Name _______________________________ Date ____________________Mrs. Labuski / Mrs. Portsmore Period ______ Mid- Module 3 Review

1. True or False?

______a. Negative numbers are less than positive numbers.

______b. 0 is less than all negative numbers.

______c. Zero is not positive or negative.

______d. A negative number can be a rational number.

______e. The absolute value of a negative number will always be a positive number.

______f. The absolute value of any number will always be a positive number.

______g. Positive numbers will always have a higher absolute value than negative numbers.

______h. The order of positive numbers is the same as the order of their absolute values.

______i. The order of negative numbers is the opposite order of their absolute values.

______j. Two integers can have the same absolute value

2. Always, Sometimes, or Never

__________________a. Will the opposite of a positive number always, sometimes, or never be a positive number?

__________________b. Will the opposite of zero always, sometimes, or never be zero?

__________________c. Will the opposite of a number always, sometimes, or never be greater than the number itself?

__________________d. A decimal can be a rational number

__________________e. One integer can have two absolute values.

__________________f. Any given absolute value, will there always be two numbers that have that absolute value?

3. The table shows the elevations of several locations in a state park. Graph the locations on a number line according to their elevations.

LocationLittle Butte

ACradle Creek

BDinosaur Valley

CMesa Ridge

DJuniper Trail

E

Elevation (ft) −8 5 −7 8 −3

a) What point on the number line represents sea level? ______________________________

b) Which location is closest to sea level? _________________________________________

c) Is location C above or below sea level? ________________________________________

d) Which two locations are the same distance from sea level? ________________________

_____________________________________________________________________________

4. Identify two words that represent a “positive integer” or addition to your bank account.

_________________________ _________________________

5. Identify two words that represent a “negative integer” or subtraction from your bank account.

_________________________ _________________________

6. Write an integer to represent each of the following situations:

a) A plane takes off and reaches 1000 ft. of altitude. ____________

b) John owes his best friend $20. ____________

c) The temperature hit a high of -4 degrees Celsius ____________

d) The baseball was hit 420 feet. ____________

e) You earn $ 50 for babysitting one Friday night. ____________

f) A debit of $17 appears on your bank statement. ____________

7. A credit of $55 and a debit of $70 are applied to your checking account. What is an

appropriate scale to graph a credit of $55 and a debit of $70? Explain.

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

8. Read each statement about a real-world situation and the two related statements. Circle the correct way to describe each situation. If both ways are true, circle both letters.

The highest elevation of Dix Hills, New York with respect to sea level is given as 299 feet.

a. The highest point of Dix Hills is +299 feet.

b. The highest point of Dix hills is 299 feet above sea level.

Xavier’s body weight went up 7 pounds after he broke his leg.

a. Xavier’s weight increased 7 pounds.

b. The integer 7 represents the change in Xavier’s body weight in pounds.

9. On the number line below, locate the opposites of the numbers on the number line.

A. 5 B. -3 C. 7 D. -8

10. Write the integer that represents the opposite of each real-world situation. In words, write the meaning of the opposite:

A. A gain of 15 pounds

B. A withdrawal of $20

C. A loss of 12 yards in football

D. Two degrees below zero

11. Read each description carefully and write an equation that represents the description.

a. The opposite of negative five.

b. The opposite of the opposite of thirty - two.

c. The opposite of twenty six.

d. The opposite of negative fifty-eight.

12. Read each real-world description. Write the integer that represents the opposite of the opposite. Show your work to support your answer.

a. temperature rise of degrees Fahrenheit.

b. gain of yards.

c. A loss of pounds.

d. A withdrawal of .

13. Write the integer that represents the statement. Locate and label each point on the number line below.

e. The opposite of a gain of .

f. The opposite of a deposit of .

g. The opposite of the opposite of .

h. The opposite of the opposite of .

i. The opposite of the opposite of a loss of .

14. In math class, Jody claimed the following: Since 5 is greater than 4 , -5 must be greater

than -4 . Explain whether or not Jody is correct.

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

15. Order the following rational numbers from least to greatest:

-3.5, -3 , 3.25, - , 3, -3.2, 2.75, 2

16. For each of the relationships described below, write an inequality that relates the rational numbers.

a) A loss of $500 in the stock market is worse than a gain of $300 in the stock market.

b) A quiz score of 58 is worse than a quiz score of 57, and a quiz score is worse than a quiz score of 59 ½.

c) In February the total snowfall was 15.3 inches, which is more than the total snowfall in January and March which was 5.7 and 7.4 inches.

d) Nine and one-fourth yards of material is less than three-fourths yards of material.

17. Fill in the blanks with numbers that correctly complete each of the inequalities statements.

a) Three integers between -2 and 2 _____<_____<______

b) Three rational numbers between 18 and 17 _____<_____<____

c) Three integers between 3 and -3 _____<______<_____

18.

Number Absolute Value Number Line Diagram

Different Number with the

same Absolute Value

18. For each of the following two quantities, which has the greater magnitude? (Use absolute value to defend your answers.)

a) 600 feet below sea level and 500 feet above sea level ______________________

b) $450 lose and a $45.00 credit ______________________

c) deposit of $1,250 and a withdrawal of $1,205 ______________________

d) 13.05 feet and 13 feet ______________________

e) 25 degrees and 25 degrees ______________________

f) 33.37 tons and 33.375 tons ______________________

19. The following temperatures were reported as the high temperatures each day for one week in January in Anchorage, Alaska. Represent each reported temperature using a rational number and then order the rational numbers from least to greatest.

Temperatures as Reported

below zero

above zero

below zero

below zero

above zero

below

zero

Temperature (F)

20. As you approach zero from the left on the number line, the integers __________, but

the absolute values of those integers ________________. This means that the order of

negative integers is __________ the order of their absolute values.

21. Mason was ordering the following rational numbers in math class:

j. Order of the numbers from least to greatest.

k. List the order of their absolute values.

l. Explain why the orderings in parts (a) and (b) are different.

Name _______________________________ Date ____________________Mrs. Labuski / Mrs. Portsmore Period ______ Mid- Module 3 Review

1. True or False?

__T____a. Negative numbers are less than positive numbers.

__F____b. 0 is less than all negative numbers.

___ T __c. Zero is not positive or negative.

__ T ___d. A negative number can be a rational number.

__ T ___e. The absolute value of a negative number will always be a positive number.

__ T ___f. The absolute value of any number will always be a positive number.

__F____g. Positive numbers will always have a higher absolute value than negative numbers.

___ T __h. The order of positive numbers is the same as the order of their absolute values.

_ T _____i. The order of negative numbers is the opposite order of their absolute values.

__ T __j. Two integers can have the same absolute value

2. Always, Sometimes, or Never

____ ___never_________a. Will the opposite of a positive number always, sometimes, or never be a positive number?

_____always__________b. Will the opposite of zero always, sometimes, or never be zero?

______sometimes_____c. Will the opposite of a number always, sometimes, or never be greater than the number itself?

____sometimes_______d. A decimal can be a rational number

______never_________e. One integer can have two absolute values.

________sometimes___f. Any given absolute value, will there always be two numbers that have that absolute value?

3. The table shows the elevations of several locations in a state park. Graph the locations on a number line according to their elevations.

LocationLittle Butte

ACradle Creek

BDinosaur Valley

CMesa Ridge

DJuniper Trail

E

Elevation (ft) −8 5 −7 8 −3

a) What point on the number line represents sea level? ___0__________________________

b) Which location is closest to sea level? _____Juniper Trail (E)_____________________

c) Is location C above or below sea level? __below________________________________

d) Which two locations are the same distance from sea level? ________________________

Little Butte and Mesa Ridge

4. Identify two words that represent a “positive integer” or addition to your bank account.

____deposit________________ ____credit_______________

5. Identify two words that represent a “negative integer” or subtraction from your bank account.

_______withdrawal_________ ___debit_______________

6. Write an integer to represent each of the following situations:

g) A plane takes off and reaches 1000 ft. of altitude. __+1000_______

A BC E D

h) John owes his best friend $20. __-20________

i) The temperature hit a high of -4 degrees Celsius __-4__________

j) The baseball was hit 420 feet. __420________

k) You earn $ 50 for babysitting one Friday night. __50__________

l) A debit of $17 appears on your bank statement. __-17_________

7. A credit of $55 and a debit of $70 are applied to your checking account. What is an

appropriate scale to graph a credit of $55 and a debit of $70? Explain. I would count by

because both numbers are multiples of .

8. Read each statement about a real-world situation and the two related statements. Circle the correct way to describe each situation. If both ways are true, circle both letters.

The highest elevation of Dix Hills, New York with respect to sea level is given as 299 feet.

a. The highest point of Dix Hills is +299 feet.

b. The highest point of Dix hills is 299 feet above sea level.

Xavier’s body weight went up 7 pounds after he broke his leg.

a. Xavier’s weight increased 7 pounds.

b. The integer 7 represents the change in Xavier’s body weight in pounds.

9. On the number line below, locate the opposites of the numbers on the number line.

A. 5 B. -3 C. 7 D. -8

10. Write the integer that represents the opposite of each real-world situation. In words, write the meaning of the opposite:

DA BC

A. A gain of 15 pounds -15

B. A withdrawal of $20 20

C. A loss of 12 yards in football 12

D. Two degrees below zero 2

11. Read each description carefully and write an equation that represents the description.

. The opposite of negative five. 5

. The opposite of the opposite of thirty - two. 32

. The opposite of twenty six. -26

. The opposite of negative fifty-eight. 58

12. Read each real-world description. Write the integer that represents the opposite of the opposite. Show your work to support your answer.

a. temperature rise of degrees Fahrenheit. 22

b. gain of yards. 24

c. A loss of pounds. -15

d. A withdrawal of . -5000

13. Write the integer that represents the statement. Locate and label each point on the number line below.

. The opposite of a gain of . -8

. The opposite of a deposit of . -12

. The opposite of the opposite of . 0

. The opposite of the opposite of . 2

. The opposite of the opposite of a loss of . -4

14. In math class, Jody claimed the following: Since 5 is greater than 4 , -5 must be greater

than -4 . Explain whether or not Jody is correct.

Jody is not correct. - 5 is further to the left on the number line so it has less value. -4 is

further to the right on the number line so it has a larger value.

15. Order the following rational numbers from least to greatest:

-3.5, -3 , 3.25, - , 3, -3.2, 2.75, 2

- , -3 , -3.5, -3.2, 2 , 2.75, 3, 3.25,

16. For each of the relationships described below, write an inequality that relates the rational numbers.

a) A loss of $500 in the stock market is worse than a gain of $300 in the stock market.

-500< 300

ab c de

b) A quiz score of 58 is worse than a quiz score of 57, and a quiz score is worse than a quiz score of 59 ½.

57< 58< 59½

c) In February the total snowfall was 15.3 inches, which is more than the total snowfall in January and March which was 5.7 and 7.4 inches.

15.3 > 7.4 > 5.7

d) Nine and one-fourth yards of material is less than three-fourths yards of material.

9¼ < ¾

17. Fill in the blanks with numbers that correctly complete each of the inequalities statements.

a) Three integers between -2 and 2 _-1____<__0___<__1___

b) Three rational numbers between 18 and 17 __17.25___<__17.5___<_17.75___

c) Three integers between 3 and -3 __-2___<___0___<__1___

(answers may vary for “b” and “c”)

18.

Number Absolute Value Number Line Diagram

Different Number with the

same Absolute Value

│-9│= 9 9

│2│= 2 -2

│-7│= 7 7

18. For each of the following two quantities, which has the greater magnitude? (Use absolute value to defend your answers.)

a) 600 feet below sea level and 500 feet above sea level _____600______________

b) $450 lose and a $45.00 credit ___450___________________

c) deposit of $1,250 and a withdrawal of $1,205 __1250____________________

d) 13.05 feet and 13 feet _13_____________________

e) 25 degrees and 25 degrees ______25 ¼ ________________

f) 33.37 tons and 33.375 tons ____33.375__________________

19. The following temperatures were reported as the high temperatures each day for one week in January in Anchorage, Alaska. Represent each reported temperature using a rational number and then order the rational numbers from least to greatest.

Temperatures as Reported

below zero

above zero

below zero

below zero

above zero

below

zero

Temperature (F) -6 15 -4 -12 0 4 -9

-12 < -9 < -6 < -4 < 0 < 4 < 15

20. As you approach zero from the left on the number line, the integers

__increase________, but the absolute values of those integers ___

decrease______________. This means that the order of negative integers is _

opposite__________ the order of their absolute values.

21. Mason was ordering the following rational numbers in math class:

. Order of the numbers from least to greatest.

-15 < < -3.3

. List the order of their absolute values.

3.3 < < 15

. Explain why the orderings in parts (a) and (b) are different.

The order of negative numbers is the opposite order of their absolute values.