Chapter 1 Review – Guided Notes · Web viewYou can use the number line to help you find and understand how to add positive integers to other positive and negative integers. Example

NAME______________________________________________ Jacoby

Fall Semester 2013- 1 -

Chapter 7 Integers

Galileo lived in Italy in the 1500s He studied how to measure temperature Galileo found that a liquid would rise or fall in a glass tube depending on the temperature He liquid rose or dropped and the temperature as marked on the glass Sounds familiar Glass and alcohol or mercury thermometers are really number lines just like you use in math Theyrsquore marked by degrees of temperature Alcohol or mercury expands up into the positive numbers when heated and shrinks into the negative numbers when cooled Those positive and negative numbers are called integers In math integers can be a real hot topic

Goals for learningTo identify the absolute value of integersTo compare the values of negative and positiveTo add subtract multiply and divide integers

Watch Moviehttpwwwyoutubecomwatchv=2d5rWT6bHLUampfeature=channelampsafety_mode=trueamppersist_safety_mode=1

Lesson 1 The Real Number Line and Integers

I invented the thermometer I also said the sun was the

center of the universe

NAME______________________________________________ Jacoby


In arithmetic you learned to add subtract multiply and divide whole numbers greater than zero In algebra you will also use whole numbers less than zeroWarm-UpWhat are some numbers less than zero Where do you see these numbers

You can use a number line to show the relation between positive and negative whole numbers also called integers

Vocab for Understanding Integer

Real Number

Negative Integer

Positive Integer

Every point on the number line corresponds to a specific real number The arrows at the ends of the number line show that the line continues

Numbers to the left of zero are negative integers They are read as lsquonegative onersquo lsquonegative tworsquohellip and so on

Zero is neither negative nor positive

Numbers to the right of the zero are positive integers They are read as lsquopositive onersquo positive tworsquo and so onhellipA negative number is always indicated by the______________________

NAME______________________________________________ Jacoby


A positive sign is always indicated by _____________________________ or

____________________________

The absolute value of an integer is the distance ________________________________

______________________________________________________________________

The integer can be either to the left or to the right of zero The symbol for absolute value is ___

Vocab Opposites

Example 1 |4| = 4 4 is 4 units from 0The absolute value of |4| is _______

|-4| = 4 -4 is ________ units from 0The absolute value of |-4| is _____

Every number other than 0 has an opposite number Opposites are the same distance from zero

Example 29 is the opposite of __________________

NAME______________________________________________ Jacoby


-9 is the opposite of _________________

9 is 9 units from 0

Both -9 and 9 are _________ units from 0

5 is the __________________________ of -5

-5 is the opposite of _________

5 is ____________ from 0

Both 5 and -5 ____________________________

Letrsquos Try Some Out

Use the number line below to find the values

1 You earn $6 from mowing the grass2 The wind chill is 12 below zero3 The Bears took a ten yard gain on the play 4 We realized we lost five dollars5 A mailbox post rises 4 feet above the ground it is set 2 feet into the ground

In ClassFind the absolute value1 |3| 2 |-12| 3 |-3|

NAME______________________________________________ Jacoby


Name the opposite of each integer4 4 5 8 6 -7

Solve these problems using the number line

7 Which letters represent positive real numbers

8 Which letters represent negative real numbers

9 Which letter is the greatest distance from zero

10 Which letter represents the greatest absolute value

Give an integer that describes each situation11 A gain of 3 yards in football

12 A loss of 15 yards in football

13 A withdrawal of $40 from a bank account

14 A deposit of $100 in a bank account

15 A temperature of 13˚ F below zero

Watch the first couple minutes of chttpwwwyoutubecomwatchv=-AQFWV0AdLEampsafety_mode=trueamppersist_safety_mode=1

Lesson 2 Comparing Integers- Greater Than

To compare 2 numbers and determine which is greaterTo use the symbol gt to identify the larger of two integers

E D 0 A B C

NAME______________________________________________ Jacoby


Warm-Up Here is a list of basketball scores 102 5442 5612 5984 76

LessonIntegers can be arranged in an increasing or decreasing order Consecutive integers are integers arranged from least or greatest or greatest to least without any missing integers The integers on a number line are consecutive integers

You can use a number line to compare two integers On a number line the greater of two numbers is the number to the right

Example 1 Compare 2 and -3

_________ is to the __________ of ______________ on the number line

______ is greater than -3

Example 2 Compare -1 and -5 Remember The symbol gt read ldquois greater thanrdquo is used to show that one integer is greater than another

2 gt -3 -1 gt -5

Example 3 Compare |-5| and |-3|

Which ones are the winning scores How do you see scores posted

less greater

Common ErrorSome students may have a hard time perceiving -1 as greater than -5 Visualize on the number line and recall that lsquofarther right is greaterrsquo

NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5

-3 is 3 units from zero so _______________________

________ is farther to the right than ____ so | | gt | -3 |

Letrsquos try it out

Compare each pair Use gt or =

1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|

All Class Each student will get a note card with an integer Try to arrange yourselves from least on the left and the greatest on the right

Lesson 3 Less ThanObjectiveTo compare two numbers and decide which is smaller To use the symbol lt to identify the smaller of two numbers

Warm-Up What does this mean

gtTry writing a true number sentence using that sign

What do you think this means lt

You can use a number line to compare to integers On a number line the lesser of two numbers is the number farthest to the left

less

NAME______________________________________________ Jacoby


Example 1 Compare -3 and 1

Example 2 Compare -5 and -3

Remember the symbol lsquoltrsquo means less than It is used to show that one integer is less than another

Example 3 Compare -5 and |-3|

In Class Compare each pair Use lt or =

1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10

5 A student lists these five numbers and says that they are consecutive integers

-2 -1 0 1 2 3

Is she right

6 The temperature was 0˚ F on Saturday and -11 ˚F today Which temperature is higher Explain

All Class Get into pairs Try to come up with a word problem comparing two different temperatures from the data given below You have 3 minutes

January TemperaturesMonday 5˚ F

NAME______________________________________________ Jacoby


Tuesday 2˚ FWednesday -3˚ FThursday 0˚ F

Homework

Lesson 4 Even and Odd Integers

Objectives To identify integers as odd or evenTo add subtract and multiply integersTo notes the pattern of answers obtained by operations on odd and even numbers

Warm-Up 1 Count by 2s up to 20

Even Odd

LessonZero is an _______________________________ because it is situated between -1

and 1 on the number line

Also any number ending with a zero is a ______________ of 2

Integers that have a factor of 2 without leaving a remainder are even integers -6 -4 -2 0 +2 +4 and +6 are examples of even integers

Integers that do not have a factor of 2 are odd integers -5 -3 -1 +1 +3 and +5 are examples of odd integers

You can tell whether a number is even or odd by ______________________________________

If the digit in the ones position is odd ______________________________________________

If the digit in the ones position is even ______________________________________________

Example 1 Even or odd

2478563

NAME______________________________________________ Jacoby


3556430

Consecutive even integers are

Consecutive odd integers are

When you add or subtract integers you can predict whether the sum or difference will be odd or even

Adding Integers Subtracting IntegersEven + even = even Even ndash even = evenEven + odd = odd Even ndash odd = oddOdd + odd = even Odd ndash odd = even

You can also predict whether or not a product will be even

Multiplying IntegersEven even = evenEven odd = evenOdd odd = odd

Example 2 Tell whether the following numbers are odd or evena 24004 b 35793 c 12457753456899

Tell whether the answer will be even or odd without solving the problem

d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43

Tell which operation will give the desired even or off integer Then solve the problem There may be more than one correct answer

h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby


Make a table for divisionSee if there are rules for division

Homework

Lesson 5 Adding Positive IntegersObjectives To visualize sums of integers on the number lineTo add positive integers to positive or to negative integers

Warm- Up

NAME______________________________________________ Jacoby


The temperature of the fluid is -4 degrees Mark this on a number line

If you add heat to the fluid and raise it by 3 degrees What is the new temperature of the fluid

You can use the number line to help you find and understand how to add positive integers to other positive and negative integers

Example 1 Find the sum of 3 + 5Begin at 3Move to the right 5 units3 + 5 =

Rule Adding a positive to a positive gives a result farther to the right on the number line

Example 2 Find the sum of -3 + 5Begin at -3Then move ______________________________

-3 + ________ = ___________

Rule Adding a positive to a negative gives a result farther to the right on the number line

ExamplesFind each sum

1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby


Calculator practice 1 652 + 978 2 -57 + 784 3 -441 + 239

Further Understanding

Lesson 6 Adding Negative Numbers

Objectives To move left along the number line to represent the sum of a positive or negative integer and a negative integerTo add negative integers to positive or negative integers

Warm-UpldquoWhen could you add two numbers and get a sum with a value smaller than wither addend ldquo

LessonYou can use the number line to help you find and understand how to add negative integers to other positive or negative integers

RULE Adding a negative to a positive gives a result farther to the left on the number line

- +Example 1 Find the sum of 3 + (-5) Begin at 3 Then move to the left 5 units

Here is a trickThink of -7 + 7 as 7 ndash 7

-6 + 8 as 8 ndash 6

You can do this do to the commutative property

NAME______________________________________________ Jacoby


Example 2 Find the sum of -3 + (-5)

Begin at ________________________

Then move _____________________ 5 units

1 -2 + (-7)which number is the biggest

What will our sign be for our answer

2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)

Letrsquos Step It Up 1 Find the number that is the biggest The sign that is with the biggest number will be your sign for your answer

2 If the numbers are both negative treat it as an addition problem and carry down the negative sign

3 If the numbers are of opposite sign with the bigger number being negative treat the problem like a subtraction problem Take the smaller number away from the larger number But carry down the negative sign

4 If the numbers are of opposite signs with the bigger number being positive treat the problem like a subtraction problem Take the smaller number away from the larger number Your answer will be positive

NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6

Try these harder ones with a calculator

1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)

Word Problems1 An airplane flying at 25000 feet climbs an additional 2000 feet What is the final altitude of the airplane

2 At midnight the temperature was 29˚C During the day the temperature fell 4 degrees What is the final temperature

Homework Lesson 7 Subtracting Positive amp Negative Integers

ObjectivesTo model subtraction of positive and negative integers on the number lineTo convert subtraction expressions to addition expressionTo subtract positive and negative integers from positive and negative integers

Warm-Up white board +++ --- 3 5 2

NAME______________________________________________ Jacoby


LessonA number line can be used to show that subtracting a number gives the same result as adding the opposite of the number

Example 1Find the difference of 3 ndash (+5)Begin at 3Then move to the ___________ 3 units

RULE _______________________________________________________________________

Example 2Find the difference of -3 ndash (-5)Begin at -3Then move to the right _____ units

RULE _____________________________________________________________________

___________________________________________________________________________Example 3Find the difference of 3 ndash (-5)Begin at 3Then move to the ___________ 5 units

NAME______________________________________________ Jacoby


RULE ___________________________________________________________________

Example 4 Find the difference of -3 ndash (+5)Begin at __________

Then move to the left __________________

RULE ___________________________________________________________________

Look again at addition of positive and negative integers Compare the results with subtraction of integers

Subtraction Addition 3 ndash (+5) = -2 is the same as is the same as -3 + 5 = 2 3 ndash (-5) = 8 is the same as is the same as -3 + (-5) = -8 Subtraction is the same asRULE____________________________________________________Try some out1 4 ndash (+5) 2 -6-4 3 8 ndash 4

4 -2 ndash (+4) 5 10 ndash (+7) 8 -9 ndash (-11)

Mental Math In-Class Work 10-9 10-8 10- (-1) 10- (-2)hellip

NAME______________________________________________ Jacoby


Word Problems

9 The highest point on Earth is Mt Everest 29028 feet above sea level The shore of the Dead Sea is the lowest place on Earthrsquos surface at 1312 feel below sea level What I the vertical distance from the shore of the Dead Sea to the top of Mount Everest

10 What is the difference between Alaskarsquos record low temperature of -80˚F and Utahrsquos record low of -69˚F

Homework

Lesson 8 amp 9 Multiplying by Positive and Negative NumbersObjectives To identify the sign of a product as positive or negativeTo multiply positive and negative integers

Example 1 Find the product of (+4) and (+3)

Rule_______________________________________________________________________

NAME______________________________________________ Jacoby


Example 2Find the product of (-4) (3)

Rule ______________________________________________________________________

Try some out

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

Example 3 Find the product of (-4)(-3)

Rule_________________________________________________________________________

To be successful in Algebra you will need to memorize these rules

Try some more out look at your rules for help

5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems

Every year for the past five years the forest preserve has lost 16 trees due to disease or weather How many trees have been lost in the past five years

NAME______________________________________________ Jacoby


At a local movie theater senior citizens receive a $200 discount How much less will a senior pay to attend 15 movies in a year

Homework

Lesson 10 Dividing Positive and Negative Integers

Objectives To model division of negative and positive integers on the number lineTo divide negative and positive integers and identify the sign of a quotient

Warm-Up(-8)(4) (4)(3) (-2)(-3)

Because multiplication and division are opposite operations the rules for multiplying positive and negative integers are similar to those of division

Complete the table below

Multiplication Division(3)(4) =Rule

and 12 divide 4 =Rule

NAME______________________________________________ Jacoby


(3)(-4) = Rule

and 12 divide (-4) =Rule

(-3)(4)=Rule

and (-12) divide (4) =Rule

(-3)(-4)Rule

and (-12) divide (-4) =Rule

A general statement can be made that covers all the multiplication and division rules

Try some out Use the rules to help you out

1 4 divide 2 2 32 divide (-4) 3 (-24) divide (4)

4 (30) divide (-5) 5 (-20) divide (-4) 6 (-28) divide (-4)

7 The theater complex has 1440 seats in six theaters All theaters have the same number of seats How many seats does each theater have

NAME______________________________________________ Jacoby


8 A submarine moving underwater at -390meters It dives to that level in 13 minutes How many meters does it dive per minute

Homework

NAME______________________________________________ Jacoby


In arithmetic you learned to add subtract multiply and divide whole numbers greater than zero In algebra you will also use whole numbers less than zeroWarm-UpWhat are some numbers less than zero Where do you see these numbers

You can use a number line to show the relation between positive and negative whole numbers also called integers

Vocab for Understanding Integer

Real Number

Negative Integer

Positive Integer

Every point on the number line corresponds to a specific real number The arrows at the ends of the number line show that the line continues

Numbers to the left of zero are negative integers They are read as lsquonegative onersquo lsquonegative tworsquohellip and so on

Zero is neither negative nor positive

Numbers to the right of the zero are positive integers They are read as lsquopositive onersquo positive tworsquo and so onhellipA negative number is always indicated by the______________________

NAME______________________________________________ Jacoby



____________________________


______________________________________________________________________


Vocab Opposites





NAME______________________________________________ Jacoby



9 is 9 units from 0


5 is the __________________________ of -5


5 is ____________ from 0

Both 5 and -5 ____________________________





NAME______________________________________________ Jacoby
















E D 0 A B C

NAME______________________________________________ Jacoby









2 gt -3 -1 gt -5



less greater


NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5





1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|







less

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



____________________________


______________________________________________________________________


Vocab Opposites





NAME______________________________________________ Jacoby



9 is 9 units from 0


5 is the __________________________ of -5


5 is ____________ from 0

Both 5 and -5 ____________________________





NAME______________________________________________ Jacoby
















E D 0 A B C

NAME______________________________________________ Jacoby









2 gt -3 -1 gt -5



less greater


NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5





1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|







less

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



9 is 9 units from 0


5 is the __________________________ of -5


5 is ____________ from 0

Both 5 and -5 ____________________________





NAME______________________________________________ Jacoby
















E D 0 A B C

NAME______________________________________________ Jacoby









2 gt -3 -1 gt -5



less greater


NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5





1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|







less

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby
















E D 0 A B C

NAME______________________________________________ Jacoby









2 gt -3 -1 gt -5



less greater


NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5





1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|







less

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby









2 gt -3 -1 gt -5



less greater


NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5





1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|







less

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby


-5 is _________________________ so |-5| = 5





1 5 2 2 |-2| 2

3 |8| -3 4 |-8| |-3|







less

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby







1 2 5 2 -2 1

3 12 |-12| 4 |-1| 10


-2 -1 0 1 2 3

Is she right




NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



Homework




Even Odd










2478563

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby


3556430









d 432 + 444 e 669 ndash 571 f 24 x 36 g 22 x 43


h 4 5 = (even) i 9 3 = (even)

j 6 3 = (odd)

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



Homework


Warm- Up

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby








-3 + ________ = ___________



1 -12 + 4 2 -7 + 7 3 -6 + 8

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

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby











-6 + 8 as 8 ndash 6


NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



Begin at ________________________

Then move _____________________ 5 units



2 -4 + (-5)

3 2 + (-3)

4 5 + (-2)





NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby


Try some out

1 -2 + (-5) 2 12 + (-32) 3 28 + (-32)

4 -6 + (-6) 5 6 + (-6) 6 6 + 6


1 -359 + (-243) 2 233 + (-873) 3 -649 + (-573)






NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby




RULE _______________________________________________________________________


RULE _____________________________________________________________________


NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby


RULE ___________________________________________________________________



RULE ___________________________________________________________________





NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby


Word Problems



Homework



Rule_______________________________________________________________________

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



Rule ______________________________________________________________________

Try some out

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


Rule_________________________________________________________________________



5 (-2)(6) 6 (-10)(-11) 7 (23)(30) 8 (-2)(-6)

Word Problems


NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



Homework



Warm-Up(-8)(4) (4)(3) (-2)(-3)





NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby


(3)(-4) = Rule


(-3)(4)=Rule


(-3)(-4)Rule







NAME______________________________________________ Jacoby



Homework

NAME______________________________________________ Jacoby



Homework

Documents

Chapter 1 Review – Guided Notes · Web viewYou can use the number line to help you find and understand how to add positive integers to other positive and negative integers. Example