Bellwork Copy and Answer 5 – x ÷ x -10

2 Tuesday 10/18

2-5 Solving Equations Containing Integers pg. 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 Variable 3. 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  How can you solve equations that contain integers?

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. Pick my nose to continue

16 When you worry about what you wear, W e worry about having our Pocket Protectors. Pick my nose to continue

17 When you worry that you won’t meet your friends, W e worry that we won’t have our calculators. Pick my nose to continue

18 We are just a little bit opposite. That may be why we are so good at Algebra, because that is all Algebra is… Pick my nose to continue …doing the opposite.

19 Think of some words that are opposites. For example, what do you think of as the opposite of word below. Pick my nose to continue 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. Pick my nose to continue Up = __________ Out = __________ Small = __________ Stinky = __________

21 Some possible answers are… Pick my nose to continue 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. Pick my nose to continue Add = __________ Subtract = __________ Multiply = __________ Divide = __________

23 Your answers should have been… Pick my nose to continue 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. Pick my nose to continue + = __________ - = __________ x = __________ ÷ = __________

25 Your answers should have been… Pick my nose to continue + = __________ - = __________ x = __________ ÷ = __________ - + ÷ x

26 Congratulations! You just did some ALGEBRA Pick my nose to continue 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. Pick my nose to continue

28 One Step Equations Algebra Geek Patrol Pick my nose to continue 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 One Step Equations X + 3 = 17 Click on the answer below that is the opposite of add 3. Add 3 Subtract 3 Multiply 3 Divide 3

30 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 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 One Step Equations 4x = 20 Click on the answer below that is the opposite of multiply by 4. Add 4 Subtract 4 Multiply by 4 Divide by 4

33 Algebra Geek Patrol One Step Equations No, not really. Remember, we are looking for the opposite of multiply by 4. Click on Buck and give it another try.

34 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 One Step Equations x5x5 Click on the answer below that is the opposite of divide by 5. Add 5 Subtract 5 Multiply by 5 Divide by 5 = 10

36 Algebra Geek Patrol One Step Equations Uhh, in a word, no. Remember, we are looking for the opposite of divide by 5. Click on Buck and give it another try.

37 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 One Step Equations Click on the answer below that is the opposite of x 7 ÷ 7 X – 7 = 8

39 Algebra Geek Patrol One Step Equations Almost Remember, we are looking for the opposite of - 7. Click on Buck and give it another try.

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 Pick my nose to continue 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 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. Click on Buck and give it another try. 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 = _________ 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 Pick my nose to continue 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

Steps to Solving Equations: 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 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. Click on Buck and give it another try. Algebra Geek Patrol

50 2 One Step Equations Nice Job! Algebra Geek Patrol X + 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. Pick my nose to continue

51 One Step Equations Algebra Geek Patrol Pick my nose to continue 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 = _________ 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 One Step Equations Nice Work You are one pen closer to being an Official Algebra Geek Don’t worry, I won’t tell anyone. Pick my nose to continue

55  Now, try these on your own! X + -6 = x = -12

56 One Step Equations Algebra Geek Patrol Pick my nose to continue 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 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. Click on Buck and give it another try. Algebra Geek Patrol

59 I know all the cool words. 1 One Step Equations Sweet! X - 4 = 11 _________ X =15 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 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 Third, combine the other side. Pick my nose to continue Algebra Geek Patrol Write this problem in the box on your worksheet.

60 One Step Equations Algebra Geek Patrol Pick my nose to continue 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. Pick my nose when you are finished Are you sure you are done? Check your answer before moving on. Algebra Geek Patrol Go ahead and give it a try! I won’t tell anyone. Write this problem in the box on your worksheet.

62 Make sure you have copied all the steps on your paper and then click on Buck. 2 One Step Equations X - 6 = 14 _________ 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! Pick my nose to continue Algebra Geek Patrol

65 Thursday 10/20/11

 2-5  Solving Equations Containing Integers  pg. 100

Essential Question  How can you solve equations that contain integers?

68 Algebra Geek Patrol The Pocket Protectors of Algebra

69 One Step Equations Algebra Geek Patrol Pick my nose to continue 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. Pick my nose to continue Add = __________ Subtract = __________ Multiply = __________ Divide = __________

71 Your answers should have been… Pick my nose to continue 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. Pick my nose to continue + = __________ - = __________ x = __________ ÷ = __________

73 Your answers should have been… Pick my nose to continue + = __________ - = __________ x = __________ ÷ = __________ - + ÷ x

74 Who REMEMBERS?  What are the 3 steps to solve a one step equation? I___________ S___________ C___________ 74

Steps to Solving Equations: 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 x 2 ÷ 2 2x = 18 Algebra Geek Patrol Write this problem in the box on your worksheet.

77 1 One Step Equations Not quite. Remember, we are looking for the opposite of x 2. Click on Buck and give it another try. Algebra Geek Patrol

78 You remember from working with fractions, what happens when one number is divided by the same number? ÷ ___ __2x 18 1 One Step Equations Yes! So, let’s put ÷ 2 on each side of the equation. 2x = _________ 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

x = 15 2 One Step Equations Rama-Lama–Ding-Dong 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 do the problem on your paper. First, put the opposite on both sides. Remember to rewrite it as a fraction. Write this on your paper, and work this part of the problem. Click the pens to continue Third, combine the other side. Pick my nose to continue Don’t worry. It’s a Geek Thing. ÷ ___ __3x 15 X = = Algebra Geek Patrol Second, cancel out one side. 5 Write this problem in the box on your worksheet.

80 One Step Equations Algebra Geek Patrol Pick my nose to continue Congratulations, Now let’s try one last problem.

81 3 One Step Equations 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. Go ahead and give it a try! I’ve been sworn to secrecy. 4x = 24 Write this problem in the box on your worksheet.

82 ___ __4x 244x = 24 3 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. Click the pens to continue 4 4 X = = 6 Algebra Geek Patrol

83 3 One Step Equations Great! Your future’s so bright, I gotta wear shades. Actually, I already am. Pick my nose to continue Algebra Geek Patrol

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

85 One Step Equations Algebra Geek Patrol Pick my nose to continue 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 ÷ x 3 ÷ 3 x3x3 = 12 Algebra Geek Patrol

87 1 One Step Equations Doh! Not Really. Remember, we are looking for the opposite of ÷ 3. Click on Buck and give it another try. 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. x3x3 = 12 Algebra Geek Patrol 3 3 That’s Right! Write this problem in the box on your worksheet.

89 2 One Step Equations 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 do the problem on your paper. First, put the opposite on both sides. Write this on your paper, and work this part of the problem. Click the pens to continue Third, combine the other side. Pick my nose to continue Second, cancel out one side. x7x7 = 3 Algebra Geek Patrol 7 x x 7 X = 21 Write this problem in the box on your worksheet.

90 One Step Equations Algebra Geek Patrol Pick my nose to continue And Now…. (Drum Roll, Please) THE LAST Practice PROBLEM!

91 3 One Step Equations 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. Go ahead and give it a try! I can’t tell anyone. I don’t even have a mouth. x5x5 = 6 Write this problem in the box on your worksheet.

92 5 x 3 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. Click the pens to continue x5x5 = 6x 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 Pick my nose to continue 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 = –1 Check –6 + x = –7 –6 + (–1) = –7 –7 = –7

Professor Burger the Math Man Example  dia/homework_help/msm2/msm2_ch 02_05_homeworkhelp.html

Example 2 Solve each equation. Check each answer. y – 9 = – y = –31 Check –31 – 9 = –40 ? y – 9 = –40 –40 = –40 ?

Example 3 Solve each equation. Check each answer. c4c4 = –24 c4c4 c4c4 = 4(–24) 4 c = –96 Check c4c4 = –24 –96 4 = –24 –24 = –24

Professor Burger the Math Man Example  dia/homework_help/msm2/msm2_ch 02_05_homeworkhelp.html

Example 4 Solve each equation. Check each answer. –400 = 8y 8 –50 = y Check –400 = 8 y –400 = 8(–50) –400 = –400

Professor Burger the Math Man Example  dia/homework_help/msm2/msm2_ch 02_05_homeworkhelp.html

In 2003, a manufacturer made a profit of $300 million. This amount was $100 million more than the profit in What was the profit in 2002? Example 5 Let p represent the profit in 2002 (in millions of dollars). This year’s profit 300 is = 300 = p – = p The profit was $200 million in million 100 More than + Last year’s profit p

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 =  X = -14  -6 + X = -4  X =  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 = 8+5  X = 13  5 - X = 6  X =  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) 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