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## Algebra 1 Chapter 1

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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**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**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!!**Guided Practice Page 20**2. S-5 = 3 +5+5 S = 8 3. 17= w-4 +4+4 21 = w**Independent Work Time**Page 20 Problems: 21-25, 33-37, 51-56 Reminder: Math Vocab Quiz Monday**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**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:**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 Solving Ch1**Sec 3 #’s 21-25, 52-55, 61-64**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**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**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**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:**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**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**Practice and Problem Solving pg 36**#’s 24,30,33,37,38,39,41,43,44,45,46,50,51,52,**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**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**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**Distribution Problem:**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**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**#’s 23,24,38,48,49,50 Reminder: Quiz Friday Sections 1-4**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!!!**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**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.**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**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**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**HW Problems: Practice and Problem Solving page 51**#’s 4-7,10-13**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)**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**Quiz Time!!**Please put everything under your desk except a water bottle and a pencil! Take your time!**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**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**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**Practice and Problem Solving pg 57**#’s 15, 16, 17, 28, 35, 36