Mr. Northcutt's Math Classes Class Presentation

Transcription

1 Mr. Northcutt's Math Classes Class Presentation October 2, 2009 (22) Transition Math Math 1 Math 2 1

2 Transition Math Daily Summary Announcement(s): Retests: Can take a retest is you work with me or Ms. Foot prior. Objective(s): Refine your skills with adding and subtracting integers - become experts! Assignment: Worksheet: Adding and Subtracting Integers 2 MT Ability to perform operations with Rational Numbers

3 EX 1-8: 2, 9, 10, : 78 students 9: C 10: J 15: 0 16: 17 17: 25 3

4 Rules for Adding & Subtracting Single (1) Operation + the first number increases ( on number line) - the first number decreases ( on number line) Rules to Get a Single (1) Operation +(-2) -2 -(-2) +2 Right Left 4

5 Examples ( 6) ( 6) ( 6) 5

6 6 Math 1 Daily Summary Announcement(s): Retest if you work with me prior o Before/After School, 2 nd or 3 rd Period, 2 nd Lunch Objective(s): Understand and be able to identify an EQUATION. Understand and state the INVERSE operation for addition and subtraction. Know how to SOLVE an equation (w/ add. & sub.) Assignment: EX 2-1 (D1): 1-19 ODD, 55, 57, 60, 71, 74, 77, 81, 85, ODD

7 = Identifying an Equation 7

8 Equality Properties Addition Subtraction 8

9 Inverse Operations Addition Subtraction 9

10 Solving an Equation What does it mean to SOLVE an EQUATION? x + 5= 6 12 = x + 6 How do you know if a SOLUTION is correct? How do you SOLVE it? 10

11 Examples Solve n 2= 5 2 x = y = x =

12 Example Kellen withdrew $25 from his bank account at an ATM. The transaction slip said his balance was $ Write and solve an equation to find his previous balance. 12

13 Math 2 Daily Summary Announcement(s): QUIZ: Lessons 2.4 thru 2.5 Monday Objective(s): Know what a PROOF is and use 2-Column Proofs. Write proofs about segments and angles using geometric theorems (Proofs - NCTM 7). Assignment: EX 2.6 (D1): 1-13, 34, 36 Reading: Lesson 2.6 NCTM Standards Recognize reasoning & proof as fundamental skills. Develop mathematical arguments and proofs. 13

14 EX 2.5: 22, 24, 32, 39, 40, 41, 42 22: m 2 = m 1 24: 5, 40 32: A = (½)bh. Solve for h (justify). 68 in (work) 39: 32 o (work) 40: 92 o (work) 41: 1 Example: Square 42: is 14

15 Algebraic Properties of Equality Addition Property If a=b, then a + c = b + c Subtraction Property If a=b, then a - c = b - c Multiplication Property If a=b, then ac = bc Division Property If a=b and c 0, then a c = b c Distributive Property a(b +c) = ab + ac Substitution Property These are properties of Real Numbers. Segment lengths & angle measures are real numbers, so these properties will be used in geometric proofs. R If a = b, than a can be substituted for b in any equation or expression. 15

16 More Properties of Real Numbers Reflexive Property R For any real number a, a = a Symmetric Property For any real numbers a and b, if a = b then b = a Transitive Property For any real numbers a, b, and c, if a = b and b = c, then a = c 16

17 Example: Give Reasons for Each Step Given : m 1 = m 3 Prove : m EBA = m DBC C E D A 1. m 1 = m 3 2. m EBA = m 3 + m 2 3. m EBA = m + 1 m 2 4. m + 1 m 2 = m DBC 5. m EBA = m DBC B 17

18 Theorems (Can be Proven) Congruence of Segments and Angles Segment and Angle congruence is Reflexive, Symmetric and Transitive. AB AB A A AB CD CD AB A B B A ( ) AB CD & CD EF AB EF ( A B& B C) A B 18

19 Symmetric Prop. of Angle Congruence Given: Prove: STATEMENTS 2-Column Proof REASONS Typically the 1 st Reason Given Given Facts Definitions Properties Postulates Theorems 19