4. Algebra! The area of mathematics that generalizes the concepts and rules of arithmetic using symbols to represent numbers

5. What is arithmetic?  Addition  Subtraction  Multiplication  Division  Exponents

6. What are some examples of symbols you see inside and outside of school?

7. In algebra, we use different symbols that we call variables  Many times, you will use letters as your symbol X, a, b, c, etc.  Sometimes you may see some Greek alphabet letters β = beta

8. How to set a problem up!  Add three to a number  A number plus 3  The sum of a number and 3  3 more than a number  A number increased by 3

9. How to set up a problem!  Subtract 12 from a number  A number minus 12  The difference of a number and 12  12 less than a number  A number decreased by 12  Take away 12 from a number  A number less 12

10. Set up the problem!  2 times a number  2 multiplied by a number  The product of 2 and a number

11. Set up the problem!  6 divided into a number  A number divided by 6  The quotient of a number and 6

12. What would the expression be?  Five less than a number  The product of three and a number  The sum of a number and 10  A number divided by 9

13. Try one on your own!  Make up an algebraic expression on your own. Write it on your whiteboard.  When your finished, pass it to a neighbor and see if they can figure it out!

14. Two step algebraic expressions  Three times a number decreased by two  Four more than five times a number  The sum of a number and four divided by two  The difference of a number and four added to nine

15. Write a verbal phrase for each algebraic expression

16. Write each sentence as an equation The product of four and a number is sixteen Three less than an number is twenty Nine more than “n” is eleven

18. To evaluate an algebraic expression, substitute a number for the variable!  Example: Evaluate n + 7 when n = 4

19. To evaluate an algebraic expression, substitute a number for the variable!  Example: Evaluate 5n + 3 when n = 6

20. To evaluate an algebraic expression, substitute a number for the variable!  Example: Evaluate 6n² + 2n when n = 3

21. Let’s try a few on our own!  1. p ÷ 2 + p when p = 4  2. 3a – 5when a = 5  3. 6/s + 4swhen s = 2

22. What about two variables?  Example: Evaluate a + 7 - c when a = 9 b = 6

23. What about two variables?  Example: Evaluate 2n + 7b when n = 5 b = 2

24. Let’s try a few on our own!  1. p ÷ 2 + 3x when p = 6 and x = 7  2. 3a – 5twhen a = 6 and t = 2  3. 12/s + y²when s = 3 and y = 5

25. Try one on your own!  Make up an algebraic expression and assign the variable or variables values. Write it on your whiteboard.  When your finished, pass it to a neighbor and see if they can figure it out!

27. Definitions  Term: A term can be a number, a variable, or a product of numbers and variables.

28. Definitions  Please list all of the terms in this algebraic expression.

29. Definitions  Like terms: Terms that have the same variable raised to the same power. Examples

30. Definitions  Unlike terms: Terms that do not have the same variable raised to the same power. Examples

31. Definitions  Like terms: Terms that have the same variable raised to the same power.

32. Identify the like terms in the list:

33. You can only combine LIKE TERMS  Example: _s_ + 10s = 5  Example: 72c + 5b =  Example: 4x² + 53x =  Example: 7x + 5x =

34. Now let’s practice!  1. 3m + 4m =  2. 6t + 4 – 3t =  3. 17y + 3y – 2y²  4. 5 + 4r – 3 =

35. What about the more difficult ones? 3b² + 5b + 11b² - 4a² = Step 3 : solve and bring down the rest of the terms Step 2 : circle the numbers and the sign to the left of them Step 1 : underline like terms

36. What about the more difficult ones? 2(b + 2a²) + 2b Step 3 : solve and bring down the rest of the terms Step 2 : circle the numbers and the sign to the left of them Step 1 : distribute and underline like terms 2b + 4a² + 2b

37. Let’s try some on our own! 1. a + 2b + 2a + 3b + 4c 2. 18 + 2d³ + d + 3d 3. a² + 9b + 5a² + 2b + 6c 4. 3(4x + z) – 4x

38. Try one on your own!  Make up an algebraic expression with several variables. Write it on your whiteboard.  When your finished, pass it to a neighbor and see if they can figure it out!

40. Lets try a few!  2 + x = 7 2 plus “some number” equals 7 Answer = 5 How did you know this?

41. 2 + x = 7 subtract two from both sides -2 -2 0 + x = 5 Additive inverse Step 1: Draw a line down the equal sign Step 2: Look at the number on the same side as the variable Step 3: Look at the sign next to the number you underlined (no sign = positive) Step 4: Do the opposite! Add or subtract that number from both sides

42. X + 14 = 27 subtract 14 from both sides -14 -14 X + 0 = 13 Additive inverse Step 1: Draw a line down the equal sign Step 2: Look at the number on the same side as the variable Step 3: Look at the sign next to the number you underlined (no sign = positive) Step 4: Do the opposite! Add or subtract that number from both sides

43. Now try on your own! 1. 16 + x = 29 2. X + 11 = 34 3. 18 + X = 86 4. X + 12 = 19 5. 27 + X = 258

44. Problem #1  16 + x = 29

45. Problem #2  X + 11 = 34

46. Problem #3  18 + X = 86

47. Problem #4  X + 12 = 19

48. Problem #5  27 + X = 258