2008 USM Summer Math Institute CoSponsored by Institutions

2008 USM Summer Math Institute Co-Sponsored by Institutions of Higher Learning (IHL) U. S. Department of Education (No Child Left Behind Funding) The Center for Science and Mathematics Education The Department of Mathematics College of Science and Mathematics College of Education and Psychology Calculator: Evaluating expressions, mean, median, mode and data graphs Day Seven 1

2008 USM Summer Math Institute Your Mathematics Instructors, Staff and Partners • Ms. Michelle Green, Co-Director and Co. Instructor for (SM)2 I – Stringer Attendance Center – National Board Certified/Early Adolescence – Email mgreen@westjasper. k 12. ms. us , Phone 601428 -5508 • Dr. Myron Henry, Director and Co-Instructor for (SM)2 I – Department of Mathematics and the Center for Science and Mathematics Education – Johnson Science Tower 314 – Email myron. henry@usm. edu, Phone 601 -266 -4739 or 266 -6516 • All Participants (that’s you) 2

Day Seven of (SM)2 I 1. Calculator Activities • Evaluating expressions • Boolean Algebra 2. Mean, median, mode • Calculator spreadsheets from created lists • Box-and-Whisker Plot • More calculator spreadsheets-from applications 3

Day Seven of (SM)2 I . 4

Evaluating Expressions • Example: Evaluate 2/3 x + 100 when x = 16. 5 Keystrokes: (16. 5 will be x until you store a new value for x. ) * advise your students to always put fractions in parentheses!!!! • Example: Evaluate 5/(8 x) when x = 2. üIs 5/8 x the same expression? Evaluate and see if you obtain the same answer for x = 2. üMoral of story: using “( )” makes it clear what you mean: to others and your calculator! 5

Practice: Evaluate the following expressions 1. if x = 4, m = 5, and p = -2 ü xmp ü m 2/px, ü m 2 p/x, 2. 4 y 3 z if y = -2 and z = 10 3. -x - (-a + b) if x = 2, a = -4, and b = -6 4. x - y( - a 2 + x ) if x = -2, y = 3, and a = - 4 6

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Suppose you want to evaluate a formula: V = r 2 h if the radius of a right cylinder is 12. 5 inches and the height is 18 inches. You would store the values for r and h just like the above example and then type the formula on the home screen. Suppose you were comparing the volume of two right cylinders and the other cylinder had a radius of 18 inches and a height of 12. 5 inches. Simply store the new values for r and h, but in stead of retyping the formula use the “replay” feature: 8

Boolean Algebra (True or False) This activity will allow students to check their work without getting the answer from the calculator. Example: + 47 = 102 The student wants to check her answer of 54 Assign the box an alphabetical letter such as X. 9

Keystrokes: The calculator will either show a 1 which means TRUE ( their answer is correct) or a 0 which means false ( their answer is incorrect ). Students can check any kind of problems that they encounter using the “Boolean” method. Try these: 1. X - 47 = 229, 2. ½ + ¼ = X = ______ (ALWAYS PUT FRACTIONS IN PARENTHESIS) 3. 2. 97 x 104 = 4. 34 = ______ 10

Mean, Median and Mode Let’s use Smart Notebook! Find the mean, median and mode and graph data in a Box -and-Whisker Plot. 85 72 94 85 76 94 81 52 79 100 50 52 55 60 65 70 75 76 80 83 85 90 95 94 100 11

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Mean, Median and Mode 82 91 74 78 94 68 74 88 64 42 72 82 79 99 98 75 61 78 86 69 Enter this data in L 1 To clear list Enter data The calculator will put this in ascending or descending order for you. or T To access: 1 var-stats 13

Note: If your information is not in L 1 you must tell the calculator where it is with a comma and the correct list. List numbers are in blue above the numbers 1 – 6. Ex. 14

This whisker shows the lowest value This line shows the lower quartile This line shows the median This line shows the This upper whisker quartile shows the highest value The width of the box shows the interquartile range This shows an 15

Box-and-Whisker Plots To Graph your data: To select the type of graph: (use arrows) and Select your Xlist (L 1) and Ylist (1) Manually set your window according to the data. For our data: To see your graph and data: 16

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More Lists on the TI-84 Plus Silver Edition • To access the lists There are six preset lists L 1, L 2, L 3, L 4, L 5 and L 6. These names** can also be accessed through and numbers 1 to 6 on the face of the calculator • Names can also be given to lists. To name** a list . The calculator will be in alpha mode. Type the name of the list using up to five characters. Once a list has been named, the calculator is automatically in Set. Up. Editor mode. Use the arrow keys to highlight the name placeholder and type a name in a new column using up to five characters. 19

A Practice Problem: There are 20 units of string. By making as many rectangles as possible with integer lengths and widths, which rectangle has the largest area? • Create four lists titled length, width, perimeter, and area • Enter the numbers 1 – 9 into list length • Use the formula “(20 – 2*LLENGT)/2” for the WIDTH list • Use the formula “(2*LLENGT + 2*LWIDTH)” for the PERIM list • Use the formula “(LLENGT *LWIDTH)” for the AREA list NOTE: YOU MUST USE THE NAMES** OF THE LISTS IN THE FORMULA 20

TI Screen One 21

TI Screen Two 22

Editing and Deleting of Lists • To delete a list To delete the name of a list after the entries have been cleared To delete the name of the list from the name menu 23

Spreadsheet on TI-84 Plus Silver Edition Using APPS • To activate the Spreadsheet through [APPS] • The Cell. Sheet Help window shows which buttons access the functions needed to do operations. • The top left hand corner shows the name of the spreadsheet (S 01) • A Problem: Listed is check amounts before taxes for eating out: – $ 42. 95 – $ 13. 77 – $ 78. 00 – $ 25. 88 • Use the spreadsheet to compare 15% tips with 20% tips. Also compare the 15% tip rate with the estimation method of doubling the tax. 24

Collecting and Graphing Data “Biloxi” Random Number Generators Outcomes 2 3 4 5 6 7 8 9 10 11 12 Frequency 0 1 2 1 3 8 6 2 0 25

Collecting and Graphing Data Activity: Roll two “Random Number Generators” 25 times. Record the results in a table. To enter data in the calculator: Put the possible outcomes in L 1 ( 2, 3, 4, …, 12) Put the frequency results in L 2 To generate a bar graph: Other ideas: Sort Skittles, Sort M & M’s, Count shapes in the classroom…. . 26

More on Random Number Generators • • Press Use Press Select Press to <Prob Sim> press 27

Mean, Median and Mode Let’s use Smart Notebook! Find the mean, median and mode and graph data in a Box -and-Whisker Plot. 85 72 94 85 76 94 81 52 79 100 50 52 55 60 65 70 75 76 80 83 85 90 95 94 100 28