Manual / Guide
TI-30XS MultiView Teacher Guide
Texas Instruments' teacher guide for the TI-30XS MultiView, with classroom activities.
Manual / Guide
Texas Instruments' teacher guide for the TI-30XS MultiView, with classroom activities.
TI-3OXS MultiView™ A Guide for Teachers Developed by Texas Instruments Incorporated Activities developed by Gary Hangon, Aletha Paskett, and Margo Lynn Mankus lllustrated by Jay Garrison and David Garrison About the authors Gary Hanson and Aletha Paskett are math teachers in the Jordan Independent School District in Sandy, Utah. They developed several of the activities and assisted in evaluating the appropriateness of the examples in the How to use the TI-3OXS MultiView™ section of this guide. Margo Lynn Mankus currently works in Mathematics and Technology Education at the State University of New York at New Faltz. She has reviewed and updated the materials for the TI-3OXS MultiView and developed several activities for this guide. 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TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Table of contents CHAPTER PAGE | CHAPTER PAGE About the teacher guide v | How to use the TI-30XS MultiView About the TI-30XS MultiView™ calculator (Continued) calculator vi 11 Statistics 8&3 seas 12 Probabilit & Activities rovary 9 13 Function table 97 Star voyage . Scientific notation 3 14 Powers, roots, and reciprocals 101 Heart rates 15 Logarithms and \-variable statistics 7 exponential functions 109 At the movies 16 Pi "3 Data formulas at the box office 13 17 Angle settings and conversions 17 Name that rule 18 Polar and rectangular Algebraic expressions 21 conversions 121 19 Trigonometry 123 How to use the TI-30XS MultiView 20 Hyperbolics 131 calculator 1 Tl-3OXS MultiView basic operations 29 Appendix A 2 Clearing and correcting Al Quick reference to keys Al 3 Basic math 45 Appendix B Display indicators B-1 4 Order of operations and . parentheses 49 Appendix C Error messages C-1 5 Numeric notation 55 ; Appendix D 6 Fractions 59 Support and service information D-1 7 Decimals and decimal places 65 Appendix E & Constant 67 Battery information E-1 Q Memory and stored variables 11 10 Data editor and list formulas 79 © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED About the teacher guide How the teacher guide is organized This guide is for the TI-3OXS MultiView™ and TI-ZOXB MultiView scientific calculators. All subsequent references in this guide refer to the TI-BOXS MultiView, but are also applicable for the TI-ZOXB MultiView. This guide consists of two sections: Activities and How to use the TI-30XS MultiView calculator. The Activities section is a collection of activities for integrating the TI-3OXS MultiView into mathematics instruction. The How to use the TI-3OXS MultiView calculator section is designed to help you teach students how to use the calculator. Each section uses the default settings, including the MathPrint™ mode, unless indicated otherwise. Activities Each activity is self-contained and includes the following: ¢ An overview of the mathematical purpose of the activity. ¢ The mathematical concepts being developed. ¢ The materials needed to perform the activity. © The detailed procedure, including step-by- step TI-3OXS MultiView key presses. e A student activity sheet. How to use the TI-3OXS MultiView This section contains examples on transparency masters. Chapters are numbered and include the following. LU ¢ An introductory page describing the calculator keys presented in the example, the location of thoge keys on the TI-ZOXS MultiView, and any pertinent notes about their functions. ¢ Transparency masters following the introductory page provide examples of practical applications of the key(s) being discussed. The key(s) being discussed are shown in black on the TIl-3OXS MultiView keyboard. The mode settings for the example are also shown. Reset the TI-3OXS MultiView e You can ensure that everyone starts at the same point by having students reset the calculator: Press and simultaneously or press [reset] and then select 2 (Yes). Conventions used in the teacher guide ¢ In the text, brackets [ ] around a key's symbol/name indicate that the key is a second, or alternate, function. For example: [2nd] [sin] How to order additional teacher guides To place an order or to request information about Texas Instruments (Tl) calculators, use our e-mail address: [email protected], visit our home page: education.ti.com, or call our toll-free number: 1-800-TI-CARES (1-600-842-2737) © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers About the TI-3OXS MultiView™ calculator Home screen On the Home screen, you can enter mathematical expressions and functions, along with other instructions. The answers are displayed on the Home screen. The TI-3OXS MultiView screen can display a maximum of four lines with a maximum of 16 characters per line. For entries and expressions of more than 16 characters, you can scroll left and right (© and Q) to view the entire entry or expression. When you press [2nd] [quit], the TI-3OXS MultiView calculator returns you to a blank Home screen. Press © and © to view and reuse previous entries. (See Previous Entries, page vii.) In the MathPrint™ mode, you can enter up to four levels of consecutive nested functions and expressions, which include fractions, square roots, exponents with *, xh, e*, and 10”. When you calculate an entry on the Home screen, depending upon space, the answer is displayed either directly to the right of the entry or on the right side of the next line. Display indicators Refer to Appendix B for a list of the display indicators. Order of operations The Tl-3OXS MultiView uses the Equation Operating System (EOS™) to evaluate expressions. The operation priorities are listed on the transparency master in Chapter 4, Order of operations and parentheses. Because operations inside parentheses are performed first, you can use to change the order of operations and, therefore, change the result. Mode Use [mode] to choose modes. Press © © © & to choose a mode, and EY to select it. Press [dear] or [2nd][quit] to return to the Home screen and perform your work using the chosen mode settings. Default settings are shown. vee RAG GRAD i) SCT EMG OLZ245 RFE poe THER TAT) Classic mode displays inputs and outputs in a single line. MathPrint mode displays most inputs and outputs in textbook format. Use MathPrint mode for better visual confirmation that math expressions have been entered correctly and to better reinforce the correct math notation. Note: Switching the mode between Classic and MathPrint clears calculator history and the Constant value. 2nd functions Pressing displays the 2nd indicator, and then accesses the function printed above the next key pressed. For example, [v-] 25 Gg calculates the square root of 25 and returns the result, 5. vi TI-3OXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED About the TI-3OXS MultiView™ (Continued) Menus Certain keys display menus: [2nd] [angle], [data], [2nd][stat], [2nd][reset], [2nd][recall], and [2nd][clear var], Press) or © to scroll and select a menu item, or press the corresponding number next to the menu item. To return to the previous screen without selecting the item, press [dear]. To exit a menu or application and return to the Home screen, press [2nd][quit] Previous entries © © After an expression is evaluated, use © and © to scroll through previous entries, which are stored in the TI-3OXS MultiView history. You can reuse a previous entry by pressing BIG to paste it on the bottom line, and then editing and evaluating a new expression. Answer toggle & The toggle key displays the last calculated result into different output formats, where possible. Press BJ to toggle between fraction and decimal answers, exact square root and decimal, and exact pi and decimal. Last answer (Ans) The most recently calculated result is stored to the variable Ans. Ans is retained in memory, even after the TI-3OXS MultiView is turned off. To recall the value of Ans: ° Press [ans] (Ans displays on the screen), or ° Press any operation key ((4], E], and go forth) as the first part of an entry. Ans and the operator are both displayed. Resetting the TI-30XS MultiView Pressing and simultaneously or pressing [reset] and then selecting 2 (Yes) resets the calculator. Resetting the calculator: ¢ Returns settings to their defaults — standard notation (floating decimal) and degree (DEG) mode. ¢ Clears memory variables, pending operations, entries in history, statistical data, constants, and Ans (Last answer). Note: The examples on the transparency masters assume all default settings. Automatic Power Down™ (APD™) If the TIl-3OXS MultiView remains inactive for about 5 minutes, the APD feature turns it off automatically. Press to restore power. The display, pending operations, settings, and memory are retained. Error messages Refer to Appendix C for a listing of the error messages. © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers TI-3OXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Activities WWW UT UCU CUCU UCT CEOES Star Voyage — Scientific notation 3 Heart Rates — 1-variable statistics 7 At the movies — Data formulas at the box office 13 Name that rule — Algebraic expressions 21 © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers TI-3OXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Star voyage — scientific notation Math Concepts Materials ¢ scientific notation ¢ TI-3OXS MultiView™ ° addition © pencil ¢ division ¢ student activity Overview Students investigate scientific notation by changing numbers into scientific notation, and then using them in calculations. Introduction Set up the activity by telling your students: The standard form for scientific notation is ax 10",where a is greater than or equal to 1 and less than 10, and n Is an integer. 1. Have students practice writing the following numbers in scientific notation using pencil and paper. a. 98 000 000 9.38% 107 b. 384 000 000 000 3.84x 10" c. 0.00000000000234 2.384% 10°? d. 0.0000000157 L57x 10% 2. Have students change the following numbers into scientific notation (SCI) using the TI-30XS MultiView scientific calculator. Follow these steps: 1. Enter the first number, 12000000. a. 12000 000 12x 107 2. Press [mode] . b. 974 000 000 9.74 10° 3. Press© O BY jenter ft ec. 0.0000034 3.4x10¢ display the number in scientific tation. d. 0.000000004 4x 10° moron 1.2#107 Note: Answers assume the default floating decimal setting. 8. Have students change the following numbers into standard (NORM) notation. Follow these steps: a. 5.8 107 58 000 000 b. 7.32 x 105 732 000 1. Enter 5.8; press (e107) . c. 6.2% 106 0.0000062 2. Enter 7; press [mode] . d. 3x 108 0.00000003 3. Press@ GY jenter f 58000000 Note: To enter a negative number, press [=] and then enter the number. © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 3 Star voyage — scientific notation (continued) Activity Hint: Make sure the TI-30XS MultiView calculator is in MathPrint™ mode to work Present the following problem to students: this problem. You are a captain ofa starship in the distant RAD GRAD future. You have been assigned to go to Alpha Pe eree cere Centauri and you have 6 years to get there. The TC adalat distance from our sun to Alpha Centaurl is 2.8 x 10 miles. The distance from the earth to our sun Is approximately 9.8 x 10’ miles. Although we have not yet discovered how to travel at the speed of light, you live in a time where your ship can travel at the speed of light. Light travels the approximate distance of 6 x 10!” miles in 1 light year. You will take a path from earth by our sun and then on to Alpha Centauri. Will you be able to get to Alpha Centauri on time? Hint: The Earth is approximately 9.3 x 107 miles from the Sun. Procedure 1. Using the TI-30XS MultiView™ calculator, find the total distance you need to travel. 2.5% 10" +9.3x 10? = 2.5000093 x 10 miles Follow these steps: 2. Next, find out how long it will take you to travel : : : 1. P 2.5 [x10] 13 +) 9.3 [e107] the distance. (Distance traveled + 1 light year) — ® 3 2.5000098 x10" _ 4 1g6g001679 years 2.5000093410"* 2 6x 10 2. Press [2nd] [ans] 6 3. Can you make the trip in the allotted time of 12 Gg. 5 years? Yes, if your ship really could travel at the speed of 4.166682167 light. Extension Depending on the problem, remind . . . students to include parentheses Light travels at 186,000 miles per second. A light where needed to ensure the intended year is the distance that light can travel in a year. order of operations. Have students convert one light year to miles Example: traveled per light year. (2.5000093 x 101%) + (6 x 10%) 186, 000miles | 60sec GOmin . 24hrs | 365days _ 5.87 x 10'miles must include the parentheses in Tsec Imin~ ihr ~ lday” lyear ~ lyear order to get the correct result. We approximate this value using 6x10” miles in 1 light year in this activity. Answer to student extension: It will take the starship . Students can learn more about this approximately 15 years to get to Delta Centauri. PP y y 8 topic by visiting NASA web sites on the Internet. 4 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Star voyage — Name scientific notation Date Problems 1. Write the following numbers in scientific notation. Standard Notation Scientific Notation a. 93 000 000 b. 384 000 000 000 c. 0.00000000000234 d. 0.0000000157 2. Using the TI-30XS MultiView™ calculator, change the following numbers into scientific notation using SCI mode. Standard Notation Scientific Notation a. 12 000 000 b. 974 000 000 c. 0.0000034 d. 0.000000004 3. Using the TI-30XS MultiView calculator, change the following numbers into standard decimal notation using NORM mode. Scientific Notation Standard Notation a. 5.8 x 107 b. 7.382 x 105 c. 6.2 x 10° d. 3x 10% © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 5 Star voyage — Name scientific notation Date Problem You are a captain of a starship in the distant future. You have been assigned to go to Alpha Centauri and you have 5 years to get there. The distance from our sun to Alpha Centauri is 2.5 x 10" miles. The distance from the earth to our sun is approximately 9.3 x 107 miles. Although we have not yet discovered how to travel at the speed of light, you live in a time where your ship can travel at the speed of light. Light travels the approximate distance of 6 x 10” miles in 1 light year. You will take a path from earth by our sun and then on to Alpha Centauri. Will you be able to get to Alpha Centauri on time? Procedure 1. Using the TI-30XS MultiView™ calculator, find the total distance that you need to travel. For this rough estimate, assume that you are measuring the distance as a straight line from the earth to our sun and then on to Alpha Centauri. Hint: Make sure your calculator is in scientific notation mode before you begin the calculation. Next, find out how long it will take you to travel the distance. (Distance traveled +1 light year) Hint: Make sure you use parentheses if needed in order to get the correct result for this division problem. 2. Can you make the trip in the allotted time of 5 years? Extension Now that you have been successful, you have been asked to make another trip. The distance from the Sun to Delta Centauri is 9 x 10 miles. How long will it take you to get there from Earth? Hint: The Earth is approximately 9.3 x 107 miles from the Sun. Your trip on this starship is fictitious. If you are interested in finding out more about the nearest star and cosmic distances, visit NASA web sites on the Internet. 6 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Heart rates — 1-variable statistics Overview Math Concepts Materials Students use the data editor and statistics function ¢ mean, minimum, © TI-ZOXS MultiView of the TI-3OXS MultiView™ calculator to investigate maximum, and * stopwatch or a the effect of exercise on heart rate. range watch with a second hand ¢ student activity Introduction Students may be placed in smaller groups for this activity to minimize the amount of data to be entered. Ask students: e What do you think the average heart rate is for someone your age? e What about after exercising? Activity Have students complete the following investigation to check their estimations. 1. Have students check their resting heart rate by timing their pulse for 1 minute. (You could have them time for 10 seconds and then multiply by 6, but this could be the quietest minute of your day!) 2. Collect data on the chart. Enter each student’s heart rate and a mark in the frequency column. As other students have the same heart rate, add another tally mark in the frequency column. 3. Enter the heart rate data into the Follow these steps: TI-30XS MultiView scientific calculator. 1. Press to enter the heart rates a. Enter the first heart rate on the chart in L1, and frequencies. Enter the heart and the number of tallies for that heart rate rates in L1 and the frequencies in in L2. You will use L2 as the frequency. L2. Press © between entries, and b. You must press © between entries. For © to get from L1 to L2. example, enter the first heart rate, and then 2. Continue entering until you have press ©. entered all the heart rates and f ies. c. For example, assume a class of 22 students: requencies 3. Press [stat]. Rate Students | Rate Students 4. Press 1 to choose 1-var stats. 60 3 63 3 5. Choose L1 for the data, and L2 for 61 5 64 1 the frequency. 62 6 65 4 6. Press © ERY to view the data. © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 7 Heart rates — 1-variable statistics (cont.) 4. Check the statistics calculations. After students Follow these steps: display & x (Sigma x), explain that Xx is the sum 1. View the statistical data. of all the heart rates. Ask students: n should equal the total number of e How many heartbeats were entered from all students sampled. For this example, of the student in one minute? This is Xx. n= 22. ¢ How many students were entered? This is n. 2. Press © to X to see the average heart rate. ? e How can we calculate the average heart rate: X= 62.27272727 - me DX This 1s X. = = 62.27272727 n 3. Press © until you see Ex. e Is the average heart rate higher or lower than zx = 1370 you expected? . . Note: The numbers show the results 5. Now we will see the effect of some exercise on for the example described in this heart rate. To accommodate various student's activity. Your students’ results will needs, pair students with other students who will vary depending on the size of the be able to complete the task. Also consider group and the heart rate readings. designing some task that an individual student can safely undertake to raise their heart rate. Tell students: If at any point during this portion of the activity you experience pain, weakness, or shortness of breath, stop immediately. 6. Have the students run in place for 2 minutes and then give them these instructions: a. Time your pulse for 1 minute. b. Record your heart rate as before. c. Enter the data into the calculator. d. Compare the average heart rate after running with the resting heart rate. 7. Now have the students do jumping jacks for 2 minutes. Instruct them to time their pulse for 1 minute again and record as before. Have them enter the data into the calculator again and calculate the average heart rate after jumping jacks. Compare to the other 2 averages. 8. Instruct students to make a bar graph of the 3 sets of data they collected. Ask students: e Howare the bar graphs the same? e How are they different? e Is the data grouped the same, or is it more spread out in one graph compared to another? 8 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Heart rates — Name 1-variable statistics Date Problem What do you think the average heart rate is for someone your age? What about after exercising? Procedure 1. Use this table to record your class or group data (resting). Heartbeats per minute (resting) Frequency 2. What is the class (group) average? 3. Answer the following questions from the data: a. What is the total number of heartbeats for the minute? Write the symbol and the number from the calculator. b. What is the total number of student’s heartbeats entered? Write the symbol and the number from the calculator. c. How would you compute the average heart rate? Is your answer the same as in question 2? © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers Heart rates — Name 1-variable statistics Date 4. Use this table to record your class or group data (running). Heartbeats per minute Frequency (running) 5. What is the class (group) average? 6. Answer the following questions from the data: a. What is the total number of heartbeats for the minute? Write the symbol and the number from the calculator. b. What is the total number of student’s heartbeats entered? Write the symbol and the number from the calculator. c. How would you compute the average heart rate? Is your answer the same as in question 5? 10 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Heart rates — Name 1-variable statistics Date : 7. Use this table to record your class or group data Gumping). Heartbeats per minute Frequency (jumping) 8. What is the class (group) average? 9. What is the total number of heartbeats for the minute? 10. Answer the following questions from the data: a. What is the total number of heartbeats for the minute? Write the symbol and the number from the calculator. b. What is the total number of student’s heartbeats entered? Write the symbol and the number from the calculator. c. How would you compute the average heart rate? Is your answer the same as in question 8? © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 11 Heart rates — Name 1-variable statistics Date 11. Make a bar graph for each of the 3 sets of data you collected. Resting Running Jumping 12. How are the bar graphs the same? How are they different? 13.Is the data grouped the same or is it more spread out in one graph compared to another? 12 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED At the movies — data formulas at the box office Overview Students investigate a table of values and observe patterns in the table. Students use on the TI-BOXS MultiView™ calculator to enter data into a list and test their generalizations. Introduction The warm up question is given to help you launch the student sheet activity. You can skip the warm up activity but you will have to provide more guidance during the investigation of the problem on the student sheet. Warm up Guide students in the use of tables and to seea pattern and write a generalization. Present the following story problem. Every Wednesday, Keisha gets home trom work too late to walk her dog, Max. She asked her neighbor Kyle to walk her dog after he comes home from school. Kyle is happy to help! Keisha pays Kyle $4 each week to walk Max. Kyle likes to save his money. Create a table of how much money Kyle has each week for 5 weeks. Guide students to create the following table on their papers. You can think of this table as a data list of two numbers which depend on each other. It is important to have students write their calculation and outcome in the Money (output) column in order to see any patterns. This helps them to write algebraic sentences from the words and to make generalizations using inductive reasoning. Use these columns for different learning styles if needed. Week | Money Repeated addition | Adding on 1 1x4=4 4=4 4=4 2x4=8 4+4=8 4+4=8 3x4=12 4+4+4=12 8+4=12 4x4=16 4+4+4+4=16 12+4=16 OY WB] C9) bo 5x4=20 4+4+4+4+4=20 16+4=20 Math Concepts ° patterns ¢ algebraic expressions ¢ linear functions ° variables Materials TI-3OXS MultiView pencil graph paper student activity © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 13 At the movies (continued) Point out that the Money column looks like the multiplication table for the number 4. This connects them back to something familiar. Remind the students that they know that Kyle earns $4 per week. This is the rate of Kyle's savings and it can be written in fractional form as Ask the students to fill in more of the table describing how much Kyle will save. Have them fill in the table for weeks 6 and 7, and then ask if they can determine the amount of money for 10 weeks, 25 weeks, and 100 weeks. Finally, ask them if they could fill in the amount of money after some number of weeks. Call the unknown number of weeks a variable and use the letter W to represent weeks. Use the variable M to represent money. Week (W) Money (M) 1 1x4=4 2 2x4=8 3 3x4=12 4 4x4=16 5 5x4=20 6 6x4=24 7 7x4=28 10 10x4=40 25 25x4=100 W Wx4* All of this investigation should be done without the calculator for these basic multiplication facts. If students need support with their multiplication, encourage looking up facts in a chart rather than using the calculator, to promote mental math and appropriate calculator use. Ask students to write the expression for the calculation using W, x, and 4.* (Answer: W x 4) 14 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED At the movies (continued) Ask the students the following: "If you calculate W weeks times $4, you get a number. What does that number mean to Kyle?" You are prompting the student to say Money (M) and lead them into writing the formula or sentence in two variables, M = W x 4. Typically, you write the number and then the letter with implied multiplication. Remind students that multiplication is commutative soM=Wx4=4xW=4W. Support the investigation using the data editor ( data]) on the TI-30XS MultiView™ calculator by having the students look at many values of their algebraic expression to see if they match the table they created. 1. Have students enter their table into the data list. Notice there are three lists available: L1, L2, and L3. Discuss that they will enter the Week (W) values in Ll. 2. Have the students enter the first three values of W from their table, {1, 2, 3}. 3. Enter a formula to validate the work: L2 =4 x L1. Notice that W = L1 and M =L2. 4. Add input to L1 to see L2 update automatically with the output value of the formula. Scroll to an open entry space in L1. Ask them to check their table for 4 weeks and then 100 weeks. Before starting the group investigation on the student sheet, have the students clear the data in the lists. (Continued) Remind students that for this activity they are using the features in [data]and not [table] . If students are not familiar with the TI-30XS MultiView calculator, have them turn on the calculator and press Make sure all students have their calculator mode set as shown: RAD GRAD ™ i) SCI ENG pee O1Z3456755 paar Hee IF) To return to the Home screen, press (clear). 1. Enter the first three values of W: [data] 1 ©2030. 2. Enter the formula: ® @1 4 1m. 3. Add input to L1: OOO T enter 100 . 4. To view the formula in L2 again, press @1. 5. Edit the formula, if desired, and press @@¥ to set the formula again. 6. To clear data, press 4, Hint: Remember that pressing [2nd] [quit] takes you back to the Home screen. © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 15 At the movies (continued) The students now have taken data from words to a Kyle's Money table of values, to a pattern they can view, to writing an algebraic expression. The next step is to show “8 them a view of how the number pattern plots on a 16 - graph. What is the shape of M = 4W? Have students 44 J plot the first 4 points in the table. Notice the points / fall on a straight line. You can mention that they can = 124 describe the increase of Money (M) as "for every 1 = / week (W) Kyle works, his amount of money (M) z v0 increases by $4." This is an obvious statement but 2 8 4 sets the foundation for talking about rates and how they affect the tilt of a line (slope). 8 VA The number of weeks and amount of money are both 4 7 positive so the graph makes sense in the first 2 quadrant. Have your students use graph paper to make the graphs of their data. on 0 1 2 3 4 = 5 Activity Weeks (W) Students repeat a similar investigation in groups looking at patterns to write algebraic expressions and sentences. They also create a graph of the values in the table. Have students read the problem on the student sheet before breaking up into groups so they understand their task. Students fill in the table using mental math. They write all calculations to help them see the formula. They are encouraged to use mental math as much as they can before using the calculator to find the results for the amount of money. Number of Calculation Amount of Money People (P) (M) 1 1x 11.50 $11.50 2 2x 11.50 $23.00 3 3 x 11.50 $34.50 4 4x 11.50 $46.00 10 10 x 11.50 $115.00 100 100 x 11.50 $1150.00 1000 1000 x 11.50 $11500.00 P Px 11.50 M=Px 11.50 16 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED At the movies (continued) Procedure Students should write the algebraic equation from the pattern showing in their table: M = P x 11.50 or using implicit multiplication, M = 11.50 P. Students check their formula using the data editor ( [data] ) on the TI-30XS MultiView™ calculator, as in the warm up example. 1. Have the students check to see how the calculator is set up. Enter the first three values in L1 {1, 2, 3}. Translate your formula to the calculator formula and enter the formula into L2. Your formula: M = The calculator formula: L2 = Enter more values into L1 to check the table of values and the formula. This activity validates the formula for several values. Enter 7500 in L1 to find the amount of money in L2. Write the math as M = 11.50 x 7500 = $86,250. Create a report by filling in a table of values and a graph. Write a paragraph describing the work for the presentation. Answers in the paragraph will vary. Make sure that the students explain the table, graph, and algebraic sentence (formula) in the paragraph. P M 500 $5750 1000 $11500 1500 $17250 2000 $23000 2500 $28750 Make sure the calculator mode is set as Amount of Money (M) shown. 1. Press (mode]. 2. Press [data] 1O2O3 ©. 3. Enter the formula in L2. ® @1 116) 50 1. 4, Press@ © © © 44 5 OM 6 OY 10 Oy 100 Gy 1000 Ga. 5. Press 7500 Gi. Box Office at Multiplex 35000 30000 25000 20000 15000 10000 5000 C) ° 500 1000 1500 2000 2500 Number of People (P) 3000 © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 17 Name At the movies Date Problem A blockbuster movie is opening this weekend. On the news, you hear that tickets will be $11.50 per person. The reporter says that a family of two will spend $23 and a family of three will spend $34.50. They show a graphic with this information in a table format. Number of People Amount of Money 1 $11.50 2 $23.00 3 $34.50 The reporter also mentions that the local theater, MultiPlex, has twenty-five screens and can seat 7,500 people. This blockbuster will open on all screens at the theater. The owners predict that all seats will be sold out on the first day! The owners of MultiPlex want to know how much money they can expect to take in at the ticket office. They would like a general formula so they can quickly find out the amount of money for any amount of people that buy tickets. Your job: You have been hired as the accountant for MultiPlex! Congratulations! Your boss wants a formula that will tell her how much money will be taken in at the box office, depending on how many people buy tickets. Procedure 1. Use the table to investigate the amount of money taken in at the ticket office depending on the number of people going to the movie. Fill in the following table. Write all of your calculations at each step. Use mental math as much as you can before using the calculator to find the results for the amount of money. Number of| Calculation Amount of People (P) Money (M) 1 1x 11.50 $11.50 2 2x 11.50 $23.00 3 3x 11.50 $34.50 4 5 6 10 100 1000 18 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Name At the movies Date 2. What pattern do you see from your table? Using the information in your table, write a formula (an algebraic expression) which describes the amount of money (M) depending on the number of people (P) that buy a ticket to the show. M= 3. Check your formula using the data list editor ((data]) on the TI-30XS MultiView™ calculator. a. In column L1, enter only the first three entries in the number of people (P) list from the table above. (Enter {1, 2, 3}.) b. Enter your formula from part 2 in L2. Be careful: to use the calculator, you have to translate your variables (letters). The letter P is now L1 and M is L2. Rewrite your formula here in terms of L1 and L2 so you can enter the formula in your calculator. Your formula: M= The calculator formula: L2= c. Check the numbers in L2 with the numbers in your table above. Do they match? d. Enter more values from the number of people list from your table into L1. Check the values in L2 against your table above. Do they match? Does your formula work? 4. Use the data editor on the calculator to find the amount of money (M) that the owners will take in at the ticket office if the entire theater is filled during one showing with 7500 people (P). Write how you would find this answer by hand using your formula. © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 19 At the movies Name Date 5. Your boss wants you to make a presentation to the people who invest money in MultiPlex. The investors want to see numbers and graphs in your presentation! Fill in the table below using the data editor on your calculator. Graph the points from this table. This is another way that an accountant can show how the amount of money (M) depends on the number of people (P). This gives a picture of the data! P M 500 1000 1500 2000 2500 Amount of Money (M) Number of People (P) 6. Write a paragraph below about what you would say to your boss and the investors about your work. Include how you determined the formula for the amount of money and what the table and graph tell them about the amount of money that will be taken in at the box office. 20 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Name that rule! Overview Math Concepts Materials Students guess the algebraic expression (function) © algebraic © TI-BOXS MultiView from a table of values in a game format. Students use expressions © pencil on the TI-3OXS MultiView™ calculator to enter an ° functions *° student activity . strips of paper expression as a function (y=) in order to play the game. and paper bag Introduction Students will warm up for this activity by evaluating expressions and filling out a table of values. They then play a game, "Name that rule!" The game uses the TI-30XS MultiView calculator to create a table of values. Have students fill out the following tables which appear on the student sheet. Note: Consider varying the variable letter in the warm up. The variable on the calculator, however, will always be x. x x+8 x 2x+6 | 2(x+3)* 1 2 2 -1 2 -1 4 4 0 3 0 6 6 1 4 1 8 8 2 5 2 10 10 *The students should notice that the tables for 2x + 6 and 2(x + 3) are the same. Discuss why these are equivalent expressions and verify this by using the Distributive Property of Multiplication over Addition. You can also have students use tiles to display the area model, 2(x + 3) = 2x + 6. _ { x { x+3 Show the students how to enter the expression in on the TI-30XS MultiView. They enter the expression as a function. This may be a new concept for your students. If needed, use a function machine © 2006 TEXAS INSTRUMENTS INCORPORATED TI-3OXS MultiView: A Guide For Teachers 21 Name that rule! (continued) to provide an alternate way of thinking about evaluating an expression for different values of x. Here, an input of x= 1 gives an output of y=1+3=4. Discuss that the expression, x+ 3, can be thought of as the rule to find y. Later in the game, the students will think backwards to guess the "rule." If needed, discuss how students follow the rules to their favorite board games. They need to follow the rules in order to play. When they evaluate an expression, they follow a rule to change one number to another. x= j | y=tt3=4 Set up the table on the calculator using the Auto feature in [table]. Auto automatically sets up a table of values to start at a given value and increment by a value. To have the calculator create the same table of values as above, set start at -2 and increment the x values by the step size of 1. Have students compare their table done by hand against the calculator table. Activity Play one or two games of “Name that rule!” with the whole class, using the rules on the next page. For the whole class introduction of the game, the teacher plays the role of the Ruler. This game uses and the Ask-x feature on the TI-30XS MultiView™ calculator. Follow these steps: 1. Press and set mode as shown. RAD GRAD Wy) SCI ENG ne 12S45e7e3 [in THE LH Ty 2. Enter the expression y=x+3: 3G. 3. Enter table setup values: [=] 2© Cog. 4. Use © and © to scroll through values of x and y=x +3. Hint: Copy the game sheets from the student activity section for as many games as needed. 22 TI-BOXS MultiView: A Guide For Teachers © 2006 TEXAS INSTRUMENTS INCORPORATED Name that rule! (continued) Rules for group play Form groups of t