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8/12/2019 Integers Practic
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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
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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?
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Compare and Order IntegersCompare 4 1.
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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
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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
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Show Your Work
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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
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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)
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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?
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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
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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
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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
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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.
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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.
Use with text pages 592594.
Negative Positive
less greater
fewer more
below above
fell grew
drop rise
lower higher
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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
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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.
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Model Subtraction of IntegersUse a model to find 6 3.
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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
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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?
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Enrichment22.4
Round 1 2 3 4 5 6 7 8
Player A
Total
Player BTotal
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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
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Show Your Work
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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.
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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.
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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
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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
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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
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Homework22.5
Add and Subtract Integers
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
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Add and Subtract Integers
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
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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
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Name Date EnglishLearners22.5