

labeled as opposites.

Activity 3-2: Introduction to Integers Name:

Definitions:

Integers – the whole numbers and their opposites (positive counting numbers, negative counting

numbers, and zero)

Opposite of a number – a number and its opposite are the same distance from zero on the number

line

Example: 7 and 7 are opposites

Absolute value – the number of units a number is from zero on the number line without regard to

the direction

Example: the absolute value of 6 is 6

The sign for absolute value is two parallel lines: 6 = 6

1-10. Place the correct letter corresponding to each integer on the number line below.

Place the corresponding letter above the correct place in the number line below:

-10 0 +10

A. 5 B. 2 C. 7 D. 4 E. 9

F. 1 G. 6 H. 3 I. 0 J. 6

Write an integer to represent each situation.

11. lost $72 12. gained 8 yards 13. fell 16 degrees

Name the opposite of each integer.

14. 26 15. 83 16. 100

Compare the following integers. Write <, >, or =.

17. 5 ___ 8 18. 12 ___ 13 19. 10 ___ 21 20. 7 ___ 11

Find the absolute value of the following numbers.

21. 11 22. 6 23. 55 24. 0

25. 28 26. 203 27. 75 28. 3

Activity 3-3: Introduction to Integers Name:

1. List the following temperatures from greatest to least.

A The temperature was 25 degrees Fahrenheit below zero.

B The pool temperature was 78 degrees Fahrenheit.

C Water freezes at 32 degrees Fahrenheit.

D The low temperature in December is -3 degrees Fahrenheit.

E The temperature in the refrigerator was 34 degrees Fahrenheit.

Think of the days of the week as integers. Let today be 0, and let days in the past be negative

and days in the future be positive.

2. If today is Tuesday, what integer stands for last Sunday?

3. If today is Wednesday, what integer stands for next Saturday?

4. If today is Friday, what integer stands for last Saturday?

5. If today is Monday, what integer stands for next Monday?

Circle the number that is greater.

6. 4 or 13 7. 33 or 41 8. 0 or -4 9. 0 or 7

10. 2 or 4 11. 9 or 7 12. 5 or 5 13. 1 or 11

Write true or false.

14. 3 7 15. 9 1 16. 6 2

17. 5 5 18. 8 8 19. 5 6

Write an integer to represent each situation.

20. moving backwards 4 spaces on a game board

21. going up 3 flights in an elevator

22. a 5-point penalty in a game

23. a $1 increase in your allowance

Order from least to greatest.

24. {6, 3,1, 1, 5,7,0,9}

25. {2, 1,3,4, 6,13, 8,2}

Activity 3-4: History of Negative Numbers Name:

For a long time, negative solutions to problems were considered "false" because they couldn't be

found in the real world (in the sense that one cannot have a negative number of, for example,

seeds).

The abstract concept was recognized as early as 100BC – 50BC. The Chinese discussed methods

for finding the areas of figures; red rods were used to denote positive, black for negative. They

were able to solve equations involving negative numbers. At around the same time in ancient

India, sometime between 200BC and 200AD, they carried out calculations with negative numbers,

using a "+" as a negative sign. These are the earliest known uses of negative numbers.

In Egypt, Diophantus in the 3rd century AD referred to the equation equivalent to 4x + 20 = 0 (the

solution would be negative) in Arithmetica, saying that the equation was absurd, indicating that no

concept of negative numbers existed in the ancient Mediterranean.

During the 7th century, negative numbers were in use in India to represent debts. The Indian

mathematician Brahmagupta discusses the use of negative numbers. He also finds negative

solutions and gives rules regarding operations involving negative numbers and zero. He called

positive numbers "fortunes", zero a "cipher", and negative numbers a "debt".

From the 8th century, the Islamic world learnt about negative numbers from Arabic translations of

Brahmagupta's works, and by about 1000 AD, Arab mathematicians had realized the use of

negative numbers for debt.

Knowledge of negative numbers eventually reached Europe through Latin translations of Arabic

and Indian works.

European mathematicians however, for the most part, resisted the concept of negative numbers

until the 17th century, although Fibonacci allowed negative solutions in financial problems where

they could be interpreted as debits and later as losses. At the same time, the Chinese were

indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit.

The first use of negative numbers in a European work was by Chuquet during the 15th century. He

used them as exponents, but referred to them as “absurd numbers”.

The English mathematician Francis Maseres wrote in 1759 that negative numbers "darken the very

whole doctrines of the equations and make dark of the things which are in their nature excessively

obvious and simple". He came to the conclusion that negative numbers did not exist.

Negative numbers were not well-understood until modern times. As recently as the 18th century,

the Swiss mathematician Leonhard Euler believed that negative numbers were greater than

infinity, and it was common practice to ignore any negative results returned by equations on the

assumption that they were meaningless.

Taken from Wikipedia (en.wikipedia.org)

Activity 3-5: Adding Integers with Same Sign Name:

Find each sum. White counters are positive. Black counters are negative.

1. 5 3 2. 4 7

a. How many counters are there? _______ a. How many counters are there? ________

b. Do the counters represent positive b. Do the counters represent positive

or negative integers? _________________ or negative integers? _________________

c. 5 3 _________ c. 4 7 ________

Model each addition problem on the number line to find each sum.

3. 4 2 _______ 4. 5 5 _______

5. 3 6 _______ 6. 7 5 _______

Find each sum.

7. 7 1 _______ 8. 5 4 _______

9. 36 17 _______ 10. 51 42 _______

11. 98 126 _______ 12. 20 75 _______

13. 350 250 _______ 14. 110 1,200 _______

Solve.

15. A construction crew is digging a hole. On the first day, they dug a hole 3

feet deep. On the second day, they dug 2 more feet. On the third day,

they dug 4 more feet. Write a sum of negative numbers to represent this

situation. Find the total sum and explain how it is related to the problem.

________________________________________________________________________________________

Activity 3-6: Adding Integers with Same Sign Name:

Solve.

1. A grocery sells green apples and red apples. On Monday, the store put

500 of each kind of apple on display. That day, the store sold 42 red

apples and 57 green apples. On Tuesday, the store sold 87 red apples

and 75 green apples. On Wednesday, the store sold 29 red apples and

38 green apples.

a. Write an addition expression using negative integers to show the

number of red apples the store sold.

____________________________________________________________________________________

b. Write an addition expression using negative integers to show the

number of green apples the store sold.

____________________________________________________________________________________

c. Did the store have more red apples or green apples left over?

Explain.

____________________________________________________________________________________

____________________________________________________________________________________

2. A hotel has 18 floors. The hotel owner believes the number 13 is

unlucky. The first 12 floors are numbered from 1 to 12. Floor 13 is

numbered 14, and the remaining floors are numbered from 15 to 19. The

hotel manager starts on the top floor of the apartment building. He rides

the elevator two floors down. The doors open and a hotel guest gets in.

They ride the elevator three floors down. The hotel guest gets off the

elevator. The hotel manager rides the elevator the remaining floors

down to the first floor.

a. Write an addition expression using negative integers to show the

number of floors the hotel manager rode down in the elevator.

____________________________________________________________________________________

b. On what floor did the hotel guest get off the elevator? Explain.

____________________________________________________________________________________

____________________________________________________________________________________

Activity 3-7: Adding Integers with Same Sign Name:

Find each sum. White counters are positive. Black counters are

negative. The first one is done for you.

1. 5 2 2. 4 6

a. How many counters are there? _______ a. How many counters are there? _______

b. Do the counters represent positive b. Do the counters represent positive

or negative numbers? ______________ or negative numbers? _________________

c. 5 2 ______________ c. 4 6 _______

Model each addition problem on the number line to find each sum. The

first one is done for you.

3. 3 2 ________ 4. 5 1 ________

5. 4 3 ________ 6. 1 6 ________

Find each sum. The first one is done for you.

7. 3 1 ________ 8. 6 2 _______

9. 12 7 _______ 10. 20 15 _______

Solve.

11. The table shows how much money Hannah withdrew in 3 days.

Day Day 1 Day 2 Day 3

Dollars 5 1 2

Find the total amount Hannah withdrew. ___________________________

7

7

positive

4

5

Activity 3-8: Adding Integers with Different Signs Name:

Show the addition on the number line. Find the sum.

1. 2 (3) _________________ 2. 3 4 _________________

Find each sum.

3. 4 9 4. 7 (8) 5. 2 1 6. 6 (9)

_______________ _______________ _______________ ________________

7. 5 (7) 8. 9 (5) 9. (1) 9 10. 9 (7)

_______________ _______________ _______________ ________________

11. 50 (7) 12. 27 (6) 13. 1 (30) 14. 15 (25)

_______________ _______________ _______________ ________________

Solve.

15. The temperature outside dropped 13°F in 7 hours. The final temperature

was 2°F. What was the starting temperature?

________________________________________________________________________________________

16. A football team gains 8 yards in one play, then loses 5 yards in the next.

What is the team’s total yardage for the two plays?

________________________________________________________________________________________

17. Matt is playing a game. He gains 7 points, loses 10 points, gains

2 points, and then loses 8 points. What is his final score?

________________________________________________________________________________________

18. A stock gained 2 points on Monday, lost 5 points on Tuesday, lost

1 point on Wednesday, gained 4 points on Thursday, and lost 6 points

on Friday.

a. Was the net change for the week positive or negative? ___________________________

b. How much was the gain or loss? ___________________________

Activity 3-9: Adding Integers with Different Signs Name:

Tell whether each sum will be positive or negative. Then find

each sum.

1. 3 ( 7) 2. 14 (9) 3. 12 5 4. 3 8

_______________ _______________ _______________ ________________

5. 11 (5) 6. 7 8 7. 8 7 8. 2 3

_______________ _______________ _______________ ________________

9. If two integers have the same sign, what is the sign of their sum?

________________________________________________________________________________________

10. When adding two integers with different signs, how do you find the

sign?

________________________________________________________________________________________

Evaluate a b for the given values.

11. a 9, b 24 12. a 17, b 7 13. a 32, b 19

_______________________ ________________________ ________________________

14. a 15, b 15 15. a 20, b 20 16. a 30, b 12

_______________________ ________________________ ________________________

Solve.

17. The high temperature for the day dropped 7F between Monday and

Tuesday, rose 9F on Wednesday, dropped 2F on Thursday, and

dropped 5F on Friday. What was the total change in the daily high

temperature from Monday to Friday?

________________________________________________________________________________________

18. Karen deposited $25 in the bank on Monday, $50 on Wednesday and

$15 on Friday. On Saturday, she took out $40. Karen’s original balance

was $100. What is her balance now?

________________________________________________________________________________________

19. Lance and Rita were tied in a game. Then Lance got these scores:

19, 7, 3, 11, 5. Rita got these scores: 25, 9, 5, 9, 8. Who had the

higher score? How much higher was that higher score?

________________________________________________________________________________________

Activity 3-10: Adding Integers with Different Signs Name:

Show the addition on the number line. Then write the sum. The first

one is done for you.

1. 2 (3) 2. 3 (4)

_______________________________________ ________________________________________

Find each sum. The first one is done for you.

3. 4 (9) 4. 7 (8) 5. 2 1

_______________________ ________________________ ________________________

6. 5 7 7. 9 (5) 8. 1 9

_______________________ ________________________ ________________________

9. 2 (7) 10. 6 (4) 11. 15 9

_______________________ ________________________ ________________________

Solve. The first one is done for you.

12. The temperature dropped 12F in 8 hours. If the final temperature was

7°F, what was the starting temperature?

________________________________________________________________________________________

13. At 3 P.M., the temperature was 9F. By 11 P.M., it had dropped 31F.

What was the temperature at 11 P.M.?

________________________________________________________________________________________

14. A submarine submerged at a depth of 40 feet dives 57 feet more. What

is the new depth of the submarine?

________________________________________________________________________________________

15. An airplane cruising at 20,000 feet drops 2,500 feet in altitude. What is

the airplane’s new altitude?

________________________________________________________________________________________

1

5F

5

Activity 3-11: Addition of Integers Name:

Add or subtract.

1. 2 8 2. 8 4 3. 6 3

4. 6 4 5. 1 7 6. 8 3

7. 2 6 8. 6 9 9. 5 7

10. 4 7 11. 4 7 12. 4 7

13. 2 1 3 14. 0 5 15. 3 2 1

16. 5 5 17. 6 1 18. 6 1

Some of the sixth grade teachers decide to try out for the Dallas Cowboys. They each are allowed

one rushing attempt against the Cowboys defense. The table below summarizes the results of their

attempts:

Johnsen 8 Atkins 19 Hoag +18

Underwood +24 Loewen +2 Buckmaster 26

Snow 13 Mangham +37 Landry +6

Use the table above to answer the following addition problems.

19. Mangham + Buckmaster 20. Underwood + Johnsen

21. Snow + Atkins 22. Hoag + Landry

23. Atkins + Mangham 24. Snow + Landry

25. Loewen + Underwood 26. Johnsen + Buckmaster

27. Snow + Hoag 28. Landry + Johnsen

29. Underwood + Mangham 30. Atkins + Buckmaster

31. Hoag + Atkins + Snow 32. Hoag + Landry + Loewen

33. Buckmaster + Atkins 34. Johnsen + Hoag

35. Place the teachers in order from the worst

carry (smallest) to the best carry (largest).

Compare. Write <, >, or =.

36. 5 6_____ 6 5 37. 8 10_____ 3 6

38. 4 9_____ 8 5 39. 20 12_____ 12 4

Activity 3-12: Addition of Integers on a Number Line Name:

Below are several rushing attempts in a football game. Plot the attempts on the number lines to

determine to total amount of yardage.

1. a gain of 3 yards and then a gain of 4 yards (3 + 4)

-10 -5 0 5 10

2. a loss of 5 yards and then a gain of 7 yards ( 5 7 )

-10 -5 0 5 10

3. a loss of six yards and then another loss of 2 yards ( 6 2 )

-10 -5 0 5 10

4. a gain of 8 yards and then a loss of 9 yards (8 9 )

-10 -5 0 5 10

5. a loss of 3 yards and then a loss of 1 yard ( 3 1 )

-10 -5 0 5 10

6. a gain of 7 yards and then a loss of 7 yards ( 7 7 )

-10 -5 0 5 10

Activity 3-13: Subtracting Integers Name:

Show the subtraction on the number line. Find the difference.

1. 2 3 2. 5 (1)

_______________________________________ ________________________________________

Find the difference.

3. 6 4 4. 7 (12) 5. 12 16 6. 5 (19)

_______________ _______________ _______________ ________________

7. 18 (18) 8. 23 (23) 9. 10 (9) 10. 29 (13)

_______________ _______________ _______________ ________________

11. 9 15 12. 12 14 13. 22 (8) 14. 16 (11)

_______________ _______________ _______________ ________________

Solve.

15. Monday’s high temperature was 6C. The low temperature was 3C.

What was the difference between the high and low temperatures?

________________________________________________________________________________________

16. The temperature in Minneapolis changed from 7F at 6 A.M. to 7F at

noon. How much did the temperature increase?

________________________________________________________________________________________

17. Friday’s high temperature was 1C. The low temperature was 5C.

What was the difference between the high and low temperatures?

________________________________________________________________________________________

18. The temperature changed from 5C at 6 P.M. to 2C at midnight. How

much did the temperature decrease?

________________________________________________________________________________________

19. The daytime high temperature on the moon can reach 130C. The

nighttime low temperature can get as low as 110C. What is the

difference between the high and low temperature?

________________________________________________________________________________________

Activity 3-14: Subtracting Integers Name:

For each set of values find x y. Answer the questions that follow.

1. x 14, y 2 2. x 11, y 11 3. x 8, y 15

_______________________ ________________________ ________________________

4. x 9, y 9 5. x 9, y 20 6. x 0, y 9

_______________________ ________________________ ________________________

7. x 9, y 11 8. x 1, y 1 9. x 5, y 5

_______________________ ________________________ ________________________

10. If x and y are both positive, when is x y negative? ______________________________________

11. If x and y are both negative, when is x y positive? ______________________________________

Solve.

12. The temperature changed from 7F at 6 P.M. to 5F at midnight. What

was the difference between the high and low temperatures? What was

the average change in temperature per hour?

________________________________________________________________________________________

13. The lowest point in the Pacific Ocean is about 11,000 meters. The

lowest point in the Atlantic Ocean is about 8,600 meters. Which ocean

has the lower point? How much lower?

________________________________________________________________________________________

14. At 11,560 feet above sea level, Climax, Colorado is the highest town in

the United States. The lowest town is Calipatria, California at 185 feet

below sea level. Express both of these distances as integers and tell which is

closer to sea level. How much closer to sea level is the town that is closer?

__________________________________________________________

Use the table for 15–16.

Temperatures at a Ski Resort

Day High Low

Saturday 8F 3F

Sunday 6F 2F

15. On which day was the difference in temperature greater? _________________________________

16. How much greater was the difference one day than the other? ____________________________

Activity 3-15: Subtracting Integers Name:

Show the subtraction on the number line. Then write the difference.

The first one is done for you.

1. 3 8 2. 5 (1)

_______________________________________ ________________________________________

Find each difference. The first one is done for you.

3. 3 4 4. 7 (2) 5. 12 6

_______________________ ________________________ ________________________

6. 8 8 7. 5 (5) 8. 1 (2)

_______________________ ________________________ ________________________

9. 8 1 10. 7 (9) 11. 3 8

_______________________ ________________________ ________________________

Solve. The first one is done for you.

12. The daytime temperature on the planet Mercury can reach 430C.

The nighttime temperature can drop to 180C. What is the difference

between these temperatures?

________________________________________________________________________________________

13. An ice cream company made a profit of $24,000 in 2011. The same

company had a loss of $11,000 in 2012. What is the difference between

the company’s financial results for 2011 and 2012?

________________________________________________________________________________________

14. The high temperature on Saturday day was 6F. The low temperature

was 3F. What was the difference between the high and low

temperatures for the day?

________________________________________________________________________________________

–7

–5

610C

Activity 3-16: Subtraction of Integers Name:

An integer and its opposite are the same distance from 0 on a number line. The integers 5 and -5

are opposites. The sum of an integer and its opposite is 0. To subtract an integer add its opposite.

Example 1:

6 9

6 9

3

t

t

t

Example 2:

10 12

10 12

2

m

m

m

Add or subtract.

1. 2 8 2. 8 ( 4) 3. 6 3

4. 6 4 5. 1 7 6. 3 8

7. 2 6 8. 6 9 9. 5 ( 7)

10. 4 ( 7) 11. 4 7 12. 4 7

13. 2 ( 1) ( 3) 14. 8 8 15. 2 3 1

16. 5 ( 5) 17. 6 1 18. 6 1

In hockey, each player is given a plus/minus rating. This rating is based on how many goals are

scored by their team while the player is on the ice minus how many goals are scored by the

opposing team while the player is on the ice. A high number is good and a low number is bad.

Here are the best and worst plus/minus ratings for 2009-2010:

1 Jeff Schultz – WSH +50 874 Ryan Potulny – EDM 21 2 Alex Ovechkin – WSH +45 875 Kyle Okposo – NYI 22 3 Mike Green – WSH +39 876 Steve Staios – EDM 27

4 Nicklas Backstrom – WSH +37 877 Shawn Horcoff – EDM 29

5 Daniel Sedin – VAN +36 878 Rod Brind'Amour – CAR 29

6 Alexander Semin - WSH +36 879 Patrick O'Sullivan – EDM 35

Use the table above to answer the following subtraction problems.

19. Schultz – Okposo 20. Staios – Green

21. Sedin – Ovechkin 22. O’Sullivan – Semin

23. Potulny – Backstrom 24. Brind’Amour – Horcoff

25. Green – O’Sullivan 26. Semin – Schultz

27. Staois – Brind’Amour 28. Potulny – Schultz

29. Semin – Sedin – Schultz 30. Backstrom – Green

31. Horcoff - Ovechkin 32. Ovechkin – O’Sullivan

33. Okposo – Staios 34. Potulny – Brind’Amour

Activity 3-17: Subtraction of Integers Name:

Subtracting integers is often the hardest of the four basic operations for students. Sometimes

students try to take a shortcut and they don’t change the signs to “add the opposite.” The problem

can be easy to miss when you don’t change these signs.

Here are some other explanations to help you remember why we can change the subtracting

problem to an addition problem.

PARTY #1: This is a positive party. It is filled with positive people. What could you do to make

this party less positive?

One option would be to make some of the positive people go home. This means you are

subtracting positive people.

A second option would be to bring in some negative people. This means you are adding

negative people.

Therefore you have accomplished the same thing two different ways.

Subtracting positives is the same as adding negatives.

PARTY #2: This is a negative party. It is filled with negative people. What could you do to make

this party less negative (more positive)?

One option would be to make some of the negative people go home. This means you are

subtracting negative people.

A second option would be to bring in some positive people. This means you are adding

positive people.

Therefore you have accomplished the same thing two different ways.

Subtracting negatives is the same as adding positives.

Activity 3-18: Subtraction of Integers on a Number Line Name:

1. 7 – 2

-10 -5 0 5 10

2. 4 – 6

-10 -5 0 5 10

3. 6 1

-10 -5 0 5 10

4. 5 3

-10 -5 0 5 10

5. 3 4

-10 -5 0 5 10

6. 2 5

-10 -5 0 5 10

Activity 3-19: Applying Addition and Subtraction of Integers Name:

Write an expression to represent the situation. Then solve by finding

the value of the expression.

1. Owen is fishing from a dock. He starts with the bait 2 feet below the

surface of the water. He reels out the bait 19 feet, then reels it back in 7

feet. What is the final position of the bait relative to the surface of the

water?

________________________________________________________________________________________

2. Rita earned 45 points on a test. She lost 8 points, earned 53 points, then

lost 6 more points. What is Rita’s final score on the test?

________________________________________________________________________________________

Find the value of each expression.

3. 7 12 15 4. 5 9 13

_______________________________________ ________________________________________

5. 40 33 11 6. 57 63 10

_______________________________________ ________________________________________

7. 21 17 25 65 8. 12 19 5 2

_______________________________________ ________________________________________

Compare the expressions. Write , or .

9. 15 3 7 9 1 16

10. 31 4 6 17 22 5

Solve.

11. Anna and Maya are competing in a dance tournament where dance

moves are worth a certain number of points. If a dance move is done

correctly, the dancer earns points. If a dance move is done incorrectly,

the dancer loses points. Anna currently has 225 points.

a. Before her dance routine ends, Anna earns 75 points and loses 30 points.

Write and solve an expression to find Anna’s final score.

____________________________________________________________________________________

b. Maya’s final score is 298. Which dancer has the greater final score?

Activity 3-20: Applying Addition and Subtraction of Integers Name:

Write an expression to represent the situation. Then solve by finding

the value of the expression.

1. Jana is doing an experiment. She is on a dock that is 10 feet above the

surface of the water. Jana drops the weighted end of a fishing line

35 feet below the surface of the water. She reels out the line 29 feet, and

then reels it back in 7 feet. What is the final distance between Jana and

the end of the fishing line?

________________________________________________________________________________________

2. Kirsten and Gigi are riding in hot air balloons. They start 500 feet above

the ground. Kirsten’s balloon rises 225 feet, falls 105 feet, and then rises

445 feet. Every time Kirsten’s balloon travels up or down, Gigi’s balloon

travels 15 feet farther in the same direction. Then both balloons stop

moving so a photographer on the ground can take a picture.

a. Find Kirsten’s final position relative to the ground.

____________________________________________________________________________________

b. Is Kirsten or Gigi closer to the ground when the photographer takes

the picture?

____________________________________________________________________________________

3. In a ring-toss game, players get points for the number of rings they can

toss and land on a colored stake. They earn 20 points for landing on a

red stake and 30 points for landing on a blue stake. They lose 10 points

each time they miss. The table shows the number of rings tossed by

David and Jon during the game.

a. Write and evaluate an expression that represents David’s total score.

____________________________________________________________________________________

b. Who scored more points during the game?

____________________________________________________________________________________

Player Red Blue Miss

David 2 3 3

Jon 3 2 2

Activity 3-21: Applying Addition and Subtraction of Integers Name:

Write an expression to represent the situation. Then solve by finding

the value of the expression. The first one is done for you.

1. Jeremy is fishing from a dock. He starts with the bait 2 feet below the

surface of the water. He lowers the bait 9 feet, then raises it 3 feet. What

is the final position of the bait relative to the surface of the water?

________________________________________________________________________________________

2. Rita earned 20 points on a quiz. She lost 5 points for poor penmanship,

then earned 10 points of extra credit. What is Rita’s final score on the

quiz?

________________________________________________________________________________________

Find the value of each expression. The first one is done for you.

3. 7 1 5 4. 5 9 10

_______________________________________ ________________________________________

5. 40 30 10 6. 2 8 19

_______________________________________ ________________________________________

7. 12 14 6 8. 50 60 10

_______________________________________ ________________________________________

Compare the expressions. Write , , or .

9. 20 5 10 10 11 30

10. –10 40 – 5 25 15 3

Solve.

11. Angela is competing in a dance competition. If a dance move is done

correctly, the dancer earns points. If a dance move is done incorrectly,

the dancer loses points. Angela currently has 200 points. Angela then

loses 30 points and earns 70 points. Write and evaluate an expression

to find Angela’s final score.

________________________________________________________________________________________

1

2 9 3 8; 8 feet below the surface of the water

Activity 3-22: Integer Word Problems Name:

Write the expression for each word problem and then solve.

1.

Jerry Jones has overdrawn his account by $15. There is $10

service charge for an overdrawn account. If he deposits $60,

what is his new balance?

2.

The outside temperature at noon was 9 degrees Fahrenheit.

The temperature dropped 15 degrees during the afternoon.

What was the new temperature?

3. The temperature was 10 degrees below zero and dropped 24

degrees. What is the new temperature?

4. The football team lost 4 yards on one play and gained 9 yards

on the next play. What is the total change in yards?

5.

The temperature in Tahiti is 27 degrees Celsius. The

temperature in Siberia is 33 degrees Celsius. What is the

difference in temperatures?

6. Horatio Hornswoggle was born in 57 B.C. and died in 16 A.D.

How old was Horatio when he died?

7. You have a bank account balance of $357 and then write a

check for $486. What is your new balance?

8.

A mountain climber is at an altitude of 4572 meters and, at the

same time, a submarine commander is at 609 meters. What

is the difference in altitudes?

9. The Roman Empire was established in 509 B.C. and fell 985

years later. In what year did the Empire fall?

10. A scuba diver is at an altitude of 12 meters and a shark is at

an altitude of 31 meters. What is the difference in altitudes?

11.

A submarine descended 32 feet below the surface of the

ocean. It then rose 15 feet to look at a shark. Write an

expression and solve to find the submarines current depth.

12.

In January, the temperature at Mt. Everest averages 36 C .

It can drop as low as 60 C . In July, the average summit

temperature is 17 degrees Celsius warmer. What is the

average temperature at the summit of Mt. Everest in July?

13. What is the difference in elevation between Mt. McKinley

(+20,320 feet) and Mt. Everest (+29,035 feet)?

14. Find the difference in elevation between Death Valley ( 282

feet) and the Dead Sea ( 1348 feet).

15.

The highest ever recorded temperature on earth was 136 F in

Africa and the lowest was 129 F in Antarctica. What is the

difference of these temperatures recorded on Earth?

16. The temperature in Mrs. Cagle’s room was 14 F yesterday,

but it rose 8 F today. What is the new temperature today?

17.

The boiling point of water is 212 F and 460 F is its

absolute lowest temperature. Find the difference between

these two temperatures.

Activity 3-23: More Negatives Name:

A negative sign signifies the opposite of an integer. For example, the opposite of 4 is 4 . The

opposite of 4 would be ( 4) . As we have learned from subtracting and our discussions of

subtraction ( 4) is equal to 4.

Simplify each expression.

1. ( 8) 2. (27) 3. 36 4. 45

5. 14 6. 0 7. ( 12) 8. ( 57)

9. ( 20) 10. 51 11. 25 12. ( 16)

Match the integer expression with the verbal expression.

13. 12 (A) the opposite of negative twelve

14. 12 (B) the absolute value of twelve

15. 12 (C) the opposite of the absolute value of negative twelve

16. ( 12) (D) the absolute value of negative twelve

17. 12 (E) the opposite of the absolute value of twelve

Solve and explain.

18. Is there a least positive integer? Explain.

19. Is there a greatest positive integer? Explain.

20. Is there a smallest integer that is negative? Explain.

21. Is there a largest integer that is negative? Explain.

Write always, never, or sometimes.

22. The sum of two negative integers is negative…

23. The sum of a positive integer and a negative integer is positive…

24. The sum of 0 and a negative integer is positive…

25. Zero minus a positive integer is negative…

26. The difference of two negative integers is negative…

Temperature on Pluto =

370 F

Temperature on Mercury =

950 F Temperature on Earth = 59 F

Temperature on the moon

during the day = 417 F

Temperature on the moon

during the night = 299 F

Temperature at moon’s poles

is constantly 141 F

Using the table above, write and solve five word problems involving the concepts we have learned

about integers. At least three of the problems should involve addition or subtraction.

Activity 3-24: Master’s Golf Results Name:

In golf, the goal is to get the lowest score possible. A score of “E” is equivalent to a 0. Use the

table to answer the following questions.

1. List the 12 players above in order from best to worst based on their 4th

round score. If there is

a tie, the player with the better final score should come first.

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13-24. Determine the absolute value of the final score for each player.

Phil Mickelson Lee Westwood Anthony Kim Tiger Woods

Fred Couples Ian Poulter Ernie Els Kenny Perry

Lucas Glover Retief Goosen Zach Johnson Sergio Garcia

Determine the sum of the following groups of players’ final scores.

25. Woods + Goosen 26. Perry + Couples

27. Garcia + Kim 28. Johnson + Els + Garcia

29. Mickelson + Poulter 30. Woods + Kim + Glover

31. Westwood + Els 32. Goosen + Couples + Els

Determine the difference of the following groups of players’ final scores.

33. Woods – Goosen 34. Perry – Couples

35. Mickelson – Westwood 36. Kim – Woods – Els

37. Poulter – Couples 38. Glover – Garcia

39. Johnson – Els 40. Goosen – Garcia – Woods

Place Name

4th

Round

Score

Final

Score Place Name

4th

Round

Score

Final

Score

1 Phil Mickelson -5 -16 18 Ernie Els -4 -1

2 Lee Westwood -1 -13 26 Kenny Perry +2 +1

3 Anthony Kim -7 -12 36 Lucas Glover +2 +4

4 Tiger Woods -3 -11 38 Retief Goosen +1 +6

6 Fred Couples -2 -11 42 Zach Johnson +3 +7

10 Ian Poulter +1 -5 45 Sergio Garcia +6 +10

2010 PGA Tour Masters Results

Activity 3-25: Addition and Subtraction of Integers Name:

Solve each equation.

1. 7 ( 5)x 2. 10 9 n

3. 12 ( 5)w 4. 13 ( 3)t

5. 10 12 z 6. 7 8 k

7. 11 ( 6)m 8. 0 ( 21) b

9. 13 ( 11) h 10. 52 52f

11. 6 5 ( 4) t 12. 4 ( 5) 6 m

13. 3 8 ( 9)k 14. 6 ( 2) ( 1)a

15. 10 ( 5) 6 n 16. 8 8 ( 10)c

17. 36 ( 28) ( 16) 24 y 18. 31 19 ( 15) ( 6)x

Solve each equation.

19. 4 1 f 20. 5 ( 7)h

21. 9 12z 22. 765 ( 34)a

23. 652 ( 57) b 24. 346 865c

25. 136 ( 158)d 26. 342 ( 456)x

27. 684 ( 379)y 28. 658 867b

29. 657 899 t 30. 3004 ( 1007) r

31. 21 24 b 32. 15 ( 86) a

Tell if each of the subtraction sentences would always, sometimes, or never be true. Support

your answer with examples.

33. positive – positive = positive 34. negative – positive = negative

35. negative – negative = positive 36. positive – negative = negative

37. negative – positive = positive 38. positive – positive = negative

Activity 3-26: Square Game Name:

Directions: Players take turns joining any two dots next to each other. Diagonals are not allowed. When a

player makes a square, the player's initials go in the box. When all the squares are completed, add up all the

integers in your boxes. Then subtract this total from 25. The player with the highest score is the winner.

ROUND 1

-3 2 4 -6 -2

1 7 -4 3 -1

5 3 6 2 -5

3 -4 1 4 -3

6 -1 2 5 -4

PLAYER 1: TOTAL OF ALL BOXES: ____________

Now subtract this total from 25: 25 -_____ = _______ (final score)

PLAYER 2: TOTAL OF ALL BOXES: ____________

Now subtract this total from 25: 25 -_____ = _______ (final score)

ROUND 2

-3 2 4 -6 -2

1 7 -4 3 -1

5 3 6 2 -5

3 -4 1 4 -3

6 -1 2 5 -4

Activity 3-27: Positive 4 Name:

In two minutes name as many sums of integers that yield a positive 4 as you can. You may loop

pairs of integers that are next to each other, either horizontally, vertically, or diagonally.

-4 8 -3 7 -2 4 -7 5 -1 9 -4 7

1 -8 2 -4 5 -5 1 -7 6 -4 8 -5

-9 2 -5 7 -3 8 -8 2 -3 6 -5 4

5 -1 2 -4 4 -6 5 -4 9 -1 4 -7

-7 6 -1 8 -3 2 -1 4 -3 6 -7 3

3 -2 8 -5 7 -9 4 -3 7 -2 5 -5

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

2 -4 6 -2 5 -1 7 -5 5 -6 9 -3

-6 9 -2 8 -1 7 -2 3 -3 9 -1 6

4 -3 2 -9 7 -3 6 -5 7 -8 3 -2

In two minutes name as many sums of integers that yield a positive 4 as you can. You may loop

pairs of integers that are next to each other, either horizontally, vertically, or diagonally.

-4 8 -3 7 -2 4 -7 5 -1 9 -4 7

1 -8 2 -4 5 -5 1 -7 6 -4 8 -5

-9 2 -5 7 -3 8 -8 2 -3 6 -5 4

5 -1 2 -4 4 -6 5 -4 9 -1 4 -7

-7 6 -1 8 -3 2 -1 4 -3 6 -7 3

3 -2 8 -5 7 -9 4 -3 7 -2 5 -5

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

2 -4 6 -2 5 -1 7 -5 5 -6 9 -3

-6 9 -2 8 -1 7 -2 3 -3 9 -1 6

4 -3 2 -9 7 -3 6 -5 7 -8 3 -2

Activity 3-28: Adding and Subtracting Integers Name:

Integer Operation Game

Using a deck of cards, pull out two cards. Add the two cards together using these rules:

Reds are negative and blacks are positive

Jacks are 11, Queens are 12, Kings are 13, and Aces are 1.

Activity 3-29: Multiplication and Division of Integers Name:

The Official Kissing Rules help you remember answer signs on multiplying or dividing problems.

A boy sees a girl he likes. (+)

The boy does kiss her. (+)

The boy is happy! (+) + + +

A boy sees a girl he likes. (+)

The boy does not kiss her. (-)

The boy is not happy. (-) + - -

A boy sees a girl he does not like. (-)

The boy does not kiss her. (-)

The boy is happy! (+) - - +

A boy sees a girl he does not like. (-)

The boy does kiss her. (+)

The boy is not happy. (-) - + -

When multiplying/dividing two positives or

two negatives, the answer is positive.

When multiplying/dividing one negative and

one positive, the answer is negative.

Solve each equation.

1. 2( 8)m 2. 3( 4)t 3. 8( 4)x

4. ( 5)( 5)p 5. ( 12)(5)r 6. 2( 4)w

7. 12(13)e 8. 14( 3)v 9. ( 14) 5n

10. 2( 12)h 11. 7 8d 12. 9(10)b

Evaluate each expression if 6m , 3n , and 4p .

13. 4m 14. np 15. 2mn

16. 22m 17. 5np 18. 10mp

19. 12np 20. mnp 21. 2p

Solve each equation.

22. 16 4f 23. 100 10v 24. 28 7m

25. 52 4g 26. 125 25d 27. 32 16q

28. 120 12e 29. 45 9t 30. 33 3p

31. 36 12z 32. 200 25d 33. 88 11c

Evaluate each expression if 36e , 4f , and 3g .

34. f

e 35. 2g

e 36.

fg

e

37. 2e

f 38.

48

g

39.

eg

f

40. fg

e 2

41. f

100 42.

2

2

g

e

Activity 3-30: Multiplying Integers Name:

Find each product.

1. 4(20) 2. 6(12) 3. (8)(5)

_______________________ ________________________ ________________________

4. (13)(3) 5. (10)(0) 6. (5)(16)

_______________________ ________________________ ________________________

7. (9)(21) 8. 11(1) 9. 18(4)

_______________________ ________________________ ________________________

10. 10(8) 11. 9(6) 12. 7(7)

_______________________ ________________________ ________________________

Write a mathematical expression to represent each situation. Then find

the value of the expression to solve the problem.

13. You play a game where you score 6 points on the first turn and on each

of the next 3 turns. What is your score after those 4 turns?

________________________________________________________________________________________

14. The outdoor temperature declines 3 degrees each hour for 5 hours.

What is the change in temperature at the end of those 5 hours?

________________________________________________________________________________________

15. You have $200 in a savings account. Each week for 8 weeks, you take

out $18 for spending money. How much money is in your account at the

end of 8 weeks?

________________________________________________________________________________________

16. The outdoor temperature was 8 degrees at midnight. The temperature

declined 5 degrees during each of the next 3 hours. What was the

temperature at 3 A.M.?

________________________________________________________________________________________

17. The price of a stock was $325 a share. The price of the stock went down

$25 each week for 6 weeks. What was the price of that stock at the end

of 6 weeks?

________________________________________________________________________________________

Activity 3-31: Multiplying Integers Name:

Find each product.

1. (14)(7) 2. (24)(5) 3. 12(12)

_______________________ ________________________ ________________________

4. 15(9)(1) 5. 2(3)(4) 6. 3(6)(2)

_______________________ ________________________ ________________________

7. 40(78)(0) 8. 6(60)(4) 9. 24(7)(7)

_______________________ ________________________ ________________________

Write a mathematical expression to represent each situation. Then find

the value of the expression to solve the problem.

10. A football team loses 4 yards on each of three plays. Then they

complete a pass for 9 yards. What is the change in yardage after those

four plays?

________________________________________________________________________________________

11. You have $220 in your savings account. You take $35 from your

account each week for four weeks. How much is left in your account at

the end of the four weeks?

________________________________________________________________________________________

12. A submarine is at 125 feet in the ocean. The submarine makes three

dives of 50 feet each. At what level is the submarine after the three

dives?

________________________________________________________________________________________

Find each product. Use a pattern to complete the sentences.

13. 1(1) __________ 14. 1(1)(1) __________ 15. 1(1)(1)(1) _________

16. 1(1) (1)(1)(1) __________ 17. 1(1)(1)(1)(1)(1) __________

18. When multiplying integers, if there is an odd number of negative factors,

then the product is _________________.

If there is an even number of negative factors, then the product is

_________________.

Activity 3-32: Multiplying Integers Name:

Find each product. The first one is done for you.

1. 3(2) 2. 5(0) 3. (1)(8)

_______________________ ________________________ ________________________

4. (4)(7) 5. (3)(4) 6. (6)(6)

_______________________ ________________________ ________________________

7. 10(5) 8. 2(9) 9. 7(10)

_______________________ ________________________ ________________________

10. 1(1) 11. 2(6) 12. 2(2)

_______________________ ________________________ ________________________

Write a mathematical expression to represent each situation. Then find

the value of the expression to solve the problem. The first one is done

for you.

13. You play a game where you score 3 points on the first 5 turns. What is

your score after those 5 turns?

________________________________________________________________________________________

14. The outdoor temperature gets 1 degree colder each hour for 3 hours.

What is the change in temperature at the end of those 3 hours?

________________________________________________________________________________________

15. A football team loses 4 yards on each of 2 plays. What is the change in

yardage after those 2 plays?

________________________________________________________________________________________

16. You take $9 out of your savings account each week for 7 weeks. At the

end of 7 weeks, what is the change in the amount in your savings

account?

________________________________________________________________________________________

17. The price of a stock went down $5 each week for 5 weeks. What was the

change in the price of that stock at the end of 5 weeks?

________________________________________________________________________________________

6

5(3) 15; 15 points

Activity 3-33: Multiplying Integers Name:

Complete the table below using your knowledge of integers as well as noticing the pattern that the

table creates.

5 15

4 12

3 0 3 6 9 12 15

2 6

1 3

0 0

-5 -4 -3 -2 -1 x 0 1 2 3 4 5

-1

-2

-3

-4

-5

Activity 3-34: Multiplying Integers Name:

The multiplication table below contains 42 mistakes. Shade in each box that contains a mistake. You will end up with a famous

farming expression.

X 2 -4 -9 6 3 8 -1 4 -8 -2 -6 7 -5 9 -7

-3 6 -12 -27 -18 9 -24 -3 12 -24 6 -18 -21 -15 27 -21

9 -18 -36 -81 54 -27 72 9 36 -72 -18 54 63 45 81 63

-6 12 -24 54 -36 18 -48 -6 24 48 12 -36 -42 -30 -54 -42

5 -10 -20 -45 30 -15 40 5 20 -40 -10 30 35 25 45 35

-7 14 -28 -63 -42 21 -56 -7 28 -56 14 -42 -49 -35 63 -49

Activity 3-35: Dividing Integers Name:

Find each quotient.

1. 7 84 2. 38 2 3. 27 81

_________________ _________________ _________________

4. 28 7 5. 121 (11) 6. 35 4

_________________ _________________ _________________

Simplify.

7. ( 6 4) 2 8. 5( 8) 4 9. 6( 2) 4( 3)

_________________ _________________ _________________

Write a mathematical expression for each phrase.

10. thirty-two divided by the opposite of 4

________________________________________________________________________________________

11. the quotient of the opposite of 30 and 6, plus the opposite of 8

________________________________________________________________________________________

12. the quotient of 12 and the opposite of 3 plus the product of the opposite

of 14 and 4

________________________________________________________________________________________

Solve. Show your work.

13. A high school athletic department bought 40 soccer uniforms at a cost of

$3,000. After soccer season, they returned some of the uniforms but

only received $40 per uniform. What was the difference between what

they paid for each uniform and what they got for each return?

________________________________________________________________________________________

14. A commuter has $245 in his commuter savings account. This account

changes by $15 each week he buys a ticket.

a. If the account changed by $240, for how many weeks of tickets

did the commuter buy?

____________________________________________________________________________________

b. If the commuter wants to buy 20 weeks of tickets, how much must

he add to his account?

____________________________________________________________________________________

Activity 3-36: Dividing Integers Name:

Simplify.

1. 8

( 12)2

2. 6 15 7

3 2

3. 3 2(4 7) 9

_________________ _________________ _________________

The integers from 3 to 3 can be used in the blanks below. Which of

these integers produces a positive, even integer for the expression?

Show your work for those that do.

4. 8

2 4 (______) 2 5.

(_____) 3

4 2

_____________________________________ _____________________________________

6. ______ 2

3

7. 1 1

_____ 2

_____________________________________ _____________________________________

Solve. Show your work.

8. In a sports competition, Alyssa was penalized 16 points. She received

the same number of penalty points in each of 4 events. How many

points was she penalized in each event?

________________________________________________________________________________________

9. The surface temperature of a deep, spring-fed lake is 70F. The lake

temperature drops 2F for each yard below the lake surface until a depth

of 6 yards is reached. From 6 yards to 15 yards deep, the temperature is

constant. From 15 yards down to the spring source, the temperature

increases 3F per foot until the spring source is reached at 20 yards

below the surface.

a. What is the temperature at 10 yards below the surface?

____________________________________________________________________________________

b. What is the temperature at 50 feet below the surface?

____________________________________________________________________________________

____________________________________________________________________________________

c. Write an expression for finding the lake temperature at the spring

source.

____________________________________________________________________________________

Activity 3-37: Dividing Integers Name:

Find the quotient. The first one is done for you.

1. 3 15 2. 27 3 3. 28

7

_________________ _________________ _________________

Compare the quotients. Write , , or .

4. 4 16 16 4 5. 11 77 77 11 6. 48

6

48

6

Write a mathematical expression for the written expression. Then

solve. The first one is done for you.

7. the opposite of 45 divided by 5 8. fifty-five over negative eleven

_____________________________________ _____________________________________

9. negative 38 divided by positive 19 10. negative four divided by negative two

_____________________________________ _____________________________________

Solve. Show your work. The first one is done for you.

11. Four investors lost 24 percent of their combined investment in a

company. On average, how much did each investor lose?

________________________________________________________________________________________

_______________________________________________________________________________________________________________________________

12. The temperature in a potter’s kiln dropped 760 degrees in 4 hours. On

average, how much did the temperature drop per hour?

_______________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________

13. The value of a car decreased by $5,100 over 3 years. On average, how

much did its value decrease each year?

_______________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________

5

45 5 9

24 4 6; On average, each investor lost 6%.

Activity 3-38: Applying Integer Operations Name:

1. (3)(2) 8 2. (18) 3 (5)(2) 3. 7(3) 6

________________________ ________________________ ________________________

4. 24 (6)(2) 7 5. 4(8) 3 6. (9)(0) (8)(5)

________________________ ________________________ ________________________

Compare. Write , , or .

7. (5)(8) 3 (6)(7) 1

8. (8)(4) 16 (4) (9)(3) 15 (3)

Write an expression to represent each situation. Then find the value of

the expression to solve the problem.

9. Dave owns 15 shares of ABC Mining stock. On Monday, the value of

each share rose $2, but on Tuesday the value fell $5. What is the change

in the value of Dave’s shares?

________________________________________________________________________________________

10. To travel the Erie Canal, a boat must go through locks that raise or lower

the boat. Traveling east, a boat would have to be lowered 12 feet at

Amsterdam, 11 feet at Tribes Hill, and 8 feet at Randall. By how much

does the elevation of the boat change between Amsterdam and Randall?

________________________________________________________________________________________

11. The Gazelle football team made 5 plays in a row where they gained

3 yards on each play. Then they had 2 plays in a row where they lost 12

yards on each play. What is the total change in their position from where

they started?

________________________________________________________________________________________

12. On Saturday, Mrs. Armour bought 7 pairs of socks for $3 each, and a

sweater for her dog for $12. Then she found a $5 bill on the sidewalk.

Over the course of Saturday, what was the change in the amount of

money Mrs. Armour had?

Activity 3-39: Applying Integer Operations Name:

Complete the table to answer questions 1–4.

You Own Company Monday Tuesday Wednesday Net Gain or Loss

1. 5 shares ABC $2 $5 $1

2. 2 shares DEF $8 $7 $10

3. 8 shares GHI $2 $9 $6

4. 7 shares JKL $5 $12 $3

5. What expression shows your net gain or loss on GHI Company?

________________________________________________________________________________________

6. How much value did you gain or lose overall? ___________________________________

Write an expression to represent each situation. Then, find the value of

the expression to solve the problem.

7. A submarine cruised below the surface of the water. During a training

exercise, it made 4 dives, each time descending 45 feet more. Then it

rose 112 feet. What is the change in the submarine’s position?

________________________________________________________________________________________

8. A teacher wanted to prevent students from guessing answers on a

multiple-choice test. The teacher graded 5 points for a correct answer, 0

points for no answer, and 2 points for a wrong answer. Giselle answered

17 questions correctly, left 3 blank, and had 5 wrong answers. She also got

8 out of 10 possible points for extra credit. What was her final score?

________________________________________________________________________________________

9. Hugh wrote six checks from his account in the following amounts: $20,

$20, $12, $20, $12, and $42. He also made a deposit of $57 and was

charged a $15 service fee by the bank. What is the change in Hugh’s

account balance?

________________________________________________________________________________________

10. a. Without finding the product, what is the sign of this

product? Explain how you know.

(4)(1)(2)(6)(3)(5)(2)(2)

________________________________________________________________________________________

b. Find the product. _____________________________________________________________________

Activity 3-40: Applying Integer Operations Name:

Find the value of each expression. Show your work. The first one is

done for you.

1. 15 (6)(2) 2. (5)(3) 18

________________________________________ ________________________________________

________________________________________ ________________________________________

3. 42 (6) 23 4. 52 45 (9)

________________________________________ ________________________________________

________________________________________ ________________________________________

Write an expression to represent each situation. Then find the value of

the expression to solve the problem. The first one is done for you.

5. Mr. Carlisle paid his utility bills last weekend. He paid $50 to the phone

company, $112 to the power company, and $46 to the water company.

After he paid those bills, what was the change in the total amount of

money that Mr. Carlisle had?

________________________________________________________________________________________

6. Over 5 straight plays, a football team gained 8 yards, lost 4 yards, gained

7 yards, gained 3 yards, and lost 11 yards. What is the team’s position

now compared to their starting position?

________________________________________________________________________________________

7. At the grocery store, Mrs. Knight bought 4 pounds of apples for $2 per

pound and 2 heads of lettuce for $1 each. She had a coupon for $3 off the

price of the apples. After her purchases, what was the change in the

amount of money that Mrs. Knight had?

________________________________________________________________________________________

8. The depth of the water in a water tank changes every time someone in

the Harrison family takes a bath or does laundry. A bath lowers the water

level by 4 inches. Washing a load of laundry lowers the level by 2 inches.

On Monday the Harrisons took 3 baths and washed 4 loads of laundry.

By how much did the water level in the water tank change?

________________________________________________________________________________________

15 (12) Multiply

3 Add.

(50) (112) (46) 208; He had $208 less.

Activity 3-41: Negative times a Negative is WHAT? Name:

Why is it when you multiply two negative numbers you get a positive number? Good question!

The First Answer

Some people think of a negative as meaning “not”. So if I say, “I am not going to the store,” that is

sort of the negative version of “I am going to the store.”

So what do two “nots” mean? Consider this sentence: “You may tell me NOT to go to the store, but

I’m NOT going to do what you say!” By negating your negation, I am insisting that I will go to the

store.

Two “nots” cancel each other out, just like two negatives.

The Second Answer

Let’s use negatives with money. A green chip is worth $5. A red chip means that I owe you $5. So

if you lose $5, you can represent that by giving up a green chip or by picking up a red chip. So a

green chip is +$5 and a red chip is -$5.

If you gain three green chips, what happens? 3 times $5 equals a $15 gain.

If you gain three red chips, what happens? 3 times -$5 equals a $15 loss.

What if you lose three green chips? You just lost $15. -3 times $5 equals a $15 loss.

What is you lose three red chips? You just gained $15. -3 times -$5 equals a $15 gain.

The Third Answer

How about proving it with a pattern?

3 5 +15

2 5 +10

1 5 +5

0 5 0

1 5 -5

2 5 -10

So….

3 5 -15

2 5 -10

1 5 -5

0 5 0

1 5 +5

2 5 +10

Activity 3-42: Multiplying and Dividing Integers Name:

Solve each equation.

1. 6 8x 2. 12 4y

3. 9 ( 11)x 4. ( 7)(17)y

5. 14( 4) h 6. 15(10) k

7. (10)( 8)( 2) r 8. ( 3)(3)( 10) t

9. ( 12)( 1)(6)w 10. (20)( 5)( 5)y

11. (4)( 16)( 6)x 12. (16)(9)( 2)n

Evaluate each expression if x=-5 and y=-6.

13. 3y 14. 8x 15. 4y 16. 12x

17. 15x 18. 19y 19. 6xy 20. 4xy

Divide.

21. 16 4 22. 27 3 23. 25 ( 5)

24. 63 ( 9) 25. 15 ( 3) 26. 14 ( 7)

27. 56 ( 8) 28. 72 8 29. 21 ( 7)

Solve each equation.

30. 150

25x

31.

98

14k

32.

312

24x

33. 208

26t

34.

180

15n

35.

930

30z

36. 189

21p

37.

288

18d

38.

396

36b

Evaluate each expression if 8x and 12y .

39. 2x 40. ( 4)x 41. 36 y 42. 0 y

43. 6

y

44.

4

x 45.

144

y

46.

136

x

47.

At noon on Friday, the temperature was 0 degrees. Six hours later the

temperature was -18 degrees. On average, what was the temperature

change per hour?

48. Mangham Architecture has monthly profits of $1200, $755, -$450, $210,

and -$640 over 5 months. What was the average profit for those months?

Activity 3-43: All Integer Operations Name:

Solve.

1. 9 ( 13) 2. 2( 25) 3. ( 6 17) 20

4. 50 30 5. 56 ( 8) 6. ( 5 6) 87

7. 32 37 8. ( 15 3) 14 9. ( 13 2) 12

10. ( 10 5)( 2) 11. ( 3 4) 7 12. ( 5 30)(3)

13. ( 9 6) 4 14. ( 30 22) 6 15. ( 8 8) 8

16. (20 4) 11 17. (28 10) 7 18. 12 36

19. ( 13 12)( 4) 20. (4 6) 8 21. ( 64 2) 2

22. 5 20 23. 30 2 24. ( 40 50) 9

25. 9 ( 19) 26. 7 11 27. (42 7) 6

28. 7 11 29. 60 5 30. ( 12 18) 15

The symbols , , x, and can be used only once in each number sentence below. Remember the

correct order of operations!

31. +6 -3 2 = 0 32. -6 -3 -7 = -2

33. 10 (5 5) = 9 34. (-4 -2) (-10 5) = 6

35. 30 [(-6 -3) -1] = 28 36. -6 (-2 -1)2 = -54

37. (30 -6) (-3 -1) = 20 38. (-3 8) (5 6) = -1

39. 5 -5 (5 -5) = 9 40. -3 (-6 -2) -3 = 12

41. (-4 4) (4 -4) = -8 42. (-8 2)2 -4 = -9

43. (3 -3)2 (-3 3)

2 = 36 44. -1 2 1 -2 2 = -4

45. I am an integer. When you add -1 to me, the sum is the opposite of the

difference when you subtract -5 from me. What integer am I?

46. Find two integers having a product of negative 15 and a sum of positive 2.

47. Find two integers having a product of negative 30 and a sum of negative 1.

48. Find two integers having a product of positive 27 and a sum of negative 12.

49. Find two integers having a product of negative 64 and a sum of positive 12.

50. Find two integers having a product of positive 40 and a sum of negative 13.

Activity 3-44: Absolute Value Name:

Complete the table below.

x x 2x 2 x

1. 4

2. 3

3. 2

4. 1

5. 2

6. 1

7. 2

8. 3

9. 4

10. When x is negative, its absolute value is….

11. x is negative always, sometimes or never?

12. 2x is positive always, sometimes or never?

13. x is less than 2 x always, sometimes or never?

14. 2 x is greater than 2x always, sometimes or never?

Kyle has four integer cards. Two cards show positive integers and two cards show negative integers.

15. What is the sum of all four cards?

16. What is the largest sum Kyle can make with two cards?

17. What is the smallest sum Kyle can make with two cards?

18. What is the smallest sum that Kyle can make with three cards?

19. What is the largest difference Kyle can make with two cards?

20. What is the smallest difference Kyle can make with two cards?

21. What is the difference closest in value to 10 that Kyle can make with two cards?

22. What is the largest product Kyle can make with two cards?

23. What is the smallest product Kyle can make with two cards?

24. What is the largest product Kyle can make with three cards?

25. What is the smallest quotient Kyle can make with two cards?

-9 8 4 -5

Activity 3-45: Survival Guide to Integers Name:

Choose one of the following topics: Weather (Temperature), Money, Golf, Time (Years), Elevations

and Altitudes, Game/Video Game Scores, Football, or Physical Science (Atoms and Molecules).

Then pick a more specific theme such as “Jeopardy!” under the main topic of Games or “Scuba Diving”

under the topic Elevations and Altitudes. Check with Mr. Mangham if you have another topic you

wish to use which is not on this list.

Your Survival Guide will consist of 8 pages (2 folded pieces of construction paper). The goal is to

teach integers to students who have not learned about them yet. The following details what

information should be included on each page.

Page 1: Title Page – Title, Pictures, Theme

Your title must include the words “Survival Guide to Integers”

(10 points)

Page 2: Introduction to Integers

State at least three places of where we use negative numbers in real life (include

specific examples of how they would be used in each)

Give definitions and examples for these words:

o Integer (provide examples of integers and numbers that are not integers)

o Opposite of a number

o Absolute value

(20 points)

ADDITION – Pages 3 and 4 – Make sure to include a variety of samples (positive plus negative

where there are more positives, positive plus negative where there are more negatives, negative plus

negative, etc.)

Page 3: Addition of integers

Teach how to add integers using both:

o Yellow and red chips (introduce zero pairs)

o Number lines

Explain in words what is happening

Provide specific examples of each

Page 4: Addition of integers

Teach how to add integers in mathematical expressions (without chips or a number

line) by providing specific examples

Write 4 word problems involving adding integers and relating to your theme. Do

not solve. Your problems must include a mixture of negative and positive numbers

and must make logical sense.

(20 points)

SUBTRACTION – Pages 5 and 6 – Make sure to include a variety of samples which show all the

different possibilities for subtraction problems

Page 5: Subtraction of integers

Teach how to subtract integers using both:

o Yellow and red chips (make sure to include zero pair problems)

o Number lines

Explain in words what is happening

Provide specific examples of each

Page 6: Subtraction of integers

Teach how to subtract integers in mathematical expressions (without chips or a

number line) by providing specific examples

Write 4 word problems involving subtracting integers and relating to your theme.

Do not solve. Your problems must include a mixture of negative and positive

numbers and must make logical sense.

(30 points)

MULTIPLICATION AND DIVISION – Pages 7 and 8

Page 7: Rules for multiplying and dividing integers

Create your own graphic to demonstrate “The Official Kissing Rules”

Your graphic should relate to your theme in some way

Teach (explain) how the rules work and how they apply to problems

Provide specific examples with numbers

Page 8: Multiplying and dividing integers

Write 5 problems which involve a mixture of multiplication and division of

integers. You do not need any word problems.

Write 5 problems which involve integers and order of operations. You must

include at least one multiply or divide in each. Also include other operations

(addition, subtraction), parenthesis, exponents, square roots, etc.

(20 points)

The following, in order, will play a major part in your overall grade:

1) Each topic above is completed with mathematical accuracy

2) Each topic is well explained (i.e. pretend you are teaching someone who has never seen a negative

number before)

3) A wide variety of examples are given (combinations of positive and negative numbers)

4) Your overall use of a theme

5) Neatness, Colorful, Easy-to-follow

Want another example instead of the Kissing Rules? How about this one:

Good things happen to good people, this is good

Good things happen to bad people, this is bad

Bad things happen to good people, this is bad

Bad things happen to bad people, this is good

SURVIVAL GUIDE TO INTEGERS GRADING RUBRIC

NAME: _______________________________________

Possible Points Your score

Cover and

Theme

Contains Theme 5

Says Survival Guide to Integers 3

Neat and interesting 2

Intro to

Integers

What are integers (definition/examples) 6

Where used in real-life 6

Opposite definition/examples 4

Absolute value definition/examples 4

Addition

Add with chips (zero pairs) 3

Add on number line 3

Add mathematically 3

Written explanation 4

Wide variety of examples 4

Four word problems with +/- integers 3

Subtraction

Subtract with chips (zero pairs) 4

Subtract on number line 4

Subtract mathematically 6

Written explanation 6

Wide variety of examples 6

Four word problems with +/- integers 4

Multiplication/

Division

Kissing Rule table with theme 4

Apply rules in examples 3

Written explanation 4

5 problems 3

5 order of operation problems 3

10 correct answers listed 3

TOTAL 100

Activity 3-46: How Do I Learn Name:

In the space provided write an “A” if you agree or a “D” if you disagree.

1. I prefer reading a story rather than listening to someone tell it.

2. I would rather watch television than listen to the radio/IPod.

3. I remember faces better than names.

4. I like classrooms with lots of posters and pictures around the room.

5. The appearance of my handwriting is important to me.

6. I think more often in pictures.

7. I am distracted by visual disorder or movement.

8. I have difficulty remembering directions that were told to me.

9. I would rather watch athletic events than participate in them.

10. I tend to organize my thoughts by writing them down.

11. My facial expression is a good indicator of my emotions.

12. I tend to remember names better than faces.

13. I would enjoy taking part in dramatic events like plays.

14. I tend to sub vocalize and think in sounds.

15. I am easily distracted by sounds.

16. I easily forget what I read unless I talk about it.

17. I would rather listen to the radio/IPod than watch TV.

18. My handwriting is not very good.

19. When faced with a problem, I tend to talk it through.

20. I express my emotions verbally.

21. I would rather be in a group discussion than read about a topic.

22. I prefer talking on the phone rather than writing a letter/email to someone.

23. I would rather participate in athletic events than watch them.

24. I prefer going to museums when I can touch exhibits.

25. My handwriting gets worse when the space becomes smaller.

26. My mental pictures are usually accompanied by movement.

27. I like being outdoors and doing things like biking, camping, swimming,

hiking, etc.

28. I remember best what was done rather than what was seen or talked about.

29. When faced with a problem, I often select the solution involving the greatest

activity.

30. I like to make models or other hand crafted items.

31. I would rather do experiments than read about them.

32. My body language is a good indicator of my emotions.

33. I have difficulty remembering verbal directions if I have not done the

activity before.

SCORING:

Total number of A responses in questions 1-11

Total number of A responses in questions 12-22

Total number of A responses in questions 23-33

The first number is your visual score. If this number is much higher than your other two you are a

visual learner: These learners need to see the teacher's body language and facial expression to fully

understand the content of a lesson. They tend to prefer sitting at the front of the classroom to avoid

visual obstructions (e.g. people's heads). They may think in pictures and learn best from visual

displays including: diagrams, illustrated text books, overhead transparencies, videos, flipcharts and

hand-outs. During a lecture or classroom discussion, visual learners often prefer to take detailed notes

to absorb the information.

Visual Learner Characteristics

Visual learners are those who learn through seeing things. Look over the characteristics below to see if

they sound familiar. A visual learner:

Is good at spelling but forgets names.

Needs quiet study time.

Has to think awhile before understanding lecture.

Is good at spelling.

Likes colors & fashion.

Dreams in color.

Understands/likes charts.

Is good with sign language.

Learning Suggestions for Visual Learners Draw a map of events in history or draw scientific process.

Make outlines of everything!

Copy what’s on the board.

Ask the teacher to diagram.

Diagram sentences!

Take notes, make lists.

Watch videos.

Color code words, research notes.

Outline reading.

Use flashcards.

Use highlighters, circle words, underline.

Best Test Type for Visual Learners: Diagramming, reading maps, essays (if you’ve studied using an outline), showing a process

Worst test type: Listen and respond tests

The second number is your auditory score. If this number is much higher than your other two you are

an auditory learner: They learn best through verbal lectures, discussions, talking things through and

listening to what others have to say. Auditory learners interpret the underlying meanings of speech

through listening to tone of voice, pitch, speed and other nuances. Written information may have little

meaning until it is heard. These learners often benefit from reading text aloud and using a tape

recorder.

Auditory Learner Characteristics Auditory learners are those who learn best through hearing things. Look over these traits to see if they

sound familiar to you. You may be an auditory learner if you are someone who:

Likes to read to self out loud.

Is not afraid to speak in class.

Likes oral reports

Is good at explaining.

Remembers names.

Notices sound effects in movies.

Enjoys music.

Is good at grammar and foreign language.

Reads slowly.

Follows spoken directions well.

Can’t keep quiet for long periods.

Enjoys acting, being on stage.

Is good in study groups.

Auditory Learners Can Benefit from: Using word association to remember facts and lines.

Recording lectures.

Watching videos.

Repeating facts with eyes closed.

Participating in group discussions.

Using audiotapes for language practice.

Taping notes after writing them.

Worst test type:

Reading passages and writing answers about them in a timed test.

Best test type:

Auditory Learners are good at writing responses to lectures they’ve heard. They’re also good at oral

exams.

The third number is your tactile/kinesthetic score. If this number is much higher than your other two

you are a tactile/kinesthetic learner: Tactile/Kinesthetic persons learn best through a hands-on

approach, actively exploring the physical world around them. They may find it hard to sit still for long

periods and may become distracted by their need for activity and exploration.

Kinesthetic Learner Characteristics

Kinesthetic learners are those who learn through experiencing/doing things. Look over these traits to

see if they sound familiar to you. You may be a kinesthetic learner if you are someone who:

Is good at sports.

Can’t sit still for long.

Is not great at spelling.

Does not have great handwriting.

Likes science lab.

Studies with loud music on.

Likes adventure books, movies.

Likes role playing.

Takes breaks when studying.

Builds models.

Is involved in martial arts, dance.

Is fidgety during lectures.

Kinesthetic Learners Can Benefit from: Studying in short blocks.

Taking lab classes.

Role playing.

Taking field trips, visiting museums.

Studying with others.

Using memory games.

Using flash cards to memorize.

Worst Test Type: Long tests, essays.

Best Test Type: Short definitions, fill-ins, multiple choice.

Activity 3-47: Integer Overview Name:

Integer – all whole numbers and their opposites (or positive and negative counting numbers and zero)

Absolute value – the distance a number is from zero. The absolute value of -8 is 8. The absolute

value of 11 is 11. 88 1111

Opposite of a number – To find the opposite, simply change the sign. A number and its opposite add

up to zero. The opposite of 5 is -5. The opposite of -12 is 12.

Adding Integers

two positives Add the numbers like usual

Adding a positive and a positive will create more positives.

two negatives Add the numbers, put a negative sign in front of the answer

Adding a negative and a negative will create more negatives.

one positive and one

negative

When adding a positive and a negative, some positives and

negatives will combine and cancel each other out.

Ask: Do I have more positives or more negatives? The answer will

determine the sign of the final answer. Then ask, how many more

positives do I have than negatives (or how many more negatives do

I have than positives?). This will determine the correct number to

go with the sign.

Subtracting Integers

all

Subtracting is the opposite of addition. Thus, the easy way to

subtract a number is to simply add its opposite.

Ex. 6 - -3 = 6 + +3 = 9

Ex. -12 – 7 = -12 + -7 = -19

Multiplying/Dividing Integers

When multiplying and dividing, determine the number as with normal multiplication and

division. Use the table below, The Kissing Rules, to determine the sign.

Phrase to remember…. This x this = this

A girl sees a boy see likes (+). She does kiss him (+).

She is happy (+). + + +

A girl sees a boy she likes (+). She does not kiss him (-).

She is sad (-). + - -

A boy sees a girl he doesn’t like (-). He does kiss her (+).

He is sad (-). - + -

A boy sees a girl he doesn’t like (-). He does not kiss her (-).

He is happy (+). - - +

Activity 3-S: Chapter 3 Summary Name:

ADDING INTEGERS

When adding two positive integers, add the numbers together. Your answer is always going to be

positive. Ex. 5 + 6 = 11

When adding two negative integers, add the two numbers together and place a negative sign in front of

your answer. Ex. -6 + -3 = -9

When adding a positive and a negative integer, first ask yourself, “Are there more positives or

negatives?” If there are more positives, you answer is going to be positive. If there are more negatives,

then you answer is going to be negative. Then ask yourself, “How many more (negatives/positives)

are there than (positives/negatives)?”

Ex. -8 + 6 Are there more negatives or positives? Negatives. How many more? 8 – 6 = 2. So there

are 2 more negatives than positives and your final answer is -2.

SUBTRACTING INTEGERS

The easiest way to subtract integers is to always turn the expression into an addition problem.

To subtract an integer add its opposite. An integer and its opposite are the same distance from 0 on a

number line so the integers 5 and -5 are opposites.

Then follow the rules above for adding.

Ex. -7 - -8 Change the problem to -7 + +8. There are more positives than negatives. How many more?

One. So your answer is +1.

MULTIPLYING/DIVIDING INTEGERS

When multiplying or dividing integers, multiply and divide just like you would for positive numbers

to get the number part of the answer. Then use the table below to determine the correct sign.

First Sign Second Sign Answer Sign First Sign Second Sign Answer Sign

+ + + + - -

- - + - + -

When multiplying two positives or two negatives,

the answer is positive.

When multiplying one negative and one positive,

the answer is negative.

Activity 3-POW (Guess and Check): Farmer Ann Name:

Farmer Ann was chosen to go into town and spend the entire amount of $100 of a tax return on exactly

100 farm animals – some cattle, some sheep, and some horses. She discovered that sheep cost $0.50

each, cattle cost $1.00 each, and horses cost $10.00 each. This purchase, to buy exactly 100 animals

for $100 and have some of each kind of animal, proved more difficult that she had thought it would be.

Your job is to find a solution to Farmer Ann’s dilemma.

A good method to solve this type of problem is to use guess and check. There are several possible

ways and the one we are going to use is to guess some total of animals that add up to 100. From those

three numbers determine what your overall price is. Based on whether it was too high or too low, you

can now switch out some animals and make another guess.

Make at least 10 guesses to determine a correct answer to this problem. For each guess you must have

a total of 100 animals. There is more than one right answer, so keep guessing even if you guess

correctly early on.

Cattle ($1) Sheep ($0.50) Horses ($10) Total $$$

Guess 1

Guess 2

Guess 3

Guess 4

Guess 5

Guess 6

Guess 7

Guess 8

Guess 9

Guess 10

Guess 11

Guess 12

Guess 13

Guess 14

Guess 15

10 all-time hottest

temperatures Obtained from state temperature

records, NCDC

1. Death Valley, California 134

2. Lake Havasu, Arizona 128

3. Laughlin, Nevada 125

4. Lakewood, New Mexico 122

5. Alton, Kansas 121

6. Steele, North Dakota 121

7. Ozark, Arkansas 120

8. Tipton, Oklahoma 120

9. Seymour, Texas 120

10. Usta, South Dakota 120

1. Prospect Creek, Alaska -80

2. Rogers Pass, Montana -70

3. Peters Sink, Utah -69

4. Riverside, Wyoming -66

5. Maybell, Colorado -61

6. Tower, Minnesota -60

7. Parshall, North Dakota -60

8. Island Park Dam, Idaho -60

9. McIntosh, South Dakota -58

10. Couderay, Wisconsin -55

PRESS CONTROL & CLICK ON THE LINK

http://www.homeschoolmath.net/online/integers.php

http://www.gamequarium.com/integers.html

http://www.kn.pacbell.com/wired/fil/pages/listintegersbr.html

http://www.interactivemaths.net/taxonomy/term/99

http://teacherweb.com/MA/KingPhilipMiddleSchool/MrsMcGovern-7thGradeMathematics/ap3.st

m

http://www.squidoo.com/integers

http://www.quia.com/cb/64603.html

http://classroom.jc-schools.net/basic/math-integ.html

http://cte.jhu.edu/techacademy/web/2000/heal/siteslist.htm

(Go down to Algebra and Pre-Algebra sites and many integer links are listed.)

http://www.learningwave.com/chapters/workingfront/integersfront.html

http://www.shodor.org/interactivate/activities/ArithmeticFour/

http://www.onlinemathlearning.com/integer-games.html

http://www.mathgoodies.com/lessons/vol5/subtraction.html

http://www.learningshortcuts.com/s62/60/chapterA1.html

http://www.mathguide.com/cgi-bin/quizmasters/IntegersSubtract.cgi