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Algebra 1 Chapter 1

Algebra 1 Chapter 1

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Algebra 1 Chapter 1

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  1. Algebra 1 Chapter 1 Ms. Fisher

  2. 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

  3. 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

  4. 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!

  5. 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

  6. 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

  7. 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

  8. Your Turn Now! 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

  9. 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!

  10. 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

  11. 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

  12. 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

  13. Solving Equations Using Subtraction X + 7 = 9 -7-7 X = 2 Check: X + 7 = 9 ALWAYS CHECK 2 + 7 = 9 YES!!

  14. Guided Practice Page 20 2. S-5 = 3 +5+5 S = 8 3. 17= w-4 +4+4 21 = w

  15. Independent Work Time Page 20 Problems: 21-25, 33-37, 51-56 Reminder: Math Vocab Quiz Monday

  16. 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

  17. 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!

  18. Quiz Time Put everything under your desk expect a pencil and water bottle

  19. 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!!

  20. Solving Equations That Contain Fractions 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!!

  21. Guided Practice: 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

  22. Students Independently do Practice and Problem Solving Ch1 Sec 3 #’s 21-25, 52-55, 61-64

  23. Agenda • 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

  24. Review of HW: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

  25. Solving Two Step Equations: 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

  26. 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

  27. Simplifying before Solving: 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

  28. Distributing 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

  29. Practice and Problem Solving pg 36 #’s 24,30,33,37,38,39,41,43,44,45,46,50,51,52,

  30. Agenda: • 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

  31. Review of 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

  32. Solving Equations with Variables on Both Sides 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

  33. Distribution Problem: 2(y+6)=3y Step #1: Distribute 2 2y +12 = 3y Step 2:Subtract 2y from each side 12=y

  34. Combining Like Terms and Distributing 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

  35. Someone Come up to the board and do the following Problem… Guided Practice 2x-1= x+11

  36. Practice and Problem Solving page 43 #’s 23,24,38,48,49,50 Reminder: Quiz Friday Sections 1-4

  37. AGENDA • 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!!!

  38. HW Problems: Practice and Problem Solving page 43 Answers#’s 23,24,38,48,49,50 23. 6 24. -1 38. -3 48. 1 49. 4 50. 4

  39. Solving for a Variable 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.

  40. F=9 C + 32 Solve for C 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

  41. Guided Practice: page 51 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

  42. Review for quiz tomorrow: 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

  43. HW Problems: Practice and Problem Solving page 51 #’s 4-7,10-13

  44. Agenda • 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)

  45. HW page 51 #’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

  46. Quiz Time!! Please put everything under your desk except a water bottle and a pencil! Take your time!

  47. Section1.7 Solving Absolute-Value Equations • 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

  48. Solve: 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

  49. Guided Practice: pg 57 2. 9= x+5 Case 1 Case 2 9= x+5 -9= x+5 -5 -5 -5 -5 4=x-14=x

  50. Practice and Problem Solving pg 57 #’s 15, 16, 17, 28, 35, 36