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Week 1 September 13, 2011

Welcome to Math Helps!. Week 1 September 13, 2011. Colleen Finley. Introductions. First you… in chat or on mic tell us: Your name Something about your family One thing you hope to do someday An interesting fact about yourself What do you want to know about me?. Slide designed by

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Week 1 September 13, 2011

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  1. Welcome to Math Helps! Week 1September 13, 2011 Colleen Finley

  2. Introductions • First you… in chat or on mic tell us: • Your name • Something about your family • One thing you hope to do someday • An interesting fact about yourself • What do you want to know about me? Slide designed by Lita Bledsoe, Landry Academy

  3. Blackboard Tour • Chat • Emoticons • Audio • Webcam • Permissions • Whiteboard

  4. Algebra 1 – class structureAlgebra is a skill.  Like any skill -- driving a car, baking cookies, playing the guitar -- it requires practice. A lot of practice. Written practice. • Weekly class meeting 60 minutes covering topics listed on syllabus and questions you have on your daily work! • Each week: • Work your regular math assignments. If you have questions, email them to me so we can go over them next class. • Work assignments given in or class. • Bring completed assignments as a file to be push to me in class. • Meet me in office hour, call, IM or set appointment time for us to work on any questions.

  5. Variables In algebra, we use letters as well as numbers, but the letters (variables) represent numbers.  The rules of algebra correspond to the rules of arithmetic, but we write those rules using letters (variables). For example, we know in arithmetic that the order in which we add two numbers does not matter. 7 + 3 = 3 + 7. Commutative Property In algebra, we express that as the rule: a + b = b + a. Letter a simply means the first number -- whatever it might be. Letter b means the second number.  We use letters because we mean that the rule will be true for any numbers.  http://www.themathpage.com/alg/algebraic-expressions.htm

  6. When numbers are added or subtracted, they are called terms. When numbers are multiplied, they are called factors. Here is a sum of four terms:  a − b + c − d. In algebra we speak of a sumof several terms, even though there are subtractions.  In other words, anything that looks like what you see above, we call a sum. Here is a product of four factors:  abcd. The word factors always signifies multiplication. And again, we speak of the "product" abcd, even though we do not name an answer. http://www.themathpage.com/alg/algebraic-expressions.htm

  7. Algebraic Properties Distributive Property: a(b + c) = ab + ac; a(b – c) = ab – ac Commutative Property: a + b = b + a; ab = ba Associative Property: a(bc) = (ab)c Symmetric Property: a = b then b = a Reflexive Property: a = a Transitive Property: If a = b and b = c, then a = c Identity Property of Multiplication: Any number multiplied times 1 equals itself; 1 x 5 = 5 Identity Property of Addition: Any number added w/ 0 equals itself; 0 + 7 = 7 Additive Inverse: Any number added to another number w/ the answer equaling zero; 4 + -4 = 0 Multiplicative Inverse: Any number multiplied to another number w/ the answer equaling 1; Any # multiplied by its reciprocal; 3 * 1/3 = 1 FLVS V10 tutoring slides

  8. A variable, such as x, is a kind of blank or empty symbol.  It is therefore available to take any value we might give it:  a positive number or, as we shall see, a negative number; a whole number or a fraction. In arithmetic, we might show a blank or a box in a problem: 2 + = 5 In algebra, we would show it like this: 2 + x = 5 http://www.themathpage.com/alg/algebraic-expressions.htm

  9. ObjectiveThe student will be able to: recognize and use the commutative and associative properties and the properties of equality. SOL: A.3 Designed by Skip Tyler, Varina High School

  10. Commutative Property Commutative means that the order does not make any difference. a + b = b + a a • b = b • a Examples 4 + 5 = 5 + 4 2 • 3 = 3 • 2 The commutative property does not work for subtraction or division.

  11. Associative Property Associative means that the grouping does not make any difference. (a + b) + c = a + (b + c) (ab) c = a (bc) Examples (1 + 2) + 3 = 1 + (2 + 3) (2 • 3) • 4 = 2 • (3 • 4) The associative property does not work for subtraction or division.

  12. Name the property1) 5a + (6 + 2a) = 5a + (2a + 6) commutative (switching order) 2) 5a + (2a + 6) = (5a + 2a) + 6 associative (switching groups) 3) 2(3 + a) = 6 + 2a distributive

  13. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y) • Associative property of multiplication • Distributive property • Addition property of zero • Commutative property of multiplication

  14. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y) • Associative property of multiplication • Distributive property • Addition property of zero • Commutative property of multiplication

  15. Which property would justify the following statement? 8x + 4 = 4 + 8x • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  16. Which property would justify the following statement? 8x + 4 = 4 + 8x • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  17. Which property would justify the following statement?8 + (2 + 6) = (8 + 2) + 6 • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  18. Which property would justify the following statement?8 + (2 + 6) = (8 + 2) + 6 • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  19. www.mathslideshow.com/PAlgH/1-7.ppt 8 + 4 = 12 Objective - To solve simple equations involving addition and subtraction. Identity Property of Addition additive identity Equation - A mathematical sentence that shows two expressions are equal. “fulcrum” Equations must always stay perfectly balanced.

  20. Determine which value is the correct solution to the equation.

  21. Determine which value is the correct solution to the equation.

  22. Addition Property of Equality If a = b, then a + c = b + c or Given a = b and c = c then a + c = b + c Subtraction Property of Equality If a = b, then a - c = b - c or Given a = b and c = c then a - c = b - c

  23. x + 3 = 7 Heavier - 3

  24. x = 7 Heavier

  25. x = 7 Heavier

  26. x = 7 Heavier

  27. x = Heavier 7

  28. - 3 - 3 x = 4 x + 3 = 7 Algebraically, x + 3 = 7 x + 3 = 7 -3 -3 x + 3 - 3 = 7 - 3 x = 4 x = 4

  29. For Next Week… • Complete Practice Assignments • Submit questions for next week. • Questions?

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