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### Algebra 1 Chapter 1

Ms. Fisher

How Each Math Class Will Be Conducted:

- I will teach the lesson
- We will do the Guided Practice together
- You will do the Practice and Problem Solving Independently

Math Vocabulary you should be familiar with:

- Expression
A mathematical phrase that contains operations, numbers,

and/or variables Example: 25 + a(b)

- Variable
A symbol used to represent a quantity Example: a

- Constant
A value that does not change Example: 25 + a(b)

- Order of Operations
A process for evaluating expressions

PEMDAS

Parenthesis Exponents Multi/Divide Add/ Subtract

If a=5 and b=5 [25 + a(b)] = 25

2

Hmmm…. Could I have a vocabulary quiz in Math class?

YES!!!

I often give short 5 point Quizzes!!! These quizzes will help build your grade! Consider it a free 5 points! You simply need to pay attention!

Chapter 1 Section 1: Writing Algebraic Symbols to Words

- X + 3
The sum of X and 3

- M-7
The difference of m and 7

- K/5
K divided by 5

Guided Practice Ch1 Page 9

Section 1: Give two ways to write each algebraic expression in words:

2. n-5

5 less than n

or n decreased by 5

3. f/3

The quotient of f and 3

or f divided by 3

10. George drives at 45 mi/h. Write an expression for the number of miles George travels in h hours.

45h

11. The length of a rectangle is 4 units greater than its width w. Write an expression for the length of the rectangle.

W + 4

Guided Practice Chapter 1 Page 9

Evaluate each expression for a=3, b=4, and c=2

12. a-c

3-2=1

13. ab

3 (4)=12

14. b/c

4/2=2

Go Down to the Section Labeled

“Practice and Problem Solving”

Do problems 17-31 and 41, 45, 46, 47

Whatever you do not finish will be homework

When you arrive tomorrow to class what is expected?!

Homework is out on your desk and ready to be checked.

Did you check the parking lot on the board?

Are all parking lots numbers taken care of, I will need volunteers to come up and show their work!

Tomorrow: Ch 1 Section 1.2Solving Equations by adding or subtracting

Vocabulary you should be familiar with…

Equation: Mathematical statement that two expressions are equal

Solution:A value of the variable that makes the equation true. To find solutions you need to isolate the variable!

Solving Equations by using Addition:

X-10= 4

+10 +10

X = 14

Today’s Agenda

1. Parking Lot What problems would you like me to go over?!

2. Teach Ch1 Section 2

3. Together we do Guided Practice

4. Independently You Do “Practice and Problem Solving” pg 20

Vocabulary you should be familiar with…

Equation: Mathematical statement that two expressions are equal

Solution:A value of the variable that makes the equation true. To find solutions you need to isolate the variable!

Solving Equations by using Addition:

X-10= 4

+10 +10

X = 14

Solving Equations Using Subtraction

X + 7 = 9

-7-7

X = 2

Check: X + 7 = 9 ALWAYS CHECK

2 + 7 = 9 YES!!

Agenda:

- Any questions to park in our class parking lot?! Review HW
- Quiz
- Teach Ch1 Sec 1.3
- Do Guided Practice Together pg 27
- Students Independently do Practice and Problem Solving
#’s 21-25, 52-55, 61-64

Review of HW:Pg 20 Problems: 21-25, 33-37, 51-56

21. 9 33. -17 51. x-10=12 x=22

22. 7 34. -15 52. x-13=7 x=20

23. 17 35. 1,500 53. x+8=16 x=8

24. -7 36. 258 54. x-3=-8 x=-5

25. 4/7 37. -.05 55. 5+x=6 x=1

Which Questions Would You Like ME To Go Over On The Board? Park them In The Parking Lot!

Quiz Time

Put everything under your desk expect a pencil and water bottle

Chapter 1 Section 3; Solving Equations by Multiplying or Dividing

-4 = k Step #1: Isolate the variable- get the variable by itself

-5

(-5) (-4) = (-5)[ k ]

-5

(-5) (-4) = (-5)[ k ]

-5

(-5) (-4) = [ k ]

20 = k

Self Check: Go back, Plug 20 in for k 20/-5= -4 YES!!

Solving Equations That Contain Fractions Dividing

5 v=35 ** Multiple both sides by the reciprocal of 5/9 which is 9/5**

9

(9)(5) v = (9) 35

5 9 5

(9)(5) v = (9) 35

5 9 5

V= 315/5

V=63

Self Check: Go back, Plug 63 in for v; 63 (5)/9 = 35 Yes!!

Guided Practice: Dividing

19. The Baseball Birthday Batter Package at a minor league ballpark costs $192. The package includes tickets, drinks, and cake for a group of 16 children. Write and solve an equation to find the cost per child.

Step #1

For thing you do, write down your “knowns!!”

- Total cost=$192
- Total Package= 16c
- Total Package=Total cost
Step #2 Write the equation

16c=192

Step #3 Solve the Equation

C=192/16

C= $12/ cost per child

Students Independently do Practice and Problem DividingSolving Ch1 Sec 3

#’s 21-25, 52-55, 61-64

Agenda Dividing

- Any questions to park in our class parking lot?! Review HW
- Teach Ch1 Sec 1.4
- Do Guided Practice Together pg36
- Students Independently do Practice and Problem Solving

Review of DividingHW:Pg27 Problems: 21-25, 52-55, 61-64 Ch1 Sec # 3 Any Questions you would like to park in our parking lot for me to go over in detail?!

21. 24 52. 5x=45 x=9

22. -200 53. -3x=12 x=-4

23. -36 54. x/4=10 x=40

24. 12 55. x/3=-8 x=-24

25. -150

Solving Two Step Equations: Dividing

10= 6-2x

Step one: Get rid of what is NOT attached to x FIRST

10 = 6-2x

-6 -6

4 = -2x

Step two: Get x by itself, get rid of what is attached to x, divide by -2

4 = -2x

-2 -2

-2=x

Chapter 1 Section 4: Solving Two-Step and Multi-Step Equations pg 32

Alex belongs to a music club. In this club, students can buy a student discount card for $19.95. This card allows them to buy CDs for $3.95 each. After one year, Alex has spent $63.40.

Find the number of CDs c that Alex bought…

3.95c +19.95 = 63.40

-19.95 -19.95

3.95c=43.45

c= 43.45/3.95

c=11

Alex bought 11 CDs

Simplifying before Solving: Equations

6x + 3 – 8x = 13

Step #1: Combine like terms

6x +(-8X) = -2x

-2x +3 = 13

Now, Get rid of what is not attached to x first

-2x +3 = 13

-3 -3

-2x = 10

Step #3 Get x by itself by dividing by -2

-2x/-2 = 10/-2

x= -5

Distributing Equations

9= 6 – (x + 2)

Step #1 Distribute the -1 to everything inside the parenthesis

9= 6 +(-1) (x) + (-1) (2)

9= 6 + -x + -2

Step #2 Combine like terms

9 = 4-x

-4 -4

5 = -x

-5 = x

Agenda: Equations

- First HW Check 5 points
- Any questions to park in our class parking lot?! Review HW
- Teach Ch1 Sec 1.5
- Do Guided Practice Together pg43
- Students Independently do Practice and Problem Solving
- Reminders: Chapter one Quiz on Sections 1-4 Friday September 12th

Review of Equations HW:Pg36 Problems: 24,30,33,37,38,39,41,43-46,50-52 Ch1 Sec # 4 Any Questions you would like to park in our parking lot for me to go over in detail?!

24. 2 45. -1/2

30. 1/5 46. -10

33. 1 50. 2n-7=19 n=13

37. 28/5 51. 8-3n=2 n=2

38. 25 52. 2n+5=11 n=3

39. 3

41. 8

43. 7

44. 16

Solving Equations with Variables on Both Sides Equations

7k = 4k + 15

Step #1: You want to get the Variables to ONE side! Choose the side that will keep the variable POSITIVE!!

7 is BIGGER than 4, so I CHOOSE to subtract 4K

7k= 4k + 15

-4k -4k

3k= 15

3k/3= 15/3

k= 5

Distribution Problem: Equations

2(y+6)=3y

Step #1: Distribute 2

2y +12 = 3y

Step 2:Subtract 2y from each side

12=y

Combining Like Terms and Distributing Equations

3-5b +2b = -2-2(1-b)

Step one:

Combine like terms

3-3b = -2-2(1-b)

Distribute -2

3-3b= -2 -2+2b

3-3b= -4 +2b

+4 +4

7-3b=2b

+3b = +3b

7 = 5b

7/5 = 5b/5

7/5 =b

Someone Come up to the board and do the following Problem… Guided Practice

2x-1= x+11

Practice and Problem Solving page 43 Guided Practice

#’s 23,24,38,48,49,50

Reminder: Quiz Friday Sections 1-4

AGENDA Guided Practice

- Any questions to park in our class parking lot?! Review HW
- Teach Ch1 Sec 1.6
- Do Guided Practice Together pg51
- Students Independently do Practice and Problem Solving
- Reminders: Chapter one Quiz on Sections 1-4 tomorrow!!!

HW Problems: Practice Guided Practiceand Problem Solving page 43 Answers#’s 23,24,38,48,49,50

23. 6

24. -1

38. -3

48. 1

49. 4

50. 4

Solving for a Variable Guided Practice

Step One: Locate the variable you are asked to solve for in the equation.

Step Two: Identify the operations on this variable and the order in which they are applied.

Step three: Use inverse operations to undo operations and isolate the variable.

F=9 C + 32 Solve for Guided PracticeC

5

F = 9C + 32

5

-32 -32

F-32= 9C

5

5/9 (F-32)= (5/9) (9/5)C

5/9(F-32)=C

Guided Practice: page 51 Guided Practice

2. a.) Solve a= 46c Solve for c

a= 46c

/46 /46

a/46= c

5. Solve m-4n=8 Solve for m

+4n +4n

m=4n+8

Review for quiz tomorrow: Guided Practice

1. 6= 1-x

Volunteer to front board please!

2. 5x+4-2x=22

Volunteer to front board please!

3. 4=7-3(x+3)

Volunteer to front board

HW Problems: Practice and Problem Solving page Guided Practice51

#’s 4-7,10-13

Agenda Guided Practice

- Any questions to park in our class parking lot?! Review HW
- Quiz on Sections 1-4
- Teach Ch1 Sec 1.7
- Do Guided Practice Together pg57
- Students Independently do Practice and Problem Solving
(Mrs. Ruzicka walk around and assist as needed)

HW page 51 # Guided Practice’s 4-7,10-13

4. s= 6-3t/t

5. m=4n+8

6. f= 6g-4

7. a=10/b+c

10. s= -2-4r

11. x=k+5/y

12. m/p-6=n

13. x-2/z=y

Quiz Time!! Guided Practice

Please put everything under your desk except a water bottle and a pencil!

Take your time!

Section1.7 Solving Absolute-Value Equations Guided Practice

- Recall that the absolute value of a number is that number’s distance from zero on a number line. For example, -5 = 5 and 5 = 5
5 spaces both ways

5

-5

0

Solve: Guided Practice

4 x+2 = 24

4 4

X+2 = 6

Case 1 Case 2

X+2=-6 X+2=6

-2 -2 -2 -2

X=-8 X=4

The solutions are -8 and 4

Practice and Problem Solving Guided Practicepg 57

#’s 15, 16, 17, 28, 35, 36

Agenda Guided Practice

- Any questions to park in our class parking lot?! Review HW
- Teach Ch1 Sec 1.8
- Do Guided Practice Together pg65
- Students Independently do Practice and Problem Solving
(Mrs. Ruzicka walk around and assist as needed)

Reminder Chapter 1 Test this Friday!!!

Practice and Problem Solving Guided Practicepg57#’s 15, 16, 17, 28, 35, 36

15. -9, 13

16. -5, 7

17. -2, 2

28. 1

35. X = 3

36. X = 1

1.8 Rates, Ratio’s, and Proportions Guided Practice

Ratio: is a comparison of two quantities by division. The ratio of a to b can be written a:b or a/b

A statement that two ratios are equivalent, such as 1/12=2/24, is called a proportion.

The ratio of faculty members to students at college is 1:15. There are 675 students. How many faculty members are there?

Step 1: Write a ratio comparing faculty to students

Faculty 1

Student 15

Step 2: Write a proportion. Let X be the number of faculty members

1 = x

15 675

Now solve for X

(675)1 = x (675)

15 675

x= 45 faculty members

Cross Product Property: There are 675 students. How many faculty members are there?

a = c

b d

a(d)=c(b)

Look at previous example..

1 = x

15 675

1 (675)=x(15)

675=x15 Now what do we do? Divide both sides

by 15 to get x by itself! X=45

Solving Proportions: There are 675 students. How many faculty members are there?

5 = 3

9 w

5 = 3

9 w

5w=9 (3)

5w=27

5w/5 =27/5

W=27/5

Practice and Problem Solving pg. 66 There are 675 students. How many faculty members are there?

#’s 26-37

Agenda There are 675 students. How many faculty members are there?

- Any questions to park in our class parking lot?! Review HW pg 66
- Teach Ch1 Sec 1.9
- Do Guided Practice Together pg72
- Students Independently do Practice and Problem Solving
(Mrs. Ruzicka walk around and assist as needed)

Reminder Chapter one Test Friday! Bring Reading Book with you Friday for after Exam!

Practice and Problem Solving pg. There are 675 students. How many faculty members are there?66#’s 26-37

26. 3 35. 1/9

27. 10 36. 60

28. -2.4 37. 45

29. -1

30. .9

31. 13

32. 3

33. 1.2

34. 6.8

Section 1.9- Applications of Proportions There are 675 students. How many faculty members are there?

Similar: Figures that have exactly the same shape, but not necessarily the same size.

E

B

8~x

A 5 C D 12 F

When stating that two figures are similar use the symbol ~

ABC ~ DEF m<A=m<D

Find the value of x m<B=m<E

Set up a proportion:

5 = 8 x= 19.2 meaning the length of DE is 19.2

12 x

Guided Practice pg. 72 There are 675 students. How many faculty members are there?#’s 2

2. A D

5m 7m x 4m

B C F E

ABC~ DEF Find the value of X

7 = 5

X 4

Cross Product Property

5x=28

X=28

5

X=5.6m

Practice and Problem Solving pg. 72 There are 675 students. How many faculty members are there?

#’s 6,7,14, 15, 16, 17

Answers:

6. 8m 15. 2.8ft

7. 7in 16. 4cm

14. 9m

Section 1.10 Precision and Accuracy There are 675 students. How many faculty members are there?

Precise vs. Accurate

Precise: is the level of detail in a measurement and is determined by the smallest unit or fraction of a unit that you can reasonably measure.

Accurate: Is the closeness of a measured value to the actual or true value.

** A precise measurement is only useful if the measurement is also accurate**

Think of a target. This person’s throw was precise, but was NOT

accurate, he never hit the bull's-eye!

Which measurement is more precise or accurate? There are 675 students. How many faculty members are there?

More precise?

4.33g or 4337 mg answer 4337mg

47 ft or 47.3ft answer 47.3ft

A cube weighs 5 grams.

A student weighs this cube on three different scales. Which scale is more accurate?

Scale A Scale B Scale C

5.01g 5.033g 4.98g

Scale B is most precise

Scale A is most accurate

End of Chapter 1!!!! There are 675 students. How many faculty members are there?

Review Time!!!!

Chapter One Test This Friday 9/19

What sections would you like to go back over? There are 675 students. How many faculty members are there?

Why don’t we take a tour through this power-point and briefly scan Chapter 1… You stop me when you wish to review something!

Chapter 1 Test There are 675 students. How many faculty members are there?

You will have the ENTIRE Period. Bring a book to read incase you complete the test early! Pencils out, everything else under your desk!

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