Mr. Northcutt's Math Classes Class Presentation

Transcription

1 Mr. Northcutt's Math Classes Class Presentation September 9, 2009 (6) Transition Math Math 1 Math 2 1

2 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

3 EX 1-1 (D2): 8-22 EVEN, ODD, 42-45, ODD z 10. p j / n 16. z d n 22. 4g d a+ 100b 37. C 39. A 42. B 43. I 44. C 45. H a. 500 b. 400

4 Investigation 1. Simplify the Expressions: Discuss Answers 4 Mr. Northcutt: Math 1 & 2

5 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

6 Example - No Grouping Simplify

7 Example - With Grouping Simplify 2[(13 4) 3]

8 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, EVEN 8

9 EX 1-1 (Day 1): 2-16 EVEN, EVEN 2. y c k 8. v n n n n 26. 5n b v p q The sum of a number q and The product of 9 and n plus The product of 7, h, and b. 9

10 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 = 7 8 3= 4 x + 2= 8 10 Mr. Northcutt: Math 1 & 2

11 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

12 Example: Equation from a Table 1. ID RELATIONSHIP: 2. DEFINE VARIABLE: 3. WRITE EQUATION: 12

13 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,

14 14 EX 1.2: 1-5, 7-10, EVEN, 27-31, 34-35, ODD 1. MN means segment MN. MN means the length of MN. 2. Find the sum PQ+QN Find the difference MN-MP cm cm cm should be subtracted from 14 not added. BC=14-9=5 14. not congruent Yes, since FB=FC+CB, then FB>CB; No, relationship between AD & BC is not known D , , , AC=6, CD=6, AB=3, BC=3 BD=9, AD=12; P(>3)=2/3 4 out of 6 segments > 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.

15 EX 1.2: 1-5, 7-10, EVEN, 27-31, 34-35, ODD 35. a. See sketch. b. 21 ft true 45. false 15

16 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

17 Example: Segment Bisector Identify the segment bisector of segment PQ then find PQ. l Q P 5x 7 M 11 2x 17

18 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 +, y 2 y 2 M B y 1 A x 1 x 2 18

19 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

20 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 = ( x x ) + ( y y ) y 2 B (y 2 -y 1 ) y 1 A 20 x 1 x 2 (x 2 -x 1 )

21 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 units 21