Mr. Northcutt's Math Classes Class Presentation September 9, 2009 (6) Transition Math Math 1 Math 2 1
Transition Math Daily Summary Announcements None Topic 2: Variables & Expressions (D1) 1. Using the Order of Operations 2. Using Grouping Symbols Assignment EX 1-2 (D1): 1-23 GET A WHITEBOARD! 2
EX 1-1 (D2): 8-22 EVEN, 27-39 ODD, 42-45, 47-53 ODD 3 8. 6 z 10. p 2 12. j 4 14. 3 / n 16. z 8 18. d 12 20. 5n 22. 4g 27. 7 4 160 29. 16 100 31. 12 33. d 20 35. 70a+ 100b 37. C 39. A 42. B 43. I 44. C 45. H 47. 72 49. 75 51. 9563 53. a. 500 b. 400
Investigation 1. Simplify the Expressions: 3+ 5 2 2. Discuss Answers 4 Mr. Northcutt: Math 1 & 2
Order of Operation 5 The ORDER you perform operations affects the final value! ORDER OF OPERATIONS gives us an agreed order: 1. Work inside GROUPING symbols. 2. MULTIPLY & DIVIDE from left right 3. ADD & SUBTRACT from left right GROUPING SYMBOLS ( 3 + x) [ 4 y] 3+ 5 = ( 3 + 5) ( 4 2) 4 2 G E M D A S
Example - No Grouping Simplify 2+ 5 3 4 12 + 6 3 6
Example - With Grouping Simplify 2[(13 4) 3] 1+ 10 2 4 7
Math 1 Daily Summary Announcements None Topic 2: Variables & Expressions (D1) 2. Modeling Relationships with Equations and Formulas Assignment EX 1-1 (Day 2): 17-24, 39-43, 54-66 EVEN 8
EX 1-1 (Day 1): 2-16 EVEN, 26-38 EVEN 2. y -12 4. 15c 17 6. k 8. v + 3 10. n -11 8. n 12. 82 14. 13 + 2n 11 16. n 26. 5n + 6.7 3b 28. 4.5 30. 7 3v p q 32. + 14 3 34. The sum of a number q and 5. 36. The product of 9 and n plus 1. 38. The product of 7, h, and b. 9
Equation EQUATION: An EQUATION is a mathematical sentence that uses an equal sign ( = ). An equation is TRUE if the expressions on either side of the = are the same. It is FALSE if they are different. OPEN SENTENCE: An equation that contains one or more variables. Classify the following mathematical sentences: x + 6 3+ 4= 7 8 3= 4 x + 2= 8 10 Mr. Northcutt: Math 1 & 2
Example: Writing an Equation Virgin Records sells DVD s for $12 each. Write an equation for the total cost of a given number of DVD s. 1. ID RELATIONSHIP: 2. DEFINE VARIABLE: 3. WRITE EQUATION: 11
Example: Equation from a Table 1. ID RELATIONSHIP: 2. DEFINE VARIABLE: 3. WRITE EQUATION: 12
Math 2 Daily Summary Announcements QUIZ over 1.1 thru 1.3 on Friday, September 11 Topic: Use Midpoint & Distance Formulas BQ: How do you find middle and length of a segment? Assignment EX 1.3 (D1): 1-6, 9, 10, 12-15, 35-40, 48, 60-64 13
14 EX 1.2: 1-5, 7-10, 12-26 EVEN, 27-31, 34-35, 37-45 ODD 1. MN means segment MN. MN means the length of MN. 2. Find the sum PQ+QN. 22. 22 Find the difference MN-MP. 24. 32 3. 2.1 cm 4. 3.2 cm 5. 3.5 cm 7. 44 8. 65 9. 23 10. 15 12. 9 should be subtracted from 14 not added. BC=14-9=5 14. not congruent 16. 3 18. 12 20. Yes, since FB=FC+CB, then FB>CB; No, relationship between AD & BC is not known. 26. 42 27. D 28. 20,1 29. 20, 40 30. 6, 11 31. AC=6, CD=6, AB=3, BC=3 BD=9, AD=12; P(>3)=2/3 4 out of 6 segments >3. 34. a. 5, 5, 5; games lost b. ~45%, ~42%, ~38% c. The sum of the lengths of the bars for wins and losses represents the total number of games played.
EX 1.2: 1-5, 7-10, 12-26 EVEN, 27-31, 34-35, 37-45 ODD 35. a. See sketch. b. 21 ft 37. 12 39. 46 41. 3 43. true 45. false 15
Midpoint & Segment Bisector MIDPOINT: The point that divides the segment into two congruent segments. B M is the MIDPOINT of AB A M AM AM MB MB SEGMENT BISECTOR: A point, ray, line, segment or plane that intersects the segment at its midpoint. C CD is a SEGMENT BISECTOR of AB A D M B AM AM = = MB MB 16 Mr. Northcutt: Math 1 & 2
Example: Segment Bisector Identify the segment bisector of segment PQ then find PQ. l Q P 5x 7 M 11 2x 17
Midpoint Formula MIDPOINT FORMULA: The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints. If A(x 1,y 1 ) and B(x 2,y 2 ) then the midpoint M of segment AB has coordinates: x + x 1 2 y +, 1 2 2 y 2 y 2 M B y 1 A x 1 x 2 18
Example: Midpoint Formula The midpoint of segment VW is M(-1, -2). One endpoint is W(4, 4). Find the coordinates of endpoint V. 19
DISTANCE FORMULA DISTANCE FORMULA: If A(x 1,y 1 ) and B(x 2,y 2 ) are points is a coordinate plane, then the distance between A and B is: AB 2 1 2 = ( x x ) + ( y y ) 2 1 2 y 2 B (y 2 -y 1 ) y 1 A 20 x 1 x 2 (x 2 -x 1 )
Example: Distance Formula What is the approximate length of segment AB with endpoints A(-3,2) and B(1,-4)? a. 6.1 units b. 7.2 units c. 8.5 units d. 10.0 units 21