Integers Practic

8/12/2019 Integers Practic

1/24

Compare and Order IntegersCompare. Draw a number line from 10 to 10 and label each integer. Write , ,

or for each .

1. 7 6 2. 2 4 3. 4 0 4. 1 1

5. 5 10 6. 0 0 7. 6 3 8. 5 1

9. 5 2 10. 1 9 11. 0 5 12. 5 2

13. 5 2 14. 4 0 15. 3 4 16. 1 7

Write the integers in order from least to greatest. Draw a number line if you wish.

17. 6, 2, 3, 0 18. 2, 8, 1, 5 19. 7, 2, 1, 1 20. 3, 4, 9, 10

21. 4, 0, 6, 6 22. 1, 2, 3, 4 23. 10, 5, 6, 7 24. 4, 6, 5, 3

25. 7, 8, 8, 6 26. 0, 2, 2, 1 27. 5, 2, 6, 3 28. 4, 9, 1, 6

Name Date

Copyright Houghton Mifflin Company. All rights reserved. Use with text pages 588590.

Practice22.2

Test Prep

29. On the same day in January, the temper-ature in Bangor, Maine was 14; inBarrow, Alaska it was 29; in Sapporo,Japan it was 4; and in Moscow, Russiait was 14. Which of the following

shows the correct order of cities, fromcoldest to warmest, on that day?

A Sapporo, Moscow, Bangor, Barrow

B Moscow, Barrow, Bangor, Sapporo

C Bangor, Sapporo, Barrow, Moscow

D Barrow, Moscow, Sapporo, Bangor

30. The average surface temperature ofEarths moon is about 130C. Pluto isabout 240C. In comparison, Jupitersmoon, Io, averages about 143C andanother of its moons, Europa, averages

about

173C. Which of these bodieshas the greatest average temperature?


2/24

Name Date

Compare and Order IntegersCompare 4 1.


Reteach22.2

Step 1: Draw a number line. Plot points for the

two integers.

Step 2: Compare. The number on the right is

the greater number.

4 is less than 1.4 15 4 3 2 1 0 1 2 3 4 5

Compare. Draw a number line from 4 to 4 and label each integer.

Write , , or for each oval.

1. 46 2. 2 0 3. 3 0

4. 21 5. 44 6. 21

7. 22 8. 32 9. 42

10. 43 11. 33 12. 01

13. 13 14. 22 15. 32


3/24


4/24


Homework22.2

Name Date

Compare and Order Integers

Comparing Integers

Order 1, 2 and 3 from least to greatest.

The integer farthest to the left is the least, and the integer farthest to the right is the greatest.

3 2 1

Compare. Draw a number line from 8 to 8 and label each integer. Write , ,

or for each.

1. 3 0 2. 1 4 3. 5 1 4. 2 0

5. 1 4 6. 5 2 7. 1 7 8. 4 3

9. 5 7 10. 1 1 11. 5 0 12. 4 6

13. 0 7 14. 3 2 15. 4 4 16. 5 4

Write the integers in order from least to greatest. Draw a number line if you wish.

17. 4, 7, 3, 0 18. 3, 5, 2, 1

19. 12, 8, 9, 10 20. 1, 3, 2, 2

Problem Solving

21. At 6 A.M. the temperature in Oakvillewas between 1F and 5F. Namethree possible temperatures in Oakvilleat 6 A.M.

Show Your Work

1234 1 20


5/24


Show Your Work

Name Date

Compare and Order Integers

1. At the 2002 U.S. Womens Golf Open,the top three finishers had the followingscores: 4, 3, 2. The least score wins.Place the golfers scores in order frombest to worst.

2. Write three scores that are better thanthe worst score in Problem 1 but not asgood as the middle score in Problem 1.

3. Sarah ordered these integers fromleast to greatest: 2, 3, 4, 5. Explainwhat Sarahs mistake was. Then tellthe correct answer.

4. Write a mixed number, a decimal, and animproper fraction that are between 1and 2.

5. Are all negative rational numbers lessthan all positive rational numbers?Explain.

ProblemSolving22.2


6/24

Use with text pages 588590.

Name Date

Copyright Houghton Mifflin Company. All rights reserved.

EnglishLearners22.2Compare and Order Integers

Circle the word or phrase that best describes the relationship between the integers.

1. Of the floor numbers one, two, and three, one is the (lower, lowest).

2. Negative three is less than negative one. That means that negative one is(greater, greatest) than negative three.

3. One is greater than zero. That means that zero is (less, least) than one.

4. Charlene has eight more points than Dominique. That means that Dominique has eight(fewer, fewest) points than Charlene.

5. The living room is 300 square feet, the kitchen is 200 square feet, and the bedroom is

250 square feet. The living room is the (larger, largest) room.

The phrase in ordermeans in sequence.

List in order the integers between each pair. Use the number line if you need help. An

example has been done for you.

-5 -4 -3 -2 -1 1 2 3 4 50

The chart below shows some words that are used to compare integers.

Root Word -er -est

great greater greatest

high higher highest

low lower lowest

large larger largest

small smaller smallest

few fewer fewest

Example: (1, 3) 0, 1, 2

6. (1, 5) 7. (5, 0)

8. (2, 2) 9. (4, 1)


7/24

Name Date


Practice22.3

Model Addition of IntegersUse two-color counters to find each sum.

1.

4

3 2.

3

3 3.

4

1 4.

10

2

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

9. 2 6 10. 4 1 11. 3 7 12. 2 6

13. 0 6 14. 5 3 15. 1 9 16. 4 8

17. 9 6 18. 9 10 19. 2 2 20. 1 2

Use two-color counters to find each sum.Then compare. Write, , or .

21. 2 5 3 1 22. 3 6 6 3 23. 5 1 5 1

24. 7 2 3 4 25. 4 5 8 3 26. 1 1 1 1

Test Prep

27. On the first play of the football game,Curtis ran for a 5-yard gain. The next

time he carried the ball, he was tackledin the backfield for a 9-yard loss. Whatwas his total yardage on the two plays?

A 14 C 4

B 4 D 14

28. At the beginning of one dry season, thelevel of a certain African river was

already 2 feet below normal. It droppedanother 5 feet by the end of the season.The next year, the river level began thedry season 3 feet above normal, anddropped another 8 feet by the end of theseason. Did the river reach a lower pointin the first or the second year?


8/24


Reteach22.3

Name Date

Model Addition of IntegersWrite the addition expression shown by the

counters and then find the answer.

White counters represent positive numbers.Black counters represent negative numbers.

Solve 5 7.

Step 1: Match opposites. Each pair of oppo-

sites equals zero.

Step 2: Count the leftover counters.

They represent the sum.

There are 2 black counters leftover.

The sum is

2.5 7 2

Write the addition expression shown by the counters and find the sum.

1. 2.

3. 4.

Use two-color counters to find each sum.

5. 4 4 6. 3 4

7. 4 1 8. 2 5


9/24

Name Date


Enrichment22.3

Close to 0On a separate sheet of paper, copy the numbers from 9 to 9. The object of the gameis to score as close to 0 as possible.

Player A chooses an integer, crosses it out, and then records it on the scoresheet.Player B chooses a different integer, crosses it out, and records it on the scoresheet.Play continues until only one integer remains.

Each time an integer is chosen, that player adds the score to the total. Use a numberline to help add the integers, if necessary. Both players add the final integer to their scores.

The player with a final score that has an absolute value closer to 0 isthe winner. Play 3 times, each time with a different player going first.

1. How did you decide which integers to choose?

2. Did it help to go first or second? Why?

3. How do you think the game would change if you used a spinner

or a number cube to pick the numbers?

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

Round 1 2 3 4 5 6 7 8 9 10

Player A

Total

Player B

Total


10/24

Name Date


Homework22.3

Model Addition of IntegersFind 4 5.

Step 1: Use circles to show

negative integers.

Step 2: Use squares to show

positive integers.

Step 3: Match each circle to

a square.

Write the addition expression shown by the circles and squares and then find the sum.

1. 2.

Use models to find each sum.

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

7. 6 10 8. 11 6 9. 3 2 10. 10 3

Use models to find each sum. Then compare. Write, , or .

11. 7 2 1 6 12. 8 7 0 5 13. 2 9 15 4

Problem Solving

14. At noon the temperature was 54F. Atsunset the temperature was 50F. Writean integer to represent the change intemperature.

Show Your Work

Since 1 square remains, the sum is positive 1.

4 + 5 = 1


11/24

Name Date


Practice5.3

Model Addition of IntegersUse the data from the chart to solve Problems 14.

Show Your Work1. Through 6 holes Alexia has a score

of 2. On the seventh hole she getsa birdie. What is Alexias score now?

2. Using three different scores, how coulda golfer get a score of 1?

3. Bobby had a score of

1 until he gotan eagle. He said his score is now 1.Explain what Bobbys mistake was.Then tell the correct answer.

4. What score would someone have if theygot birdie, par, birdie, and eagle?

ProblemSolving22.3

Golf Scoring

Name Eagle Birdie Par Bogey Double Bogey Triple Bogey

Score 2 1 0 1 2 3

5. When is the sum of a positiveinteger and a negative integer 0?Give an example.


12/24


Name Date EnglishLearners22.3Model Addition of Integers

Underline the words that tell whether the underlined integers are positive or negative.

Then write the positive or negative integers. An example has been done for you.

Example:Melissas body temperature was degree normal when she woke up

in the morning. By the afternoon, her temperature another degrees.

1, 3

1. A farmer plants 8 fewer acres of corn than normal. He plants 3 more acres ofsoybeans instead.

2. In May, the level of a towns water supply drops 6 inches below normal. In June, itrises 2 inches.

3. Enrique grew 2 inches last year. This year, he grew another 3 inches.

4. For six months, rainfall in an area was 5 inches below normal. During the nextsix months, rainfall was another 3 inches below normal.

5. The amount of annual snow the region received was 10 inches less than last year.The amount of rainfall the region received was 6 inches more than last year.

3had risen

above1

To solve a word problem, look for words that tell whether an integer ispositive or negative. The chart below shows some words that often

describe positive and negative integers.


Negative Positive

less greater

fewer more

below above

fell grew

drop rise

lower higher


13/24

Name Date

Model Subtraction of IntegersUse two-color counters to find each difference.

1.

4

3 2.

6

2 3.

5

1 4.

4

5

5. 5 6 6. 2 3 7. 1 9 8. 2 8

9. 7 7 10. 3 2 11. 6 9 12. 4 4

13. 3 3 14. 4 2 15. 3 10 16. 6 1

17. 7 1 18. 3 5 19. 1 2 20. 5 1

Use two-color counters to find each difference. Then compare. Write , , or .

21. 3 1 4 2 22. 5 9 4 10 23. 4 2 4 2

24. 2 2 9 9 25. 7 4 6 9 26. 2 6 7 1


Practice22.4

Test Prep

27. During a recent dry spell, the water levelin a local reservoir dropped 7 feet duringJuly and another 4 feet during August.Which of the following shows how muchthe water level dropped during July andAugust?

A 7 4 C 7 4

B 7 4 D 4 7

28. Brian earned money shoveling snow inhis neighborhood. He spent $5 on abook and $3 on a snack. How muchless money did he have after he madehis purchases? Express your answeras a negative integer.


14/24

Name Date

Model Subtraction of IntegersUse a model to find 6 3.


Reteach22.4

Step 1: You can use black

counters to represent negative

numbers, and white counters to

represent positive numbers. Use

black counters to represent 6.

Step 2: You need to subtract3, but there are no white

counters to take away. You can

add pairs of black and white

counters as needed. This is the

same as adding zero.

Step 3: The black counters

that are left are the answer.

Write a subtraction expression for each.Then find the difference.

1. Take away 3 black counters. 2. Take away 7 white counters.

3. Take away 2 white counters. 4. Take away 6 black counters.

Use two-color counters to find each difference.

5. 5 7 6. 3 4 7. 1 3 8. 5 2

6 3 9


15/24

Name Date

Subtract Til You DropMake a deck of 18 cards with the integers 9 to 9, but skip 0. Play with a partner.

Player A chooses two cards. The integer on the second card is subtracted from the integer onthe first card. Use a number line to help, if necessary. Record the score on the scoresheetand discard the cards.

Player B repeats the steps.

After Player Bs first turn, players alternate picking 1 card and subtractingthat integer from the total. Low score wins.

1. What subtraction sentence would give you the lowest score?

2. What subtraction sentence would give you the greatest score?

3. If you were to pick your own numbers instead of using the cards,how do you think the game would change?


Enrichment22.4

Round 1 2 3 4 5 6 7 8

Player A

Total

Player BTotal


16/24


Homework22.4

Name Date

Model Subtraction of IntegersFind 3 1.

Step 1: Use circles to show

negative integers. Use squares

to show positive integers.

Step 2: You need to subtract1 but there are no squares to

take away. Add a circle and a

square to show 0.

Step 3: Take away a square

to subtract 1. What is left?

Write a subtraction expression for each.Then find the difference.

1. 2.

Take away 2 squares. Take away 7 circles.

Use models to find each difference.

3. 1 5 4. 2 3 5. 6 1 6. 2 2

7. 9 11 8. 7 5 9. 8 5 10. 8 1

11. 12 9 12. 11 6 13. 7 3 14. 5 10

Problem Solving

15. Amy deposited $25 into her savingsaccount. Later that month she withdrew$17. What integer shows the net changein the amount of money in her account?

Show Your Work

Since 4 circles remain, the difference is negative 4.

3 1 4


17/24


Show Your Work

Name Date

Model Subtraction of Integers

1. What is the difference when yousubtract 3 from 2?

2. What is 5 3?

3. Eileen wrote that 4 4 0. Explainwhat Eileens mistake was. Then tell thecorrect answer.

4. The sum of two integers is 3. Thedifference of the same two integersis 13. What are the integers?

ProblemSolving22.4

5. If a negative integer is subtracted froma positive integer, can the answer be 0?Explain and give an example.


18/24


Name Date


EnglishLearners22.4Model Subtraction of Integers

Read the meanings of take listed below. Then write the number of the correct meaning of

take for each sentence.

take 1. to get into ones possession; to capture or seize

2. to receive into ones body, consume

3. to choose, select

4. to subtract

1. I think Im going to take gym insteadof skating this year.

2. The teacher is going to take mycandy if I open it in class.

3. How many counters will you takeaway to subtract 4?

4. After being in school all day, I neededto take a breath of fresh air.

Practice taking away, or subtracting, integers. Find each difference. Use two-color

counters to help you.

5. 3 4 6. 2 6

7.+3 8 8. 9 9

The word take has many meanings. In mathematics, takemeansto subtract. It is often used in the phrase take away.


19/24

Name Date


Practice22.5

Add and Subtract IntegersDecide whether the answer will be positive or negative. Then use the number line

to add or subtract.

1. 6 4 2. 7 6 3. 1 6 4. 6 7

5. 5 3 6. 1 8 7. 9 2 8. 2 6

9.

4

2 10.

8

10 11.

0

1 12.

8

6

13. 4 5 14. 3 5 15. 2 3 16. 1 2

17. 7 3 18. 8 5 19. 3 4 20. 4 9

Solve each equation. Use a number line to help you.

21. 15 x 3 22. 8 x 6 23. x 5 1

24. x 8 17 25. 3 x 9 26. x 7 10

Test Prep

27. On Monday, the temperature at 7 P.M.dropped 18 degrees below what it hadbeen the day before. On Tuesday, thetemperature at 7 P.M. was 14 degreeswarmer. What integer shows the overallchange in temperature from Sunday toTuesday?

28. The highest average temperature inBeijing, China is a very hot 30C. Thelowest average temperature is 38Ccolder than that. What is the lowestaverage temperature for Beijing?

5

6

7

8

1

2

3

4

12

13

14

15

9

10

11 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


20/24


Reteach22.5

Name Date

Add and Subtract Integers

Use these rules to add and subtract integers.

For addition: Examples:

If two numbers have the same sign, keep the sign, and add 4 7 (4 7) 11

the absolute value of the numbers. The sum of two positive 3 9 (3 9) 12

numbers is positive.The sum of two negative numbers is

negative.

If two numbers have different signs, subtract the 7 4 (7 4) 3

absolute values of the numbers. The answer has the 6 8 (8 6) 2

sign of the number with the higher absolute value.

For subtration:

To subtract a number, add its opposite. Then use the 3 8 3 8 5

rules for addition. 7 10 7 10 3

7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

Decide whether the answer will be positive or negative.

Then use the number line to add or subtract.

1. 8 3 2. 6 9 3. 8 10 4. 8 4

5. 10 4 6. 5 1 7. 1 3 8. 10 4

9. 7 5 10. 9 5 11. 9 3 12. 9 8


21/24

Name Date


Enrichment22.5

Last Integer StandingAll of the integers from 10 to 10 will be used for this activity. Each questionwill help you solve the next question. Each integer will be used only once.

When an integer is used, cross it out.

1. Write a subtraction sentence with a difference of 20.

2. Write a subtraction sentence to find the least sum that is still possible.

3. Use the two remaining opposite integers with the greatest absolute valueto write an addition sentence with a sum of 0.

4. Write an addition sentence using the three largest remaining integers.

5.

What is the greatest difference you can write using the integers that still remain?

6. What is the least difference you can write using the integers that still remain?

7. Write an addition sentence using three remaining integers to get a sum of 9.

8. Write an addition sentence using four remaining integers to get a sum of 2.

9. The last integer standing is .

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


22/24

Name Date


Homework22.5


Rules for Adding and Subtracting Integers You can turn any subtraction expression into addition by adding the opposite

The sum of two positive integers is positive.

The sum of two negative integers is negative.

The sum of a positive integer and a negative integer will have the same sign as the integer with the

greater absolute value.

Decide whether the answer will be positive or negative. Then use

the number line to add or subtract.

1. 0 6 2. 3 11 3. 9 1 4. 6 4

5. 11 4 6. 12 8 7. 3 6 8. 4 7

9. 6 9 10. 12 5 11. 5 0 12. 8 2

Problem Solving

13. Stacey got on an elevator on the ground

floor. She rode up 8 floors, then down5 floors and got off. On what floor didStacey get off the elevator?

Show Your Work

5

6

7

8

1

2

3

4

12

13

14

15

9

10

11 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


23/24

Name Date



Show Your Work1. In 2001, the lowest temperature in

Anchorage, Alaska, was 15F. Thelowest temperature in Fairbanks, Alaska,was 41F. How many degrees colderwas the lowest temperature in Fairbanks?

2. The lowest temperature in Chicago, Illinois,was 27F. The lowest temperature in

Portland, Maine, was 12 colder. Whatwas the lowest temperature in Portland?

3. The lowest temperature ever recordedin Florida was 2F. If you subtract 38,you will find the lowest temperatureever recorded in Arizona. What is that

temperature?

4. The lowest temperature in Bismarck,North Dakota, was 44F. If you subtract153, you will find Bismarcks highesttemperature. What is that temperature?

5. Can you subtract two positive numbersand get a negative number? Explainand give an example.

ProblemSolving22.5


24/24

Add and Subtract IntegersRead this problem and then follow the steps to solve it.

Problem: On a warm day, 5 inches of snow melted. That night a storm brought 10 inchesof snow. If there is now 20 inches of snow, how much snow was there in the beginning?

STEP 1: Make sure you understand key terms.

warmhaving moderate heat snowice crystalsthat fall to the earth

meltchange from solid to liquid beginninga startby heat

stormweather with heavy wind,rain, or snow

STEP 2: Identify what the problem asks. Write the question you must answer:

STEP 3: Make a number line for the problem. Start with the line below.

STEP 4: On the number line, start at 0. Make arrows to show the change

in the amount of snow. Include the amount that melted and the

amount that fell. Write this change as a positive or negative integer:

STEP 5: Write an equation. Show the relationship between the amount of snownow (20 inches) and the change in the amount of snow (your integer

from Step 4). Solve the equation.

20 amount of snow at beginning

amount of snow at beginning

0

Use with text pages 598600.Copyright Houghton Mifflin Company. All rights reserved.

Name Date EnglishLearners22.5

Integers Practic

Documents

Transcript of Integers Practic