CCM1 Unit 5

1. CCM1 Unit 5

2. Warm Up – January 23 Complete the student Information sheet on your desk.

3. What Do I Remember • Spend 15 minutes going though the “What Do I Remember” worksheet

4. What you should have remembered 

5. Mean- average • Median- middle number • Describing Data- SOCS • Standard Deviation- How much variation exists from the average • Range-The difference between the highest and lowest number

6. Box Plot- Use the 5 number summary • Dot Plot- • Histogram-

7. 5 Number Summary- Minimum, Q1, Median, Q3, and Maximum • IQR- The difference between Q3 and Q1 • Outliers- A number that is numerically distant from the rest of the data

8. Categorical – data that can be separated by category EX) sorting students by the model of car they have • Quantitative – data that can be separated by numerical values EX) sorting students by the number of siblings they have

9. Algebraic Expressions- Does not have an equal sign, You evaluate Algebraic Expressions • Algebraic Equations- has an equal sign • Order of Operations- (PEMDAS) • Parenthesis • Exponents • Multiplication/Division • Addition/Subtraction • Evaluate- means to solve

10. Solving Equations- Follow reverse order of operations to get the variable by its self on one side of the equation • Whole Numbers- Includes zero and all the positives (no fractions or decimals) • Integer- Includes all negatives, zero, and all positives (No fractions or decimals) • Variable- a symbol that stands for a number • Ex) x – 2 = 10X is the variable

11. Subtracting Negatives- Keep, change, change • Multiplying Negatives- • Neg *Neg = Pos • Neg*Pos = Neg • Pos * Neg = Neg • Pos*Pos = Pos • Dividing Negatives • Neg /Neg = Pos • Neg/Pos = Neg • Pos /Neg = Neg • Pos/Pos = Pos

12. Distributive Property- Distribute to EVERYTHING inside the parenthesis • Constant- just a number, does not have a variable • Coefficient- The NUMBER in front of (multiplied by) a variable • Like Terms-Terms with the same exact variables • Substitution- Putting a number in place of a variable to simplify an expression • Equivalent expression- two expressions that have the same most simplified form • Solving Equation- Follow reverse order of operations to get the variable by its self on one side of the equation

13. Less Than < • Less than or equal to ≤ • Greater Than > • Greater Than or Equal To ≥ • Open Circle- Use for < or > • Closed Circle- Use for ≤or ≥ • Solving Inequalities- Solve like you solve equations; Follow reverse order of operations

14. Domain • Independent Variable • X’s • Goes on x-axis • Goes in L1 when finding line of best fit • Range • Dependent Variable • Y’s • Goes on y-axis • Goes in L2 when finding line of best fit

15. Function Notation • f(x) = • Example: f(x)= 2x + 4 • Now-Next Rule: A recursive rule found by relating a number to what comes before it. • Written as • Ex) NEXT = NOW + 4 • NEXT = NOW/2

16. Direct Variation- • Equation: y=kx • K = constant of variation • Goes through the origin on a graph • Finding slope through 2 ordered pairs: • (x1, y1) • (x2, y2) • Slope- Intercept Form: y = mx + b • M = slope; B = y-intercept • Point Slope: y – y1 = m( x – x1) • M = slope; X1, y1 are from the ordered pair • Standard Form: Ax + By = C • No Fractions, C is a constant

17. Parallel Lines- never intersect, have the SAME SLOPE • Perpendicular Lines- Slopes are opposite reciprocal • + change to – • – change to + • Flip the fraction

18. Pay It Forward • http://www.youtube.com/watch?v=DvKAPHvCPS8 • To 1:17 • http://www.youtube.com/watch?v=vmboo6cj8ds • From 3:10 to 4:39

19. 1. How many people would receive a Pay It Forward good deed at each of the next several stages of the process? Stage 1: Stage 2: Stage 3: Stage 4: Stage 5: Stage 6: 2. What is your best guess for the number of people who would receive Pay It Forward good deeds at the tenth stage of the process?

20. 3. Which of the graphs below do you think is most likely to represent the pattern by which the number of people receiving Pay It Forward good deeds increases as the process continues over time? Graph Number: ___________

21. 4. Take your values for each stage (from #1) and graph the data. Hint: Your x-axis needs to be the stage number and your y-axis needs to be the number of people receiving Pay It Forward.

22. Mathematical terminology This graphs represents EXPONENTIALgrowth. These data sets display properties ofEXPONENTIAL FUNCTIONS.

24. Warm Up – January 24th

25. Exponent Rules Review Exponents are a “short-hand” way of multiplying the same quantity over and over. Example: X4 = (x)(x)(x)(x)

26. Try Some: Expand the following • 43 • Y4 • X2y5 • w6z1

27. Using Exponents to simplify Write using exponents • X*x*x*x • 2*2*2*2*x*x*x*y*y • 3*3*3*4*4*4*4*x

28. Zero as an exponent • Anything with an exponent of zero equals 1. • Ex x0 = 1 • 60 = • Y0 =

29. Negative Exponents • When you have a NEGATIVE exponent you turn it POSITIVE and FLIP it. • EX x-3

30. Try Some

31. Multiplication • When multiplying like bases you ADD exponents • Ex: x4x2

32. Try some! • X3x4 • Y3x4y7 • z3y2x5z5y6x10

33. Exponents of Exponents • When you have an exponent of an exponent you MULTIPLY • EX: (x4)3

34. Try Some! • (x)5 • (x2y4)5 • (2x3)6

35. Division • When you divide like bases you SUBTRACT exponents

36. Try Some

37. Growing Sequences • Arithmetic Sequence : goes from one term to the next by always adding (or subtracting) the same value • Common Difference : The number added (or subtracted) at each stage of an arithmetic sequence • Initial Term : Starting term For example, find the common difference and the next term of the following sequence: 3, 11, 19, 27, 35, . . .

38. Growing Sequences • Geometric Sequence: goes from one term to the next by always multiplying (or dividing) by the same value • Common Ratio: The number multiplied (or divided) at each stage of a geometric sequence Determine the common ratio r of the Brown Tree Snake Sequence. 1, 5, 25, 125, 625, . . .

40. Warm Up – January 25th

41. The geometric sequence from the Brown Tree Snake problem (1, 5, 25, 125, 625 . . .) can be written in the form of a table, as shown below: The Brown Tree Snake was first introduced to Guam in year 0. At the end of year 1, five snakes were found; at the end of year 2, twenty-five snakes were discovered, and so on…

42. Since we now have a table of the information, a graph can be drawn, where the year is the independent variable (x) and the number of snakes is the dependent variable (y). See below:

43. The curved graph of this problem situation is known as an exponential growth function. An exponential growth function occurs when the common ratio r is greater than one.

44. Group Work • In your group’s complete the worksheet handed out.

46. Tuesday, January 29thWarm Up # 4

47. Homework Check – 5.4

48. What is the difference between an arithmetic and geometric sequence? What is the difference between a common ratio & a common difference? Which type of sequence does each go with?

49. The Ladybug Invasion As a biology project, Tamara is studying the growth of a ladybug population. She starts her experiment with 5 ladybugs. The next month she counts 15 ladybugs. 1) The ladybug population is growing arithmetically. How many beetles can Tamara expect to find after 2, 3, and 4 months? Write the sequence. 2) What is the common difference? 3) Now put the sequence into a table in the space below.

50. 4) How long will it take the ladybug population to reach 200 if it is growing linearly?