3.  Directions:  Look up each of the following vocabulary words on Google.  Give a definition and an example  Once you are done, compare your definitions with two other students in the room  Once everyone is done, we will compare to everyone’s definitions  Vocabulary:  Algebra  Generalize  Variables  Variable Expression  Equation  Real  Evaluate

4.  Algebra: The part of mathematics in which letters and other symbols are used to represent numbers and quantities in formulae and equations  Generalize: To infer from previous conclusions.  Variables: An element, feature, or factor that is liable to vary or change or a quantity that during a calculation is assumed to vary or be capable of varying in value.  Variable Expression: A combination of numbers (or constants), operations, and variables to create a mathematical expression.

5.  Equation: A statement that the values of two mathematical expressions are equal (indicated by the sign =).  Real: Actually existing as a thing or occurring in fact  Evaluate: Find a numerical expression or equivalent for (an equation, formula, or function)

6.  Add (+) :uses sum of, increase of, more than  Subtract ( - ) :uses difference of, less than, fewer  Multiply ( x or ● ) :uses product of, double, triple, etc  Divide ( ÷ ) :uses quotient of, divided by, per  Square ( ² )  Square Root ( √ )

7.  Letters which take the place of numbers until solved.  Examples:  X  Y  Z  A  B  Any letter you wish the variable to be!!!!

8.  Write an algebraic expression for the perimeter and area of a rectangle.  Perimeter = ?  Area = ? L W

9.  An example of a variable expression from the previous example is 2w + 2l  An example of a variable equation from the previous example is P = 2w + 2l  An expression does not have an equal sign where an equation has an equal sign.

10.  Find the value of 2x + 7  When x = 12  When x = 1  When x = 10

11.  Find the value of -9x + 2  When x = -1  When x = 1  When x = 0

12.  Many expressions have more than one variable.  To solve, substitute the appropriate value into the appropriate place  Example: Perimeter and Area of a rectangle  P = 2l + 2wA = l x w  Find the perimeter and area of a rectangle with:  Length of 12 and a width of 10

13.  Exponents are short hand notations for repeated multiplication  2 ⁴ = 2*2*2*2  The base is 2 and the exponent is 4.  Means that the base is multiplied by itself 4 times.

14.  Can also write variables with exponents  x³ = x*x*x  The base is x and the exponent is 3  Means that the base is multiplied by itself 3 times  When x is negative and the power is even the answer will be positive.  When x is negative and the power is odd the answer will be negative.  Why is this?

15.  Find the value of 5x² - 4y  When x = -4 and y = 5

16.  Find the value of 2x² - 3x³ + 5  When x = -5

18.  Each of you will pick out a random card. One will be an expression and one will be an answer. You are to find your partner and sit together, waiting for more instructions.

21.  2 + 4 x 7 – 1 = ???  How did different groups interpret this problem?  What is the correct way?

22.  PEMDAS  P- Parentheses  E- Exponents  M- Multiplication  D- Division  A- Addition  S- Subtraction With multiplication/ division as well as addition/ subtraction, you work from left to right completing BOTH as they arise in the problem. They are interchangeable.

23.  4 – 7 – 11 – 2  4 – (7 – 11) – 2  4 – [ 7 – (11 – 2)]

24.  3 x 5 – 7 ÷ 2  3 x (5 – 7) ÷ 2  (3 x 5) – (7 ÷ 2)

25.  2 – (19 – 7)² x (4³ - 2)

26.  Directions:  You are going to receive a BINGO sheet and a sheet of expressions.  Cut out the expressions, solve them and put them in the correct column.  The correct column means if the solution is between 1 and 10, the expression goes in the ‘B’ column, etc.  Tape 5 expressions to the BINGO board in each column.  We are going to play BINGO; the solutions to the expressions will be called out. If the solution matches one of your expressions, mark it. When you have a BINGO shout it out!!!

29.  What is a pattern? Create one.  What do you notice about this pattern?

30.  3, 6, 9, 12, …  1,.5,.25,.125, …  100, 200, 300, 400, …  1, 4, 9, 16, 25, 36, …

31.  We need to write an equation to find a specific term..  How could you do that?

32.  3, 6, 9, 12, …  1,.5,.25,.125, …  100, 200, 300, 400, …  1, 4, 9, 16, 25, 36, …

33.  In your groups, create at least 5 challenging patterns. DO NOT write the answers to the patterns on the paper!  When you are done, hand your patterns into me.  Each group will get another groups patterns to create equations for.

34.  What are some terms used for each of these mathematical expressions?  Addition?  Subtraction?  Multiplication?  Division?  Equals?

36.  What is the difference between an equation and an inequality?  Equation:  Inequality:

37.  Give three real-life examples of each of these inequalities in your group. Be prepared to share them.

38.  Grab a laptop and go to this website:  http://www.mathplayground.com/mathatthemall2. html  Read through the ‘How To’ section, then continue to the game.  When you have received all four gold coins bring your computer to the front and I will check it.

39.  Defining the variables means assigning letters to an unknown quantity in the problem  Translating the sentence means that you change the word expression into a mathematical expression containing variables and mathematical operations with an equal sign or an inequality sign

40.  Key Words:

41.  Define the variable and translate the expression for each example:  A number plus 12 is 20  9 less than twice a number is 33  5 more than four times a number is 21  $20 was one quarter of the money spent on the pizza.

42.  Bob worked for 2 hours and packed 24 boxes. How much time did he spend on packing one box?  After a 20% discount, a book costs $12. How much was the book before the discount?  Remember a discount means that you are taking money off!

43.  Check that x = 5 is a solution to the equation 3x + 2 = -2x + 27  Check that z = 25 is a solution to the inequality z + 1 < z -20

44.  In a group of three, create three verbal models like previous examples.  Put your group members names on them and put them on the front desk when completed.  You will receive another groups questions at the end of class to finish before you leave.

45.  Tomatoes cost $0.50 each and avocados cost $2.00 each. Anne buys six more tomatoes than avocados. Her total bill is $8.00. How many tomatoes and how many avocados did Anne buy?  Set this up and solve within your groups.

46.  In groups of two you are going to create your own real-world problem much like the one we just completed.  Create the story problem or situation (get creative) on one of your notecards.  Work out the answer on the other note card.  Make sure your name is on both notecards for full credit.  Hand both notecards to me when finished.

48.  Function: A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.  Each input has exactly one output.

50.  To test to determine if a graph on a coordinate plane is a function you want to test using the vertical line test.  Vertical line test: If you run a vertical line across the length of your coordinate plane every point on that line should only touch the function at one point. If it ever touches at two points, then the graph is not a function.

51.  {(-5,-2), (-1,1), (3, -6), (8,1)}  {(2, -9), (2, -2), (6,8), (8,1), (11,-7)}

55.  Coordinate Plane (AKA Cartesian Plane): coordinate grid with a horizontal (x) and vertical (y) number lines.  Coordinate points are written as (x, y).  Origin is (0,0).

57.  On the floor there is a coordinate plane.  In your groups we are going to play a game.  Each group chooses one group member. That group member is going to race to their box, grab a random coordinate and race to that corresponding coordinate on the floor.  For each correct placing, groups receive one point. For each incorrect placing, groups loose one point.  Group with the most points receive candy.

58.  Group work:  Search function. What is it? Does it have any properties?  What do domain and range mean?

59.  Given the table of values, graph the function.  What is the domain?  What is the range? xy -26 8 010 112 214

60.  In your small group you are going to look up the properties of the graphs of your assigned type of graph– use old textbooks in the back cabinet, preferably Algebra 1 and 2 books.  Linear Graph  Exponential Graph  Quadratic Graph  Absolute Value Graph  Square Root Graph

61.  Linear  Exponential  Absolute Value  Square Root

62.  For each input there is EXACTLY one output!!!  Determine if the relation is a function:  (1,3) (-1, -2) (3, 5) (2, 5) (3,4)  (-3, 20) (-5, 25) (-1, 5) (7, 12) (9, 2)

63.  If you can draw a vertical (up and down) line that crosses the graph in more than one place, then the relation is not a function.  Determine why this works!?

64.  What year was the ppm 335?  What was the CO2 in 1947?

66.  Group work:  A coffee maker is on sale at 50% off the regular ticket price. On the “Sunday Super Sale” the same coffee maker is on sale at an additional 40% off. If the final price is $21.00, what was the original price of the coffee maker?  Share your solution and work with the class.

67.  How did you solve this problem?  What different strategies did you use to solve this problem?  Did everyone solve this the same way? Is one way better than another way?

68.  1. Read and understand the problem  2. Make a plan to solve the problem  3. Solve the problem  4. Check the results

69.  Answer the following questions:  What am I trying to find out?  What information have I been given?  Have I solved a problem similar to this before?  Define your known and unknowns

70.  Common strategies  Draw a diagram  Make a table  Look for a pattern  Guess and check  Work backwards  Use a formula  Write equations

71.  Use your plan to solve the problem.

72.  ALWAYS check your results to make sure they make sense.  Plug the answer back in and make sure everything works

73.  Individually work on the problem solving worksheet / mini-activity