Name: ______________________________________

Math 7RUnit #1 - The Number System

Chapter #1A – INTEGERSUnit 1A Goals:Established Goals:7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers (INTEGERS); represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers (INTEGERS).

7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Integers)

Student self-assessment checklist: 1) I understand the difference between Counting #’s, Whole #’s and Integers.

2) I can apply the commutative, associative, identity and inverse properties to perform calculations with integers.

3) I can add, subtract, multiply and divide integers.

4) I can solve real world problems involving integer operations.

AIM: SWBAT distinguish between sets of numbers.

Sets of Numbers:

Rational Numbers

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Integers

Whole Numbers

Counting Numbers

All Counting Numbers are also ____________________, ____________________ & ____________________.All Whole Numbers are also ____________________ and ____________________.All Integers are also ____________________.Answer each question with yes or no and explain your reasoning.Are all Whole Numbers Counting Numbers? _______________________________________Are all Integers Whole Numbers? ______________________________________________ Are all Integers Counting Numbers? ____________________________________________Are all Rational Numbers Integers? ____________________________________________

Place each number in ALL the sets it belongs to.

-7 0.25 12 0 4

Rational Numbers

2

Integers

Whole Numbers

Counting Numbers

Answer each question with… ALWAYS SOMETIMES NEVER

1) Whole Numbers are Integers. A S N2) Counting Numbers are Rational A S N3) Rational Numbers are Whole Numbers A S N4) Integers are Counting Numbers A S N5) Whole Numbers are Rational A S N

HOMEWORK – SETS OF NUMBERS

**Use the chart we made in class to help you answer these questions!**

Answer the following with…. SOMETIMES ALWAYS NEVER

1) Counting Numbers are Whole Numbers. S A N2) Whole Numbers are Counting Numbers. S A N3) Counting Numbers are Integers. S A N4) Integers are Counting Numbers. S A N5) Counting Numbers are Rational.. S A N6) Whole Numbers are Integers. S A N7) Integers are Rational Numbers. S A N8) Rational Numbers are Whole Numbers. S A N9) Whole Numbers are Rational. S A N10) Rational Numbers are Counting Numbers. S A N

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State ALL of the sets of numbers that each of the following belongs to:

Rational Integer Whole Natural

11) 0 __________________________________________________________________

12) -5 _________________________________________________________________

13) __________________________________________________________________

14) 2.56 ________________________________________________________________

15) 20 __________________________________________________________________

16) - _________________________________________________________________

17) 0. _________________________________________________________________AIM: SWBAT compare & order integers and find the absolute value of an integer.

DO NOW:Sets Of NumbersCounting Numbers Whole Numbers Integers1, 2, 3, 4, … 0, 1, 2, 3, 4, … …,-4,-3,-2,-1, 0, 1, 2, 3, 4, …

Counting Numbers - are the Natural Numbers 1, 2, 3, 4 …Whole Numbers - all the Counting Numbers AND zeroIntegers - all the Whole Numbers AND their opposites1) All Counting Numbers are also ____________________ and ____________________2) All Whole Numbers are also _______________.3) Are all Whole Numbers Counting Numbers? _______4) Are all Integers Whole Numbers? ________ 5) Are all Integers Counting Numbers? ________

CLASSWORK: Opposite Numbers: are the same distance from zero on a number line in opposite directions.For example 5 and -5 are opposites.

________________ is a special integer because it is neither positive nor negative.Why is zero an integer? _________________________________________________

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Comparing Integers : > and < The number farther right on the number line is the larger number. >_______________ <________________36 > 12 “36 is greater than 12” 15 < 29 “15 is less than 29”Compare using > or <. 1) 15 _____ 25 2) 92 _____ 63 3) 0 _____ 12 4) -3 _____ 15) -5 _____ 0 6) -5 _____ -18 7) -12 _____ 12 8) -2 _____ -5

Ordering Integers:Order from least to greatest.9) -5, -9, 0, -3 _________________ 10) -2, 7, -5, -1 _________________

**The three questions most often missed about Integers**1) Name a number that is not an integer? __________2) Name the largest negative integer. __________3) Name the smallest positive integer. __________

Absolute Value measures the _________________ a number is from zero on the number line. Distance is always POSITIVE, therefore, Absolute Value is ALWAYS________________.The symbol for absolute value is “| |.”|4| “ What is the absolute value of 4?” |4| = _______|-4| “What is the absolute value of -4?” |-4| = _______

True or False-4 = 4 ________________ |-4| = |4| _______________ **Absolute value bars are evaluated like parenthesis. Do whatever is inside the bars first, and then find the absolute value. Examples: |-4| + |5| |0 + -2| 4 + 5 |-2| 9 2 1) |16| + |-16| 2) |-24 + 0| 3) |12| + |-7| 4) |-20| + |-9|

The negative symbol “- “ means opposite. For example the “opposite of 4” is -4.Simplify the expression. (Start from the inside and work it out)

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5) - (-4) _____ 6) - (- (-4)) _____ 7) - [- (- (-4))] _____

8) -|-4| _____ 9) - (- |-4|) _____ 10) - - - |-4| _____

HOMEWORK – INTRODUCTION TO INTEGERS Order the integers from least to greatest:

1) 17, -16, -8, 7, 2, 2) -16, -24, 25, 11, -56, -136

___________________________ ___________________________

3) -5, -1, 4, 6, -10, 0 4) 8, -15, 17, -39, 73,

___________________________ ___________________________

First write the OPPOSITE and then write the ABSOLUTE VALUE of each integer: 5) 7 ______ ______ 6) -25 ______ ______

7) 106 ______ ______ 8) -241 ______ ______

Complete the Statement with or .

9) -6 _____ 4 10) -2 _____ -4 11) 0 _____ 8

12) -11 _____ -3 13) 31 _____ -16 14) -24 _____ -28

Match the integer expression with the verbal expression:

_____ 15) -|12| A) the opposite of negative twelve

_____ 16) |-12| B) the absolute value of twelve

_____ 17) - (-12) C) the opposite of the absolute value of twelve_____ 18) |12| D) the absolute value of negative twelve

Simplify the expression.19) |-15| 20) - (-9) 21) |-16|

22) -|-16| 23) - (-|49|) 24) - (- (-34))

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The table below shows the distances of the runners from the finish line when the winner won the race. Use the table to answer Questions 25 – 27.

Runner Distance (ft)Sarah -16Beth -2

Juanita 0Tamika -9Ingrid -36

25) Who won the race? ____________________

26) Who finished further back, Sarah or Tamika? ____________________

27) Arrange the girls’ names in order from first-place to last-place finish.

____________ ____________ ____________ _____________ _____________ 1st Place 2nd Place 3rd Place 4th Place

5th Place

28) Name a number that is not an integer. __________29) Name the largest negative integer. __________30) Name the smallest positive integer. __________31) State the first 5 Counting Numbers ____________________32) Whole Numbers are all the ____________________ and ____________________.33) Integers are all the ____________________ and ____________________.34) All Counting Numbers are also ____________________ and ____________________.35) All Whole Numbers are also ____________________.36) Are all Whole Numbers Counting Numbers? _______37) Are all Integers Whole Numbers? ________

AIM: SWBAT identify properties of addition and multiplication and begin adding integers.DO NOW:

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Write the opposite of each integer.1) 3 _______ 2) -5 _______ 3) -7 _______ 4) 9 _______Evaluate.

5) |-12| _______ 6) |9| _______ 7) |-2| _______ 8) |-12| + |-1| __Compare using or .

9) 8 _____ -6 10) -7 _____ -4 11) -9 _____ 5 12) 7 _____ 2Order from least to greatest.

13) -1, -6, 0, -3, -5 ______________________

14) -18, -20, -15, -17 ______________________

Properties of Addition and Multiplication1) Commutative Property of Addition and Multiplication: (Commutative, x; Commutative, +)

Changing the order of the numbers without changing the answer. (#’s commute)Examples: A) 2 + 3 = 3 + 2 B) 4(5) = 5(4)

2) Associative Property of Addition and Multiplication: (Associative, x; Associative, +)

Moving the grouping symbols without changing the answer.Examples: A) 6 + (2 + 3) = (6 + 2) + 3 B) 7(4 ● 6) = (7 ● 4)6

3) Additive Identity Property: (Identity, +) Identity of # does not change

Any number plus zero equals that number. *The identity element of addition is zero.Examples: A) 9 + 0 = 9 B) x + 0 = x

4) Multiplicative Identity Property: (Identity, x) Identity of # does not change

Any number times one is that number. * The identity element of multiplication is one.

Examples: A) 4 ● 1 = 4 B) x ● 1 = x5) Additive Inverse Property: (Inverse, +)

For every number, a, a + -a = 0. *Remember: Zero is the identity element Examples: A) 9 + -9 = 0 B) -x + x = 0

6) Multiplicative Inverse Property: (Inverse, x)

For every number, a, a ● = 0 *Remember: One is the identity element

Examples: A) 4 ● = 1 B) x ● = 1

7) Multiplicative Property of Zero: (Zero, x) (Everything becomes zero)8

Any number times zero is zeroExamples: A) 10 ● 0 = 0 B) x ● 0 = 0

Name the property for each of the following:1) (13 + 7) + 8 = 13 + (7 + 8) ______________________________________2) 0 ● (x + 3) = 0 ______________________________________3) 9 ● 5 = 5 ● 9 ______________________________________4) (62 + 3) + 0 = (62 + 3) ______________________________________5) (19 + 8) + 6 = (8 + 19 ) + 6 ______________________________________6) (2 ● 3) ● 7 = 2 ● (3 ● 7) ______________________________________7) 56 ● 1 = 56 ______________________________________

8) 7 ● = 1 ______________________________________

9) -6 + (3 ● 8) = -6 + (8 ● 3) ______________________________________

10) -15 + 15 = 0 ______________________________________

Adding/Subtracting Integers

Adding integers means adding with both positive and negative numbers (the whole numbers and their opposites). There is an important fact to remember when adding integers…

● “positive 1” (+1) and “negative 1” (-1) are opposites so . . . -1 + 1 = 0, meaning opposites cancel each other out

We’re going to use Integer Chips to investigate the rules of Adding/Subtracting Integers. will represent positive numbers will represent negative numbers

2 + 2 -1 + -2 -5 + 2 -1 + 4

What rules can we come up with after using the Integer Chips:

Same Signs - ____________________ Different Signs - ____________________

Evaluate:-2 + 2 = ______ -4 + 0 = ______ -5 + 5 = ______

-2 + 5 = ______ -5 + 2 = ______ -2 + -5 = ______

-2 + 3 = ______ 2 + -3 = ______ -2 + -3 = ______

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-6 + 1 = ______ -1 + 6 = ______ -6 + -1 = ______

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HOMEWORK – PROPERTIES & INTRO TO ADDING INTEGERS

State the name of the property that is shown.

1) (x + 9) + 1 = x + (9 + 1) 1) ____________________________________

2) 1 x = x 2) ____________________________________

3) (12 + 9) + 15 = (9 + 12) + 15 3) ____________________________________

4) 12 ● (7 ● 15) = (12 ● 7) ● 15 4) ____________________________________

5) 0 + (9 + 1) = 9 + 1 5) ____________________________________

6) r ● 1 = r 6) ____________________________________

7) 106 ● 0 = 0 7) ____________________________________

8) -y + y = 0 8) ____________________________________

9) (2 + y) + 8 = 8 + (2 + y) 9) ____________________________________

10) c ● = 1 10) ___________________________________

Evaluate.11) -4 + 4 = ______ 12) -4 + -3 = ______ 13) -4 + 3 = ______

14) 4 + -3 = ______ 15) -5 + 8 = ______ 16) -1 + 7 = ______

17) -9 + 3 = ______ 18) -10 + 4 = ______ 19) -2 + -8 = ______

AIM: SWBAT add and subtract integers.

DO NOW:Evaluate.

1) -8 + 2 = ______2) -10 + 5 = ______3) -6 + 6 = ______

4) -3 + 9 = ______5) 7 + -2 = ______6) -10 + 0 = ______

ADDING & SUBTRACTING INTEGERS

I) Get rid of DOUBLE SIGNS first! + - becomes a NEGATIVE (so 7 + -3 becomes 7 – 3) - - becomes a POSITIVE (so 6 - -3 becomes 6 + 3)

II) BOX YOUR TERMS! ** The sign IN FRONT of the number goes with the number **

III) When COMBINING INTEGERS with the SAME signs⇒ADD the numbers and KEEP the same sign.

Examples:

A) 12 + 4 16

*Basic Addition – adding two positive numbers*

B) –12 + –4 –12 – 4 (get rid of double signs) –12 – 4 (box terms) –16 (Same Signs Add & Keep)

C) 25 – (–16) 25 + 16 (get rid of double signs) = 41

*Basic Addition – adding two positive numbers*

D) –25 + – 16 –25 – 16 (get rid of double signs) –25 – 16 (box terms) –41 (Same Signs Add & Keep)

IV) When COMBINING INTEGERS with DIFFERENT signs IGNORE the signs and SUBTRACT numbers. Keep the sign of whatever you have more of Subtract the absolute values. Keep the sign of the number with the largest absolute value.

⇒SUBTRACT and THINK

A) 12 + –8 12 – 8 (get rid of double signs)

B) –37 + 16 –37 + 16 (box terms)

12 –8 (box terms) 4 (Different Signs Subt. & Think)

*There are more positives, so the answeris positive*

–21 (Different Signs Subt. & Think)

*There are more negatives, so the answeris negative*

Same Signs ⇒ ____________________ Different Signs ⇒ _______________________

1) 12 + 20 2) -12 + -20 3) -12 + 20

4) 12 + -20 5) -225 + 125 6) -225 + -125

7) 20 + -10 + 5 8) -15 + 7 + 8 9) -14 + -15 + -26

10) 14 + (-8) 11) -27 + -18 12) -12 + 5

13) -3 + 12 + -14 14) -15 + -7 + -13 15) 7 + -2 + 14 + -8

HOMEWORK – ADDING/SUBTRACTING INTEGERS

Evaluate.Same Signs - ____________________ Different Signs - ___________________

1) 2 + 23 2) -27 + -30 3) -28 + 6 4) 25 + -30

5) -500 + 100 6) -350 + -125 7) -75 + - 11 8) -90 + 90

9) 50 + -10 + 8 10) -18 + 10 + 8 11) -79 + 8 12) -52 + -5

13) -42 + -8 14) -80 + 14 15) 79 + -1 16) -32 + 5

Complete the statement using always, sometimes, or never.17) The sum of two positive integers is ______________ zero.18) The sum of zero and a positive integer is _________________ zero.19) The sum of zero and a negative integer is _________________ zero.20) The sum of a positive integer and a negative integer is __________________ zero.21) Name the first 5 Counting Numbers ____________________22) Whole Numbers are all the ____________________ and ____________________.23) Integers are all the ____________________ and ____________________.24) Name a number that is not an integer? __________25) Name the largest negative integer. __________26) Name the smallest positive integer. __________27) Are all Counting Numbers Whole Numbers? _______28) Are all Integers Whole Numbers? ________

AIM: SWBAT continue to add and subtract integers.DO NOW:State the property that is shown.1) (2 + 7) + 10 = 2 + (7 + 10) ____________________________________2) 5x● 1 = 5x ____________________________________3) (5 + 8) + 12 = (8 + 5) + 12 ____________________________________4) 700 + 0 = 700 ____________________________________

5) -75 + 75 = 0 ____________________________________6) 8y ● 0 = 0 ____________________________________CLASSWORK:Additive Inverse Property - For every number, a, a +-a = 0State the additive inverse of each of the following. Additive inverse ⇒ ______________

1) -2 _______ 2) 14 _______3) -4x _______ 4) -18mn _______ 5) -24 ______

ADDING & SUBTRACTING INTEGERSI) Get rid of DOUBLE SIGNS first!

+ - becomes a NEGATIVE - - becomes a POSITIVE

II) BOX YOUR TERMS! ** The sign IN FRONT of the number goes with the number **

III) When COMBINING INTEGERS with the SAME signs⇒ADD the numbers and KEEP the same sign.

IV) When COMBINING INTEGERS with DIFFERENT signs IGNORE the signs and SUBTRACT numbers. Keep the sign of whatever you have more of Subtract the absolute values. Keep the sign of the number with the largest absolute value.⇒SUBTRACT and THINK

Ex: 7 – 4 -7 – 4

(Diff signs → Subt/Think) (Same signs → Add/Keep) 3 -11BEWARE OF DOUBLE NEGATIVES!!!! Remember (-) means opposite so –(-4) = +4

DOUBLE NEGATIVES - ADD DOUBLE (Diff) SIGNS - SUBTRACTExample: 8 - -4 Example: 8 + -4 8 + 4 8 - 4

= 12 = 4

Compute. Be sure to box off your terms.

Same signs ⇒ _______________ Different signs ⇒ _______________

1) 7 + - 13 2) -8 - 5 3) -17 - 9 4) 9 - -2

5) 27 + -19 6) 5 - 8 7) 0 - -14 8) -21 - (-14)

9) -5 - 3 10) -6 - -8 11) 7 - 13 12) -13 - -18

13) -18 - -18 14) -70 + -18 15) -575 - (-600) 16) 90 - -60

17) 4 + -12 + -18 18) 8 + -10 + -19 19) 7 + -11 + 32 20) 25 + -4 + 32

21) -38 + -19 + -3 22) (-41) + (-78) + 51 23) -39 + 25 + -12 24) -31 + 31 + 45

HOMEWORK – ADDING/SUBTRACTING INTEGERS

1) What is the additive inverse of 19? _______ 2) What is the opposite of -24? _______3) How many numbers have an absolute value of 12? ______ List them. _______________4) The counting numbers are _____________________.5) The whole numbers are ALL the ____________________ and ____________.6) The integers are ALL the _______________ and their _________________.For 7-12 state whether each of the following is TRUE or FALSE.7) One-half is NOT an integer. __________8) If x is a positive integer, then x > 0 __________9) If x is a negative integer, then x < 0 __________ 10) All whole numbers are integers? __________ 11) All integers are whole numbers? __________12) Zero is a positive integer. __________Simplify each expression. REMEMBER – BOX OFF YOUR TERMS AND FOLLOW THE RULES.BEWARE OF DOUBLE NEGATIVES!

Same signs ⇒ ____________________ Different signs ⇒ ___________________

13) -21 + 7 14) -29 + -15 15) -20 + 8 + 22 + -10

16) 5 + (-7) 17) 65 - 72 18) -85 - -42

19) -32 - 74 20) –15 + 21 21) -39 + 25

22) -2 - 3 + 6 - 9 23) 47 + -15 + 8 - 10 24) -50 - 10 – 20 + 100

AIM: SWBAT to apply their knowledge of integer rules to real world situations.

DO NOW:Tell whether the sum of the two integers is always, sometimes or never positive.1) two negative integers ___________________2) a positive integer and a negative integer ___________________3) two positive integers ___________________4) a positive integer and zero ___________________5) a negative integer and zero ___________________

CLASSWORK:Write an integer for each situation.1) a bank deposit of $250 _________ 2) a loss of 12 pounds _________3) 7 below zero _________ 4) a gain of 6 yards _________5) 78 m below sea level _________ 6) a bank withdrawal of $50 _________7) a loss of 3 yards _________ 8) a gain of 5 hours _________

Read each problem carefully, write a number sentence and solve.9) The temperature one morning in Juneau, Alaska was –12oF. By the afternoon, the temperature had risen 8oF. What was the temperature in the afternoon?

10) If the high temperature for the day was 19oF and the low temperature was -5oF, what was the change in temperature?

11) Your bank account currently has a balance of -$480. You make a deposit of $350. What is your new account balance?

12) A submarine is 250 meters below sea level. The submarine then rises 175 meters. What is the new position of the submarine?

13) If the deepest point in the area is 37,800 feet below sea level and the highest mountaintop is 29,012 feet above sea level, find the difference in these elevations.

14) You enter an elevator on the eighth floor. The elevator goes up 5 floors and then down 7 floors, where you exit. On what floor did you exit the elevator?

15) At 5 P.M. the temperature read 10o above zero. At midnight it read 4o below zero. Find the change in temperature.

16) A whale that is 660 feet below sea level rises up out of the water to a height of 32 feet above sea level. How far up did the whale travel?

Write an addition expression to describe each situation, then find the sum and explain its meaning.17) A quarterback is sacked for a loss of 7 yards. On the next play, his team loses 13 yards. Then the team gains 9 yards on the third play.

18) A seagull starts at 70 feet above sea level. It descends 70 feet to catch a fish.

HOMEWORK – ADDING INTEGERS

Compute. Same Signs: _______________ Different Signs:_______________

1) 9 + –7 2) (–17) + 2 3) –11 + –18 4) 67 + (–43)

5) –6 + 6 + –14 6) –15 + 8 + (–7) 7) –21 + (–25) + (–35) 8) –16 + 7 + 19

Read each problem carefully, write a number sentence and solve. 9) At night the average temperature on the surface of the planet Saturn is –150oC. During the day the temperature rises 27 oC. What is the average temperature on Saturn’s surface during the day?

10) To get a first down, a football team must gain 10 yards in 4 plays. If the team gained 5 yards on the first play, lost 7 yards on the second play, and gained 8 yards on the third play. How many yards must they gain on the fourth play to get a first down?

11) A balloon rises 200 feet from the ground, drops 150 feet, and then rises 300 feet. What is the new height of the balloon?

12) A scuba diver is 85 feet below sea level. The diver rises 12 feet then descends 60 feet. How far below sea level is the diver?

AIM: SWBAT apply their knowledge of integer rules to real world situations.

Read each problem carefully, write a number sentence and solve.1) The temperature outside was 20oF. The wind chill made it feel like -15oF. Find the difference between the real temperature and the apparent temperature.

2) Carly has $50 in a bank account. She writes a check for $75 from the account. What is the new balance in Carly’s bank account?

3) The highest temperature ever recorded on Earth is 136oF and the lowest temperature recorded is -129oF. What is the range (difference) of temperatures on Earth?

4) The Panthers lost 5 yards on their first play and lost another 7 yards on their next play. What was their net result in yards after these two plays?

5) A submarine at -28 feet dives 70 feet. What is the submarine’s position after the dive?

6) Ms. Smith is on a diet. The first week she lost 1 pound, second week lost 3 pounds, third week gained 1 pound and fourth week lost 4 pounds. What was her net gain or loss?

HOMEWORK – INTEGER APPLICATIONSEvaluate.1) -5 + 3 2) 51 - (-11) 3) -18 - (-18) 4) -29 + 32

5) -13 - (-18) 6) 7 - 25 7) – 6 + 8 8) -11 - 9

Read each problem carefully, write a subtraction number sentence and solve.9) The record low temperature for Albany, NY was -28oF. The lowest temperature in U.S. history is 52oF lower than Albany’s record low. What is the lowest temperature in U.S. history?

10) During the day the moon can reach a high temperature of 265oF. At night, the temperature can reach a low of -170oF. What is the difference between the high temperature and low temperature on the moon?

11) Are the expressions x - y and y - x always opposites? Explain your reasoning.

12) Carl had $200 in his checking account. He wrote 3 checks, one for $57 and another for $103. He did not record the amount of the third check. Carl received a statement stating that he overdrew his account (meaning he took out more money than he had) by $55. What was the amount of the third check that Carl wrote?

AIM: SWBAT multiply and divide integers.

DO NOW:Read each word problem carefully, write a number sentence and evaluate. Your final answer must be in a complete sentence.1) A person goes from a sauna at 115F to an outside temperature of -30F. What is the change in temperature?

2) A submarine is 50 meters below sea level. It goes up 15 meters, then goes down 40 meters. What is the submarine’s new position?

3) The table shows the temperatures and wind-chill temperatures in three towns.

Town Actual Temperature Wind-Chill TemperatureEaston -3F -13FPine Hills 10F -10FWest Falls 2F -17F

Which town had the GREATEST difference between the actual temperature and the wind-chill temperature?

Evaluate:4) -9 + -22 5) - 6 - - 18 6) 34 + - 30 7) 25 - - 25

8) Whenever you have double signs that are + - you change it into a _____________ sign.

9) Whenever you have double signs that are - - you change it into a _____________ sign.

CLASSWORK:When MULTIPLYING and DIVIDING TWO integers with:

I) TWO SAME SIGNS your answer will be POSITIVE.Ex: 5 ● 4 = 20 AND -5 ● -4 = 20 18 ÷ 3 = 6 AND -18 ÷ -3 = 6

II) TWO DIFFERENT SIGNS your answer will be NEGATIVE.

Ex: -9 ● 2 = -18 AND 9 ● -2 = -18 -18 ÷ 9 = -2 AND 18 ÷ -9 = -2

You can also use the diagram below to help you choose your sign . . . Cover the two signs you have, the sign that is remaining is the sign of your answer.

+

- -

Evaluate.1) (-10)(-5) 2) (12)(4) 3) (-4)(2) 4) 7(-9)

5) (100)(-7) 6) (-6)(13) 7) -9(-11) 8) (-15)(7)

9) 10) 62 ÷ 2 11) 12) -90 ÷ -15

13) -51 ÷ 3 14) 15) -120 ÷ 6 16)

17) -9 -8 18) -360 ÷ 60 19) -8 0 20)

BEWARE OF MULTIPLYING MORE THAN 2 NUMBERS!!!!!1) -1 ● -1 ● -1 2) -1 ● -1 ● -1 ● -1 3) -1 ● -1 ● -1 ● -1 ● -1

When multiplying an ODD number of negatives your answer will be _______________.When multiplying an EVEN number of negatives your answer will be _______________.(-2)9 will be ____________ (-2)100 will be ____________ (-2)203 will be ____________

4) (-6)(-2)(3)(4) 5) (-8)(-6)(-2) 6) (-4)(-2)(-5)(-10)

Evaluate the expression when x = -9, y = -7 and z = -3. (Replace the variable with the given value.)

7) xy 8) -2yz 9) xyz 10)

Find the mean of the data: To find the mean of a set of data, you first add up all the numbers, and then divide your sum by the number of elements)11) 8, 5, -4, 9, -3, 11, 2

HOMEWORK – MULTIPLYING & DIVIDING INTEGERS

Find the product or quotient.Same Signs - ___________________ Different Signs - ___________________

1) 4(-9) 2) -5(-7) 3) -12(0) 4) -9(-11)

5) 6) 7) 50 ÷ -10 8) 0 ÷ -29

9) -12 8 10) -13 -20 11) 6(-5)(-7) 12) -5(-7)(-3)

13) -36 ÷ 3 14) 15) 16) 42 ÷ 2

17) 42(-3)(0) 18) -5(-7)( -3) 19) 4(-5)(-7)(-2) 20) (-10)(-10)(4)

Find the mean of the data: To find the mean of a set of data, you first add up all the numbers, and then divide your sum by the number of elements)

21) -16, 2, -18, 4, -11, -8, -6, 5

AIM: SWBAT multiply and divide integers.

DO NOW:DO NOT COMPUTE!! State whether the answer will be POSITIVE, NEGATIVE or ZERO. Rules for Adding/Subtracting Rules for Multiplying/Dividing two IntegersSame signs - _____________ Same signs - _____________Different signs - _____________ Different signs - _____________1) (-19)(-10) 2) -27 + 96 3) -24 - (- 19) 4) -80 + 80 _____________ _____________ _____________ _____________5) -152 ÷ 4 6) 53 + 9 7) (14)(7) 8) (0)(9) _____________ _____________ _____________ _____________

9) 10) 32 + -12 11) 0 - - 5 12) -42 - 50 _____________ _____________ _____________ _____________13) 15 - 27 14) 57 - 42 15) (29)(-30)(-20) 16) -4 - (-4) _____________ _____________ _____________ _____________17) -49 ÷ -7 18) (-4)23 19) -7 + 7 20) (-5)10

_____________ _____________ _____________ _____________

CLASSWORK:Evaluate.1) 5(-7) 2) -6 ● -3 3) -4 ● 8 4) -91 ÷ -7

5) 240 ÷ -15 6) 7) (-5)(-3)(7) 8) (7)(4)(-2)(-1)

Read each word problem carefully, write a mathematical sentence and solve. Make sure your number sentence represents whether the situation is positive or negative.9) A coin is tossed off a boat into the ocean. The coin’s depth changes by -7 inches per second. Determine the depth of the coin 15 seconds after it hits the water.

10) You have $700 in a savings account. Over a 2 month period, you make 10 withdrawals of $25 each. What is your new balance?

11) The temperature fell 24oF in 6 hours. If the temperature fell at the same rate every hour, what is the change in temperature each hour?

12) Evan withdrew a total of $500 from an ATM machine over a 5-day period. If he withdrew the same amount each day, how much money did Evan withdraw each day?

13) A submarine is diving from the surface of the water at a rate of 80 feet per minute. What is the depth of the submarine after 8 minutes?

14) Wave erosion causes a certain coastline to recede at a rate of 2 cm each year. This occurs

uninterrupted for a period of 7 years. How much will the coastline have receded?

HOMEWORK – MULTIPLYING & DIVIDING INTEGERS

Evaluate.

1) -63 ÷ 7 2) -54 ÷ -9 3) 16 ÷ 2 4) -36 ÷ -6

5) -9 ● -13 6) 4 ● -23 7) -5(-12) 8) (-13)(7)

9) -3(2)(7) 10) -3(4)( -7) 11) (-7)(-8)(5) 12) (-2)(-4)(-5)

Read each word problem, write a mathematical sentence and solve.13) A shoreline is changing -4 cm each year due to erosion. What will the change in the shoreline be in 5 years?

14) The temperature during a 5-day period in Center City were -19oF, -14oF, -8oF, 13oF and 18oF. What was the average temperature for those 5 days?

15) The price of a stock rose $3 yesterday. If the stock continues to change at the same rate each day, what will be the total change over 5 days?

CLASS WORK/HOMEWORK – REVIEW FOR INTEGER TEST

Fill in the rules.

Adding/Subtracting Integers: Multiplying/Dividing two Integers:

1) Same Signs: __________________ 2) Same Signs: __________________

3) Different Signs: __________________ 4) Different Signs: __________________

DO NOT COMPUTE! State whether the answer will be POSITIVE, NEGATIVE or ZERO.5) -27 + 19 _______________ 6) (-14)(-23) _______________

7) _______________ 8) -58 - -64 ______________

9) -17 + 17 _______________ 10) _______________

11) 19 - -12 _______________ 12) -125 ÷ -5 _______________

13) -8 - -8 _______________ 14) -28 - 45 _______________

15) -27 19 _______________ 16) -10 0 _______________

17) 19 - 32 _______________ 18) 12 + 7 _______________

19) _______________ 20) (-3)(-2)(-12) _______________

State whether the answer is ALWAYS, SOMETIMES or NEVER true.21) Counting Numbers are Rational Numbers. _______________22) Counting Numbers are Whole Numbers. _______________23) Whole Numbers are Integers. _______________24) Rational Numbers are Whole Numbers. _______________25) Integers are Whole Numbers. _______________

State ALL the sets of numbers each belongs in: COUNTING, WHOLE, INTEGER or RATIONAL26) 0 _________________________________________________________

27) -90 _________________________________________________________Evaluate.28) -9 + 40 29) -18 - 18 30) (-12)( -5) 31) -45 ÷ -9

32) 33) -12 - - 18 34) 4 - - 9 35) -10 + -19

30

36) (-9)(-10)(-1) 37) -7 - 3 + 12 + 14 38) -9 - - 8 + 1 39) (-5)(3)(-4)

Write a number sentence and evaluate. Your final answer MUST be a complete sentence.40) The temperature in the morning was 3 degrees below zero. The temperature dropped 11 degrees by night. What was the temperature at night?

41) Mary has $10 in savings. She owes her parents $50. She does some chores and her parents pay her $12. She also gets $25 for her birthday from her grandparents. Does Mary have enough money to pay her parents what she owes them? IF not, how much more money does she need?

42) Adam is scuba diving. He descends 5 feet below sea level. He then descends the same distance 4 more times. What is Adam’s final elevation?

43) Clark made four of his truck payments late and was fined four late fees. The total change to his savings from late fees was -$40. How much was one late fee?

7R Review for Integer Test1) When adding/subtracting integers with the same signs you _________________________. 2) When adding/subtracting integers with different signs you ________________________.3) Beware of double negatives! Always change them to a ______________________.4) When multiplying/dividing 2 integers with the same sign the answer will be ____________. 5) When multiplying/dividing 2 integers with different signs the answer will be ___________.6) When multiplying an ODD number of negatives your answer will be _______________.7) When multiplying an EVEN number of negatives your answer will be _______________.8) What is the only integer that is neither positive nor negative? ______9) Is 0 an integer? __________ Why or why not? _________________________________

Evaluate each of the following.

10) -8 + 8 = ____ 11) -78 -15 = _____ 12) -20 + 25 = ____ 13) -26 - -14 = ____

14) -26 ÷ 2 = ____ 15) -8 9 = _______ 16) -4 -2 = ______ 17) = ______

18) -18 - 10 + 16 + 5 = ______________ 19) -25 - 5 + 10 - 2 = ______________

20) 12 - - 7 - 8 + -9 = ______________ 21) -6 + 16 - 10 + 4 = ______________

22) (-9)(7) = ____ 23) -9 + 26 = ____ 24) -16 - -18 = ____ 25) = ____

26) - 18 - 8 = ____ 27) (-3)(-17) = ____ 28) -9 + 25 = ____ 29) -56 ÷ 8 = ____

Read each problem carefully, write a number sentence and evaluate.30) A submarine 140 feet below sea level dives another 300 feet. What is the submarine’s position after the dive?

31) The temperature outside was 22˚F. The wind chill made it feel like -8˚F. Find the difference between the real temperature and the apparent temperature.

32) The enrollment at Davis Middle School dropped by 60 students over a 5-year period. What is the average yearly drop in enrollment?

33) A hiker starts hiking at the beginning of a trail at a point which is 200 feet below sea level. He hikes to a location on the trail that is 580 feet above sea level and stops for lunch. What is the difference between the two elevations?

34) The top of an iceberg is 15 feet above sea level. The bottom of the iceberg is 105 feet below sea level. What is the distance from the top to the bottom of the iceberg?

35) An elevator takes passengers from the ground floor down to an underground parking

garage. Where will the elevator be in relation to the ground floor after 5 seconds if it travels at a rate of 3 feet per second?

36) State the first 5 Counting Numbers. ________________37) Whole Numbers are all the _____________________ and _____________________.38) Integers are all the _____________________ and their _____________________.39) Rational Numbers are any numbers that can be written in ________________ form. This includes ________________ decimals and ________________ decimals.40) Are all Counting Numbers Whole Numbers? Answer yes or no. ___________41) Are all Whole Numbers Integers? Answer yes or no. ___________42) Are all Whole Numbers Counting Numbers? Answer yes or no. ___________43) Are all Counting Numbers Rational Numbers? Answer yes or no. ___________

State ALL the sets each of the following belongs to. COUNTING, WHOLE, INTEGER, RATIONAL

44) -9 ______________________________________________________________45) 0.25 ______________________________________________________________

46) - ______________________________________________________________

47) 0 ______________________________________________________________48) 5 ______________________________________________________________State the additive inverse (opposite) for each of the following.

49) 24 _________ 50) -44 _________ 51) 4 _________Compare using or .

52) -5 ______ 0 53) -15 ______ 15 54) -9 ______ -11Put the integers in order from least to greatest.

55) -20, 8, -31, -5, 11 ______________ 56) -56, -102, 98, -58, 114 _____________Evaluate.

57) |22| _____ 58) |-13| _____ 59) |-512| + |102| = _____

60) | 5 + -8| = _______ 61) | -8 + 10 | = _______ 62) | 7 | + | -7 | = ______

State the property shown below. COMMUTATIVE, ASSOCIATE, ADDITIVE IDENTITY, MULTIPLIATIVE IDENTITY, ADDITIVE INVERSE, MULTIPLICATIVE PROPERTY OF ZERO

63) -8 + 8 = 0 _______________________64) (9 + 7) + 3 = (7 + 9) + 3 _______________________65) 9 + (8 + 4) = (9 + 8) + 4 _______________________66) -9 + 0 = -9 _______________________

67) -19 0 = 0 _______________________68) 18 1 = 18 _______________________