Bellwork Copy and Answer 5 – 7 6 + -15 -14 - -10 6 x -7 -5 ÷ -5 -10 x -10

Bellwork Copy and Answer

5 – 76 + -15-14 - -106 x -7-5 ÷ -5-10 x -10

2

Tuesday 10/18

2-5 Solving Equations

Containing Integerspg. 100

Essential Question

How can you solve equations that contain integers?

5

Who REMEMBERS?

Monday we talked about 3 steps to solve an equation.

What are the 3 steps? I___________ S___________ C___________

5

Steps to Solving Equations:

1. Use the opposite operation to ISOLATE the variable to one side of the equation

2. SOLVE for the Variable3. CHECK the answer to the equation by

substituting the number in for the variable

7

Equation Mat

Today we will use an Equation Mat and Integer Chips to model solving an equation.

LAB

7

Equation Mat Directions… Yellow=positive 1 Red= negative 1 Use the chips for our numbers. If the equation is x+3=5…on your mat you should

have

x + =

Then, use your red chips to solve the equation. The red and yellow chips cancel out. We are left with 2 yellow chips, so x=2.

Equation Mat Equations

x + 3=5 x + 4=9 x + 5=8 x + 6=6 x - 4=3 x - 2=8 x - 5=-5 x - 7=0

X=2

X=5

X=3

X=0

X=7

X=10

X=0

X=7

10

Wednesday 10/19

2-5 Solving Equations Containing Integers

pg. 100

Essential Question


13

Algebra Geek Patrol

The Pocket Protectors of Algebra

14

My name is Buck Einstein, but you can call me Buck.

Hello!

Pick my nose to continue

15

It’s that we on the Algebra Geek Patrol are… well…different.

I have a secret to tell you. What is it?

You might even say that we are the opposite of everyone else.


16

When you worry about what you wear,

We worry about having our Pocket Protectors.


17

When you worry that you won’t meet your friends,

We worry that we won’t have our calculators.


18

We are just a little bit opposite. That may be why we are so good at Algebra, because that is all Algebra is…


…doing the opposite.

19

Think of some words that are opposites. For example, what do you think of as the opposite of word below.


Old = ______ New

20

Now try some other ones. Make sure to write your answers on your paper, and when you are finished click on me.


Up = __________

Out = __________

Small = __________

Stinky = __________

21

Some possible answers are…


Up = __________

Out = __________

Small = __________

Stinky = __________

Down

In

Big

Fragrant(or non-stinky)

22

Now another set. Make sure to write your answers on your paper, and when you are finished click on me.


Add = __________

Subtract = __________

Multiply = __________

Divide = __________

23

Your answers should have been…


Add = __________

Subtract = __________

Multiply = __________

Divide = __________

Subtract

Add

Divide

Multiply

24

One last set. Make sure to write your answers on your paper, and when you are finished click on me.


+ = __________

- = __________

x = __________

÷ = __________

25



+ = __________

- = __________

x = __________

÷ = __________

-

+

÷

x

26

Congratulations!You just did some

ALGEBRA


Scary, isn’t it!

27

One Step Equations

Algebra Geek Patrol

Now you are going to work on solving some Algebra problems. Don’t be afraid of the A-word (Algebra). Remember, it is all about being opposite.


28

One Step Equations

Algebra Geek Patrol


You will complete 5 sections. After each section you will be awarded a Geek Pen to put in your official AGP Pocket Protector.

Geek Luck!

29

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

X + 3 = 17Click on the answer below that is the opposite of add 3.

Add 3Subtract 3Multiply 3

Divide 3

30

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Close, but that’s not quite it.

Remember, we are looking for the opposite of add 3.

Click on Buck and give it another try.

31

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Good Job!

The correct answer is subtract 3.

Write the answer on your paper, next to the original problem, and then click on Buck.

32

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

4x = 20

Click on the answer below that is the opposite of multiply by 4.

Add 4Subtract 4

Multiply by 4

Divide by 4

33

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

No, not really.

Remember, we are looking for the opposite of multiply by 4.


34

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Nice! You’re halfway to your first Geek Pen.The correct answer is divide by

4.Write the answer on your paper next to the original problem, and then click on Buck.

35

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

x 5

Click on the answer below that is the opposite of divide by 5.

Add 5Subtract 5

Multiply by 5

Divide by 5

= 10

36

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Uhh, in a word, no.

Remember, we are looking for the opposite of divide by 5.


37

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Good! Are you sure you’re not

a Geek? The correct answer is multiply by 5.

Write the answer on your paper next to the original problem, and then click on Buck.

38

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Click on the answer below that is the opposite of - 7.

+ 7- 7

x 7

÷ 7

X – 7 = 8

39

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Almost

Remember, we are looking for the opposite of - 7.


40

Algebra Geek Patrol

One Step Equations

Congratulations!

The correct answer is + 7.

Write the answer on your paper next to the original problem, and then click on Buck.

And here is your first Geek Pen

Algebra

Geek

Patrol

41

One Step Equations

Algebra Geek Patrol


Alright, now you are going to actually solve some problems. This is nothing to be worried about, just remember one word…

Opposite!

Geek Luck!

42

1

One Step Equations

Click on the answer below that is the opposite of + 5.

+ 5- 5

x 5

÷ 5

X + 5 = 13

Algebra

Geek

Patrol

43

1

One Step Equations

C’mon, You know this.Remember, we are looking

for the opposite of + 5.


Algebra

Geek

Patrol

44

1

One Step Equations

Good!

So, let’s put – 5 on each side of the equation.

Algebra

Geek

Patrol

X + 5 = 13 - 5 - 5_________

Let’s look at the left side. What will you get when you combine + 5 and -5 ?

That’s right, zero. And zero is nothing, so let’s cancel out + 5 and -5.

Click on the pen when you are ready.

Click on +5 or -5 to cancel them.

Now to the hard part.

X =

Just teasing!Look at the right side. All we have left is 13 and – 5. So,what is 13 – 5?

That’s right! 8

That just leaves X on the left side.Copy the entire problem and all the steps on your paper, then click on Buck.

45

One Step Equations

Algebra Geek Patrol


Congratulations, You just completed your first Algebra problem. See it wasn’t that bad.

Now let’s try another.

46

Who REMEMBERS?

What are the 3 steps to solve a one step equation? I___________ S___________ C___________

46


1. ISOLATE the variable by doing the opposite, Inverse, Operation.

2. SOLVE the equation.3. CHECK your solution.

48

2

One Step Equations

Click on the answer below that is the opposite of + 9.

+ 9- 9

x 9

÷ 9

X + 9 = 15

Algebra

Geek

Patrol

49

2

One Step Equations

Umm, I don’t think so.Remember, we are looking

for the opposite of + 9.


Algebra

Geek

Patrol

50

2

One Step Equations

Nice Job!

Algebra

Geek

Patrol

X + 9 = 15 - 9 - 9_________

X = 6 Make sure you have copied all the steps on your paper and then click on Buck.

This time I am going to give you the steps, which you will need

to write down, and then you will work the problem on your

paper.

First, put the opposite (- 9) on both sides.

Second, cancel out one side.Write this on your paper, and work this part of the

problem.Click the pen to continue

Third, combine the other side.


51

One Step Equations

Algebra Geek Patrol


Congratulations Again, Now let’s try one last problem.

52

Go ahead and give it a try!

3

One Step Equations

X + 7 = 9

Algebra

Geek

Patrol

This time you are going to work the problem on your

paper first and then we will go through it.

Pick my nose when you are finished

Are you sure you are done? Check your answer before moving

on. No one will know but you and me.

53

3

One Step Equations

Algebra

Geek

Patrol

X + 7 = 9 - 7 - 7_________

X = 2 First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.

Make sure you have copied all the steps on your paper and then click on Buck.

Click the pen to continue

54

Algebra Geek Patrol

Algebra

Geek

Patrol

One Step Equations

Nice Work

You are one pen closer to being an Official Algebra

Geek

Don’t worry, I won’t tell

anyone.


55

Now, try these on your own! X + -6 = 10 -5 + x = -12

56

One Step Equations

Algebra Geek Patrol


This time let’s try some different types of problems. Since you have gotten so good at this, let’s skip the first part, and go straight to the problems by using the 3 steps.

And remember, today’s word is…

Opposite!

57

1

One Step Equations

Click on the answer below that is the opposite of - 4.

+ 4- 4

x 4

÷ 4

X - 4 = 11

Algebra

Geek

Patrol

58

1

One Step Equations

Nope, try again. Remember, we are looking

for the opposite of - 4.


Algebra

Geek

Patrol

59

I know all the cool words.

1

One Step Equations

Sweet!

X - 4 = 11_________ +4 +4

X = 15Make sure you have copied all the steps on your paper and then click on Buck.

This time I am going to give you the steps, which you will need to write down, and then you will do

the problem on your paper.

First, put the opposite (+4) on both sides.Second, cancel out one side.

Write this on your paper, and work this part of the

problem. Click the pens to continue



Algebra

Geek

Patrol

Write this problem in the box on your worksheet.

60

One Step Equations

Algebra Geek Patrol


Congratulations Only one problem left until another Geek

Pen.Aren’t you excited?

61

2

One Step Equations

X - 6 = 14

This time you are going to work the problem on your paper first and then we will go through it.


Are you sure you are done? Check your answer before

moving on.

Algebra

Geek

Patrol


I won’t tell anyone.


62


2

One Step Equations

X - 6 = 14_________ + 6 +6

X = 20 First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.

Click the pens to continue

Algebra

Geek

Patrol

63

Now, try these on your own! X – (-2) = 7 X – 5 = -8 X – (-3) = 0

64

Algebra Geek Patrol

One Step Equations

Jeepers!You get another Geek

Pen.Come back soon to try more!


Algebra

Geek

Patrol

65

Thursday 10/20/11

2-5 Solving Equations Containing Integers

pg. 100

Essential Question


68

Algebra Geek Patrol

The Pocket Protectors of Algebra

69

One Step Equations

Algebra Geek Patrol


What’s the same as yesterday?

The word we know and love…

Opposite!

Welcome Back!

70

Now another set. Make sure to write your answers on your paper, and when you are finished click on me.


Add = __________

Subtract = __________

Multiply = __________

Divide = __________

71



Add = __________

Subtract = __________

Multiply = __________

Divide = __________

Subtract

Add

Divide

Multiply

72

One last set. Make sure to write your answers on your paper, and when you are finished click on me.


+ = __________

- = __________

x = __________

÷ = __________

73



+ = __________

- = __________

x = __________

÷ = __________

-

+

÷

x

74

Who REMEMBERS?

What are the 3 steps to solve a one step equation? I___________ S___________ C___________

74


1. ISOLATE the variable by doing the opposite, Inverse, Operation.

2. SOLVE the equation.3. CHECK your solution.

76

1

One Step Equations

Click on the answer below that is the opposite of x 2.

+ 2- 2

x 2

÷ 2

2x = 18

Algebra

Geek

Patrol


77

1

One Step Equations

Not quite.

Remember, we are looking for the opposite of x 2.


Algebra

Geek

Patrol

78

You remember from working with fractions, what happens when one number is divided by the same number?

÷ ÷ ___ __2x 181

One Step Equations

Yes!

So, let’s put ÷ 2 on each side of the equation.

2x = 18 2 2_________

Another way to write ÷ 2 is with a fraction bar. Like this.

This makes the left side a fraction.

Click on the pens when you are ready.

X = Look at the right side. All we have left is 18 divided by 2. So, what is 18 ÷ 2?

9 That just leaves X on the left side.Copy the entire problem and solution above on your paper, and then click on Buck.

=

Algebra

Geek

Patrol

That’s right! It cancels

out. That’s right! X = 9

79

3 33x = 152

One Step Equations

Rama-Lama–Ding-Dong




First, put the opposite on both sides.Remember to rewrite it as a fraction.


problem.Click the pens to continue



Don’t worry. It’s a Geek Thing.

÷ ÷ ___ __3x 15

X =

=

Algebra

Geek

Patrol

Second, cancel out one side.

5


80

One Step Equations

Algebra Geek Patrol


Congratulations, Now let’s try one last problem.

81

3

One Step Equations

Algebra

Geek

Patrol



Are you sure you are done? Check your answer before

moving on.

Go ahead and give it a try!I’ve been sworn to secrecy.

4x = 24Write this problem in the box on your worksheet.

82

___ __4x 244x = 243

One Step Equations

First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.Make sure you have copied all the steps on your paper and then click on Buck.


4 4X =

=

6

Algebra

Geek

Patrol

83

3

One Step Equations

Great!Your future’s so bright,

I gotta wear shades.

Actually,

I already am.


Algebra

Geek

Patrol

84

Now, try these on your own! -5x = -100 12x = -144 X – (-3) = 0

85

One Step Equations

Algebra Geek Patrol


Now for the final part. Just remember Opposite, and you are done.

As Always, Geek Luck!

86

1

One Step Equations

Click on the answer below that is the opposite of ÷3.

+ 3- 3

x 3

÷ 3

x 3

= 12

Algebra

Geek

Patrol

87

1

One Step Equations

Doh! Not Really.

Remember, we are looking for the opposite of ÷ 3.


Algebra

Geek

Patrol

88

You remember from working with fractions, what happens when one number is divided by the same number?

1

One Step Equations

That’s It!

So, let’s put●3 on each side of the equation. Remember,●means times.

Now, the left side cancels out just like a fraction.

Click on the pens when you are ready.

X = Look at the right side. All we have left is 12 times 3. So, what is 12 times 3?

36

Copy the entire problem and solution above on your paper, and then click on Buck.It cancels out.

x 3

= 12

Algebra

Geek

Patrol

3• •3

That’s Right!


89

2

One Step Equations




First, put the opposite on both sides.


problem.Click the pens to continue



Second, cancel out one side.

x 7

= 3

Algebra

Geek

Patrol

7 x x 7

X = 21


90

One Step Equations

Algebra Geek Patrol


And Now…. (Drum Roll, Please)

THE LAST Practice PROBLEM!

91

3

One Step Equations

Algebra

Geek

Patrol



Are you sure you are done? Check your answer before moving

on.


I can’t tell anyone. I don’t even have a mouth.

x 5

= 6Write this problem in the box on your worksheet.

92

5 x3

One Step Equations

First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.



x 5

= 6 x 5

X = 30

Algebra

Geek

Patrol

93

Now, try these on your own! X / -10 = 5 X / -9 = -8

94

Algebra Geek Patrol

One Step Equations

You’re a GEEK!I’m so happy,

I could cry


Congratulations!

Algebra

Geek

Patrol

95

What? You want more?You really are a geek.

More Practice AHEAD!

Solve each question. Check each answer.

Example 1

–6 + x = –7

–6 + x = –7+ 6 + 6

x = –1

Check

–6 + x = –7

–6 + (–1) = –7

–7 = –7

Professor Burger the Math Man Example

http://my.hrw.com/math06_07/nsmedia/homework_help/msm2/msm2_ch02_05_homeworkhelp.html

Example 2Solve each equation. Check each answer.

y – 9 = –40

y – 9 = –40+ 9 + 9

y = –31

Check

–31 – 9 = –40?

y – 9 = –40

–40 = –40?


c4

= –24

c4

= –24

c4 = 4(–24)4

c = –96

Check

c4

= –24

–964

= –24

–24 = –24




–400 = 8y

–400 = 8y

–400 = 8y

8 8

–50 = y

Check

–400 = 8y

–400 = 8(–50)

–400 = –400



In 2003, a manufacturer made a profit of $300 million. This amount was $100 million more than the profit in 2002. What was the profit in 2002?

Example 5

Let p represent the profit in 2002 (in millions of dollars).

This year’s profit300

is =

300 = 100 + p–100 –100

200 = p

The profit was $200 million in 2002.

100 million100

More than +

Last year’s profitp

Match the Equation with its Answer…

Take out a separate sheet of paper. Write your name date and period at

the top. Write each equation. Show your work. Match the question card (blue) with

the answer card (yellow).

Addition

X + 5 = -9 X + 5 - 5 = -9 -5 X = -14

-6 + X = -4 -6 + 6 + X = -4 + 6 X = 2

Try the following on your paper.

10 = X + 3

5 + X = 9

6 = 3 + X

Answers!!!

X = 7

X = 4

X = 3

Equations with subtraction

X - 5 = 8 X - 5 + 5 = 8+5 X = 13

5 - X = 6 5 - 5 + X = 6 - 5 X = 1

Try the following on your paper.

X - 7 = -1

X - 4 = 66

8 = X - 2

-8 = X - 2

Answers!!!

X = 6

X = 70

X = 10

X = -6

Multiplication of Equations

3X = -9 3X/3 = -9/3 X = -3

-5X = -40 -5X/-5 = -40/-5 X = 8

Try these on your paper.

4X = -16

-1X = 9

6 = 5X

12X = 3

Answers!!!

X = -4

X = -9

X = 6/5

X = 1/4

Division of Equations

1/2X = 4 (2/1)1/2X = 4(2) X = 8

-3/4X = 6 (-4/3)(-3/4)X = 6(-4/3) X = -8

Try these on your paper.

X/3 = 9

-X/4 = 7

1/3X = -1

4 = X/4

Answers!!!

X = 27

X = -28

X = -3

X = 16

Write the following on your paper for a quiz grade.1) _4X = 15

2) X/2 = -8

3) 9 - X = -1

4) -12 + X = 0

5) -X/3 = 4

6) X + 5 = 5

7) X - 4 = 4

7) -X = 5

8) X + 50 =-50

8) X/5 = -55

Documents

Bellwork Copy and Answer 5 – 7 6 + -15 -14 - -10 6 x -7 -5 ÷ -5 -10 x -10