TI-34 MultiView™ A Guide for Teachers Developed by Texas Instruments Incorporated Activities developed by Gary Hanson, Aletha Paskett, and Margo Lynn Mankus Illustrated by Jay 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-34 MultiView™ section of this guide. Margo Lynn Mankus currently works in Mathematics and Technology Education at the State University of New York at New Paltz.
Copyright © 1999, 2000, 2007 Texas Instruments Incorporated. Except for the specific rights granted herein, all rights are reserved. Printed in the United States of America. MultiView, MathPrint, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated.
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Table of contents CHAPTER About the teacher guide About the TI-34 MultiView™ calculator PAGE vii viii Activities Star voyage Scientific notation Heart rates 1-variable statistics My favorite recipe Fractions Next stop - fraction terminal Fractions 3 7 13 17 How to use the TI-34 MultiView calculator 1 2 3 4 5 6 7 8 9 10 TI-34 MultiView basic operations Clearing and correcting Basic math Order of operations and parentheses Numeric notation Fractions Math menu Decimals and decimal places Integer divide
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About the teacher guide location of those keys on the TI-34 MultiView, and any pertinent notes about their functions. How the teacher guide is organized This guide consists of two sections: Activities and How to use the TI-34 MultiView™ calculator. The Activities section is a collection of activities for integrating the TI-34 MultiView into mathematics instruction. The How to use the TI-34 MultiView calculator section is designed to help you teach students how to use the calculator.
About the TI-34 MultiView™ calculator Home screen Display indicators 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-34 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 ") to view the entire entry or expression.
About the TI-34 MultiView™ calculator (Continued) 2nd functions Pressing % displays the 2ND indicator, and then accesses the function printed above the next key pressed. For example, 3 %c 125 < calculates the cube root of 125 and returns the result, 5. • Press any operation key (T, U, and so forth) as the first part of an entry. ans and the operator are both displayed. Resetting the TI-34 MultiView Pressing % and then selecting 2 (Yes) resets the calculator.
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Activities © 2007 TEXAS INSTRUMENTS INCORPORATED Star voyage — Scientific notation 3 Heart rates — 1-variable statistics 7 My favorite recipe — Fractions 13 Next stop - fraction terminal — Fractions 17 TI-34 MultiView: A Guide For Teachers 1
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Star voyage — scientific notation Math Concepts Overview Students investigate scientific notation by changing numbers into scientific notation, and then using them in calculations. Materials • scientific notation • TI-34 MultiView™ • addition • pencil • division • student activity Introduction Set up the activity by telling your students: The standard form for scientific notation is a ¿ 10n,where a is greater than or equal to 1 and less than 10, and n is an integer. 1.
Star voyage — scientific notation (Continued) Activity Present the following problem to students: 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 1013 miles. The distance from the earth to our sun is approximately 9.3 x 107 miles.
Star voyage — scientific notation Name ___________________________ 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-34 MultiView™ calculator, change the following numbers into scientific notation using SCI mode.
Star voyage — scientific notation Name ___________________________ 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 1013 miles. The distance from the earth to our sun is approximately 9.3 x 107 miles.
Heart rates — 1-variable statistics Overview Students use the data editor and statistics function of the TI-34 MultiView™ calculator to investigate the effect of exercise on heart rate. Math Concepts Materials • mean, minimum, maximum, and range • TI-34 MultiView • stopwatch or a 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.
Heart rates — 1-variable statistics (Cont.) 4. Check the statistics calculations. After students display Òx (Sigma x), explain that Òx is the sum of all the heart rates. Ask students: • • • How many heartbeats were entered from all of the student in one minute? This is Òx. How many students were entered? This is n. How can we calculate the average heart rate? This is Ï. • Σx ------ = 62.27272727 n Is the average heart rate higher or lower than you expected? 5.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ Problem What do you think the average resting 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.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ 4. Use this table to record your class or group data (running). Heartbeats per minute (running) Frequency 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.
Heart rates — 1-variable statistics Name ___________________________ Date ___________________________ 7. Use this table to record your class or group data (jumping). Heartbeats per minute (jumping) Frequency 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.
Heart rates — 1-variable statistics Name ___________________________ 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.
My favorite recipe — fractions Overview Students add the volume of ingredients in a cookie recipe to determine the size bowl they need before starting the recipe. Math Concepts Materials • adding fractions • simplifying fractions • TI-34 MultiView™ • pencils • student activity Introduction Set up the activity by showing the students how to enter mixed numbers into the calculator, add and simplify them. 1. Have students practice adding mixed numbers. 4 a. 4 5--8- + 3 --57 4 b.
My favorite recipe — fractions (Continued) Activity Present the following problem to students: You are about to make your favorite cookie recipe. You check the bowls in the kitchen and the only one you can find is a 5-quart bowl.
My favorite recipe — fractions Name ___________________________ Date ___________________________ Problem You are about to make your favorite cookie recipe. You check the bowls in the kitchen, and the only one you can find is a 5-quart bowl.
My favorite recipe — fractions Name ___________________________ Date ___________________________ 2. Using the TI-34 MultiView™ calculator, add all the measurements in the recipe. Amount (in cups) Ingredient 2 1--4- C brown sugar 2 1--- C white sugar 1 1--- C butter 2 2 3 --4 C shortening 5 eggs (Enter your answer from #1) Salt, baking powder, baking soda, vanilla (Enter your answer from #1) 4 1--3- C flour 5 3--8- C oatmeal Total 3.
Next stop — fraction terminal Overview Students investigate fraction and decimal representations to determine when a base-ten fraction will be represented as a terminating or repeating decimal. Students use v on the calculator to enter fraction families and observe patterns.
Next stop — fraction terminal (Continued) Have the students work in groups to promote discussion. Have them enter a table of data from the student activity sheet into the data editor by using v. ³ Notice there are three lists available: L1, L2, and L3. Discuss that they will enter fractions using the P key. Shown is an example of entering the family of fractions with the denominator of 8. Have students enter the conversion of fraction to decimal to validate their work.
Next stop — fraction terminal (Continued) 2. Table D: Table E: 1 --- = 0.125 8 1 ------ = 0.04 25 2 --- = 0.25 8 2 ------ = 0.08 25 3 --- = 0.375 8 3 ------ = 0.12 25 4 --- = 0.50 8 4 ------ = 0.16 25 5 --- = 0.625 8 5 ------ = 0.2 25 6 --- = 0.75 8 6 ------ = 0.24 25 7 --- = 0.875 8 7 ------ = 0.28 25 8 ------ = 0.32 25 3. The decimal representations for the factions are: 20 15 10 9 ------ = 0.36, ------ = 0.4, ------ = 0.6, ------ = 0.8 25 25 25 25 4. Answers will vary.
Next stop — fraction terminal (Continued) them later formulate a rule about when a fraction will be expressed as a terminating or repeating decimal. 7. These fractions will be represented as a repeating decimal number. 8, 9, 10. Students will identify terminating and repeating decimals from their tables. Guide them to see that if the prime factorization of the denominator of the fractions, when in simplest form, have only factors of 2 and/or 5, then the fraction will be represented as a terminating decimal.
Next stop — fraction terminal Name ___________________________ Date ___________________________ Problem In this activity you will explore the decimal forms for familiar fractions. Fill in the tables below and see if you can write a rule to predict the type of decimal number that is the same as your fraction. Procedure 1. Fill in the following tables. Using mental math or pencil and paper, change each fraction to its decimal representation.
Next stop — fraction terminal Name ___________________________ Date ___________________________ 2. Use v on the TI-34 MultiView™ calculator to fill in the following tables. Change each fraction to its decimal representation. Your teacher will give you details on how to use the calculator to fill in the table. Remember to try to beat the calculator with your own calculations. You can check your work with the calculator! .
Next stop — fraction terminal Name ___________________________ Date ___________________________ 5. Mathematicians are like detectives. They investigate numbers! Observe the fractions in tables F and G, and find their decimal representation using v on the TI-34 MultiView™ calculator. TABLE F Fraction Decimal TABLE G Fraction 1 -3- 1 --6 2 -3- 2 --6 Decimal 3 --6 4 --6 5 --6 6.
Next stop — fraction terminal Name ___________________________ Date ___________________________ 8. A decimal number is called a repeating decimal if it consists of a number or set of numbers that keep repeating in a regular pattern. Did you see a repeating decimal in your work? If so, write an example of a repeating decimal. Ask your teacher for the correct notation. 9. A decimal number is called a terminating decimal if the decimal representation becomes all zeros after a certain number of digits.
How to use the TI-34 MultiView™ calculator TI-34 MultiView basic operations Clearing and correcting Basic math Order of operations and parentheses Numeric notation Fractions Math menu Decimals and decimal places Integer divide Stored operations Memory and stored variables Data editor and list conversions Statistics Probability Logarithms and exponential functions Pi Powers, roots, and reciprocals Angle settings and conversions Polar and rectangular conversions Trigonometry © 2007 TEXAS INSTRUMENTS INCORPOR
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TI-34 MultiView™ basic operations Keys 1. & turns on the calculator. 2. % turns on the 2ND indicator and accesses the function shown above the next key you press. 3. %' turns off the calculator and clears the display. 4. < completes the operation or executes the command. 5. %i recalls the most recently calculated result and displays it as ans. 6. r toggles the answer between fraction and decimal, and exact pi and decimal. 1 7.
TI-34 MultiView™ basic operations (Continued) • Resetting the calculator: – Returns mode settings to their defaults: degree angle mode (DEG), normal numeric notation (NORM), floating decimal notation (FLOAT), MathPrint™ display mode, and fraction modes (Un/d and MANSIMP). – Clears memory variables, pending operations, entries in history, statistical data, stored operations, and ans (Last answer). Notes • The examples on the transparency masters assume all default settings.
Second, off, arrows, enter • Enter 46 – 23. • Change 46 to 41. Change 23 to 26 and complete the operation. %' !" #$ < 2- + ---3- and complete the • Enter -5 10 operation. • Turn the TI-34 MultiView™ off and back on. The Home screen is blank; scroll up to view history.
Reset Reset the calculator. Press % Display % 2 - Using % returns all settings to their defaults and clears the memory.
Mode q q Use qto choose modes. Press # $ ! " to choose a mode, and < to select it. Press - or %s to return to the Home screen and perform your work using the chosen mode settings. Default mode settings are shown highlighted. DEG RAD Sets the angle mode to degrees or radians. NORM SCI Sets the numeric notation mode. Numeric notation modes affect only the display of results, and not the accuracy of the values stored in the calculator, which remain maximal.
Mode (continued) NORM displays results with digits to the left and right of the decimal, as in 123456.78. q SCI expresses numbers with one digit to the left of the decimal and the appropriate power of 10, as in 1.2345678x105 (which is the same as 123456.78). Note: C is a shortcut key to enter a number in scientific notation format. The result displays in the numeric notation format set in mode. FLOAT 0 1 2 3 4 5 6 7 8 9 Sets the decimal notation mode.
Mode (continued) q CLASSIC MATHPRINT sets the display input and output. CLASSIC displays inputs and outputs in a single line. The 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 stored operations (op1 or op2) values.
Mode (continued) q MANSIMP AUTOSIMP Determines whether or not a fractional result will be simplified automatically. MANSIMP The user simplifies fractions manually step-by-step. » next to the resulting fraction signifies that the fraction is not yet in simplest form. AUTOSIMP The calculator automatically simplifies fractional results to the lowest terms.
Menus Certain keys display menus: H, %=, %A, %B, d, % , %h, %{, vv, and %t. Press " and $ 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 -. To exit a menu or application and return to the Home screen, press %s. The Home screen is blank; scroll up to view history.
Menus (continued) %A LOG 1: log( 2: 10^( %B LN 1: ln( 2: e^( TRIG 1: sin( 2: cos( 3: tan( 4: sin-1( 5: cos-1( 6: tan-1( d MATH 1: lcm( 2: gcd( 3: 3 4: 3Ñ( NUM 1: abs( 2: round( 3: iPart( 4: fPart( 5: min( 6: max( 7: remainder( % %h %{ Reset 1: No 2: Yes Recall Var 1: x = 2: y = 3: z = 4: t = 5: a = 6: b = 7: c = 36 Clear Var 1: Yes 2: No TI-34 MultiView: A Guide For Teachers © 2007 TEXAS INSTRUMENTS INCORPORATED
Menus (continued) vv (Press v once to display the Data editor screen. Press again to display the menu.) CLEAR 1: Clear L1 2: Clear L2 3: Clear L3 4: Clear ALL CNVRSN 1: Add/Edit Cnvrs 2: Clear L1 Cnvrs 3: Clear L2 Cnvrs 4: Clear L3 Cnvrs 5: Clear ALL Press v while you are in the Add/ Edit Cnvrs option of the CONVERSION menu to display this menu: Ls 1: L1 2: L2 3: L3 %t STATS 1: 1-Var Stats 2: 2-Var Stats 3: StatVars This menu option displays after you calculate 1-Var or 2-Var stats.
Last answer (ans) Use Last answer (ans) to calculate 2 2 5 + 12 .
Answer toggle Press r to toggle the display result between fraction and decimal answers, and exact pi and decimal.
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2 Clearing and correcting Keys Notes 1. - clears characters and error messages. Press - once to clear an uncompleted entry; press it again to clear the display. You can scroll up and use - to clear entries in history. - backs up one screen in applications. • The examples on the transparency masters assume all default settings. • Pressing - does not affect the memory, statistical registers, angle units, or numeric notation. 2. %f lets you insert a character at the cursor. 3.
Delete and insert Enter 4569 + 285, and then change it to 459 + 2865. Complete the problem.
Clear - Enter 21595. Clear the 95. Clear the entry.
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3 Basic math Keys 1. T adds. Notes 2. U subtracts. 3. V multiplies. • The examples on the transparency masters assume all default settings. • The TI-34 MultiView™ calculator allows implied multiplication. Example: 3 (4+3) = 21 • Do not confuse M with U. U allows subtraction. • Use parentheses to group the negation sign with the number, if needed. Example: ½22 = ½4, and (½2)2 = 4. • Results of percent calculations display according to the decimal notation mode setting. 4. W divides. 5.
Add, subtract, multiply, divide, equals TUVW < Find: 2 + 54 - 6 = 16 × 21 = 78 ¾ 2 = 12 × (5 + 6) = Press Display 2 T 54 U 6< 16 V 21 < 78 W 2 < 12 D 5 T 6 E< 46 TI-34 MultiView: A Guide For Teachers © 2007 TEXAS INSTRUMENTS INCORPORATED
Negative numbers The temperature in Utah was ½3Ä C at 6:00 a.m. By 10:00 a.m. the temperature had risen 12Ä C. What was the temperature at 10:00 a.m.? Press M Display M 3 T 12 < The temperature at 10:00 a.m. was 9Ä C.
Percent Mike makes $80 per week. He saves 15% of his earnings. How much does Mike save per week? Press _ %N Display 15 _V 80 < Mike saves $12 per week. . 3- of her last paycheck. Crystal saved -8 What per cent of her paycheck did she save? Press Display 3P8" %N < Crystal saved 37.5% of her last paycheck.
Order of operations and parentheses Keys 4 Notes 1. D opens a parenthetical expression. • The examples on the transparency masters assume all default settings. • The transparency master showing the Equation Operating System (EOS™) demonstrates the order in which the TI-34 MultiView™ calculator completes calculations. • Operations inside parentheses are performed first. Use D E to change the order of operations and, therefore, change the result. Example: 1 + 2 × 3 = 7 (1 + 2) × 3 = 9 2.
Equation operating system (EOS™) 1 (first) Expressions inside D E 2 Functions that need a E and precede the expression, such as in, %B, %A, and some menu items. 3 Fractions 4 Functions entered after the expression, such as F and angle unit modifiers (Ä, Å, Æ, r) 5 Exponentiation (G) and roots (%c) Note: In Classic mode, exponentiation using the G key is evaluated from left to right. The expression 2^3^2 is evaluated as (2^3)^2, with a result of 64.
Equation operating system (Continued) 7 8 9 10 11 (last) Permutations (nPr) and combinations (nCr) Multiplication, implied multiplication, and division Addition and subtraction Conversions (%O, %j, %N, } and ´DMS) < completes all operations and closes all open parentheses © 2007 TEXAS INSTRUMENTS INCORPORATED TI-34 MultiView: A Guide For Teachers 51
Order of operations TVDE 1+2×3= Press Display 1T2V3 < 1 + (2 x 3) = Press Display 1TD2V3 E< (1 + 2) × 3 = Press Display D1T2E V3< 52 TI-34 MultiView: A Guide For Teachers © 2007 TEXAS INSTRUMENTS INCORPORATED
Order of operations (Continued) 5 – 4 ( 1 ) ( 3 ) = (Classic mode) 2 Press Display q$$$
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5 Numeric notation Keys Notes 1. q lets you choose from the following numeric notation menu. • The examples on the transparency masters assume all default settings. • You can enter a value in scientific notation regardless of the numeric notation mode setting. For a negative exponent, press M before entering it. • Results requiring more than 10 digits are automatically displayed in scientific notation. • For the decimal notation mode, refer to Chapter 8, Decimals and decimal places.
Floating decimal and scientific Enter 12543, which will be in floating decimal notation and normal numeric notation (both default settings in q). Alternate the display result between normal and scientific notations by changing settings on the mode screen.
Scientific notation With the TI-34 MultiView™ calculator in Norm and MathPrint™ modes (both defaults), enter the following problem in scientific notation using the C key. C The Earth is approximately 1.5 x 108 kilometers from the Sun. Jupiter is approximately 7.8 x 108 kilometers from the Sun.
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6 Fractions Keys P in MathPrint mode can also be used for 1. @ lets you enter mixed numbers and fractions. All entries must be an integers and the denominator can not be zero. more complex fractional computations that include operators and other functions by pressing P before you enter the numerator. In MathPrint mode, press $ between the entry of the numerator and the denominator. In Classic mode, press P between the entry of the numerator and the denominator.
Fractions (continued) Notes (continued) • Calculations using fractions can display fraction or decimal results, depending on input. • In MathPrint mode, fractions with P can include operation keys (T, V, etc.) and most function keys (F, _, etc.). In Classic mode, fractions with P do not allow operation keys, functions, or complex fractions in the numerator or denominator. • In MathPrint mode, you can enter variables (x, y, z, t, a, b, and c) in the numerator and denominator of a fraction.
Fractions At the party, you ate --5- of the 6 1- of the pepperoni pizza and ---10 sausage pizza. The pizzas are the same size. If you put the pieces together, how much of one whole pizza did you eat? Press P } Display 5P 6 "T 1 P 10 < }< 14 of the size of one whole You ate ---15 pizza.
Mixed numbers A baby weighed 4 --3- pounds at birth. @ 8 In the next 6 months, she gained --- pounds.
Mixed numbers (Continued) @ Mode setting n/d: Press Display 4@3$8 "T 2 @ 3 $4< After 6 months, the baby weighs 7 --1- pounds.
Converting fractions and decimals Juan swims 20 laps in 5.72 minutes. %j Mary swims 20 laps in 5 3 --- minutes. 4 Change Mary's time to a decimal to determine who swims faster. Mode setting Un/d: Press Display 5@3$4 "< %j < Mode setting n/d: Press Display 5@3$4 "< %j < Juan swims faster than Mary since he swims 20 laps in 5.72 minutes.
Converting fractions and decimals Change 2.25 to its fractional equivalent. You may have to simplify more than once to simplify the fraction to its lowest terms.
Converting fractions and decimals (Continued) Mode setting n/d: Press %j Display 2 8 25 %j < }< }< 66 TI-34 MultiView: A Guide For Teachers © 2007 TEXAS INSTRUMENTS INCORPORATED
7 Math menu NUM menu: abs(x) Displays absolute value of x. round(x , digits) Rounds x to specified number of digits. ipart(x) Returns only the integer of x. fpart(x) Returns only the fractional part of x. min(x1, x2) Returns the minimum of two values, x1 and x2 . max(x1, x2) Returns the maximum of two values, x1 and x2. remainder(n1, n2): Returns the remainder resulting from the division of two values, a whole number (n1) divided by a positive whole number (n2). Keys 1.
Absolute value Find the absolute value of ½35 and then validate the answer using the calculator. d |½35| = Press Display d" 1 M 35 " < Evaluate the expression 6 + |4 - 9| x 3 and then validate the answer using the calculator.
Rounding a number Round À to the nearest thousandths place.
Integer and fractional part Display the integer and fractional part of 7 --5- . Then, change 7 --5- to a 8 8 decimal number and display the integer and fractional part of the number.
Minimum and maximum Using max, put the following list of numbers in ascending order: 14 ---- , --7- , 3 --- . 17 9 5 Press d Display d"6 7P9"% ` 14 P 17 " E< d"6 7P9"% `3P5" E< ⎧ ⎪ ⎨ ⎪ ⎩ ⎫ 3 7 14 The list in ascending order: ---, ---, ---- ⎪⎬ .
Minimum and maximum (Continued) Using min, check if this statement is true or false: d 5.75 < 5 --78 Press Display d"5 5 8 75 %` 5@7$5 "E< 5.75 < 5 --7- is true.
Least common multiple Add --1- + --5- using lcm to find the least 4 6 common denominator. Verify your answer.
Greatest common divisor Find the greatest common divisor (gcd) for the numbers 27 and 36. 27- to its Then use gcd to simplify -----36 lowest terms.
Cube and cube root 3 Calculate 34 and Press 3 d 39304 . Display 34 d 3 < d4# <"< Notice that 3 3 34 is 34.
Remainder The night of the school dance, The Snowball Ball, 179 students will attend. There are round tables that seat 8 students each. There are just enough tables for all of the students. Will all of the tables be filled? How many tables are set up? Press d %Y Display d"7 179 %` 8 E< Not all of the tables will be filled. One table will have only 3 students. 179 %Y 8< There are 23 tables set up. There are 22 full tables, and one table with 3 students.
Decimals and decimal places 8 Keys Notes 1. 8 enters a decimal point. • 2. q lets you set the number of decimal places. Press $ $ and then " to the choice of decimal desired. Press < to select it. The examples on the transparency masters assume all default settings. • Press q $ $ < to return to standard notation (floating decimal). • The TI-34 MultiView™ calculator automatically rounds the result to the number of decimal places selected. For example, when the decimal is set to 2 places, 0.
Decimal Round 12.345 to the hundredths place, to the tenths place, and then to floating notation.
9 Integer divide Keys Notes 1. %Y divides two positive integers and displays the quotient and the remainder, r. • The examples on the transparency masters assume all default settings. • You can include integer division in an expression, but the remainder may not be displayed as part of the final answer. • After a calculation with %Y is completed, only the quotient from the result is stored in ans (last answer). Therefore, if you use the result in another calculation, the remainder is ignored.
Integer divide You have 123 music CDs. You divide them equally to store on 13 small shelves in your room. How many CDs will be on each shelf? How many will be left over? Press %Y Display 123 %Y 13 Each shelf will contain 9 CDs, with 6 CDs left over.
10 Stored operations Keys Notes 1. %n or %p lets you store an operation. • The examples on the transparency masters assume all default settings. 2. m or orecalls and displays the stored operation. • The TI-34 MultiView™ calculator stores two operations, op1 and op2. To store an operation to op1 or op2 and recall it: 1. Press %n or %p. 2. Enter the operation (any combination of numbers, operators, or menu items and their arguments). 3. Press < to save the operation to memory. 4.
Addition as "counting on" There are 4 frogs in a pond.
Multiplication as "repeated addition" Maria put new tile in her kitchen. She made 4 rows with 5 tiles in each row. Use repeated addition to find out how many tiles she used. Press %n m Display %n Press - if necessary to clear a previous operation.
Multiplication as "repeated addition" (Continued) %n m m m Maria used 20 tiles. See that 4 groups of 5 is 20. Multiplication is a shortcut to the repeated addition, 4 x 5 = 20. Check this on the calculator.
Powers as "repeated multiplication" Use this formula and repeated multiplication to find the volume of a cube with a base of 5 meters. %p o V = l × w × h = 5 × 5 × 5 = 53 cubic meters Press Display %p Press - if necessary to clear a previous operation.
Powers as "repeated multiplication" (Continued) %p o o o The volume of a cube with a base of 5 meters is 125 cubic meters. See that 5 x 5 x 5 = 125. You can also use powers notation as a shortcut for repeated multiplication, 53 = 125. Check this on the calculator.
Using a power as a constant Use this formula to find the volume of each cube. %p o v = length of side3 = S3 cubic units S = 2 units S = 3 units Press S = 4 units Display %p Press - if necessary to clear a previous operation.
Using a power as a constant (Continued) The volumes are 8, 27, and 64 cubic units. G Another notation used on a calculator to raise a number to a power is ^. Enter 4 G 3. Notice the different notations: 43 = 4^3 = 4 x 4 x 4 = 64.
Memory and stored variables 11 Keys Notes 1. L lets you store values to variables. Press L to store a variable, and press z to select the variable to store. Press < to store the value in the selected variable. If this variable already has a value, that value is replaced by the new one. • The examples on the transparency masters assume all default settings. • You can store a number or an expression that results in a number to a memory variable.
Store, variables Following are your scores for tests and homework in your math class. L z Test scores: 96, 76, 85. Homework scores: 92, 83, 97, 86. 1. Find your test grade as the average of your test scores. 2. Find your homework grade as the average of your homework scores. 3. Your teacher will compute your final grade as the average of your test grade and your homework grade. What is your final grade? Your teacher will round to the nearest whole number if needed.
Store, variables (Continued) Press L z Display P 92 T 83 T 97 T 86 $4"L zz < PzT zz$2 "< d"2# < %` 0 E< Your final grade is 88 rounded to the nearest whole number. Note: » next to the resulting fraction indicates the fraction can be simplified using }. This was not necessary for the solution to this problem.
Store, recall You are going to ship a gift to each of two friends. You see the gifts at two web sites for the same price. The shipping charges are different at each site. The packages weigh 4.5 pounds and 3.2 pounds. Store A will ship a package for $2 plus $1.40 per pound. Store B will ship the package for $3 plus $1.10 per pound. Which store will charge the least for shipping each gift? Press L z %h Display 4 8 5L z< 2 TzD1 8 40 E < 3 TzD1 8 10 E < Store A charges $8.30 and store B charges $7.95.
Store, recall (Continued) L z %h 382L z< #### ##< < #### ##< < Store A charges $6.48 and store B charges $6.52. Store A charges less to ship the gift that weighs 3.2 pounds.
Store, recall (Continued) Shop A B C Purchases shirts ties belt suspenders Qty 2 3 1 1 Cost $13.98 ea. $7.98 ea. $6.98 $9.
Store, recall (Continued) Press L %h Display %h
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Data editor and list conversions 12 Keys Notes 1. v displays a Data editor with three lists. Each list can contain up to 42 items. To enter data, navigate to a list and enter a number. Press the arrow keys to navigate list elements. • The examples on the transparency masters assume all default settings. • The “Converting fractions to decimals” transparency supports the activity: “Next stop — fraction termimal.” • List conversions accept f ¶d, ´%, ´Simp, and n/d ¶Un/d.
Converting fractions to decimals Find the decimal representation of 3- . From this pattern, can --1- , --2- , and -9 9 9 you predict the decimal representation for --7- ? Check your 9 answer using the lists on the calculator. Press v %j Display v1P9$ 2P9$3P 9$ "v"1 v1% j < Input the rest of the fractions in L1 to test the pattern. Notice L2 updates as you enter in L1.
Converting fractions to decimals (Continued) that the decimal representation is a repetition of the number in the 4- , -5- , numerator for ninths. Entering -9 9 6 --- , and finally --7- validates the 9 9 statement. Notice the last digit in the list is rounded, so 0.777777777... is shown rounded to 0.7778. Remember that 0.777777777... is written as 0.7.
Converting fractions to decimals to percents The same quantity can have different number representations. Sam and his friends ate some cake at his birthday party. v %j %N Sam ate --1- of the cake. 4 Maria ate --2- of the cake. 8 Leila ate --1- of the cake. 2 Find the amount of cake each person ate in the form of a decimal and a percent.
Converting fractions to decimals to percents Use the percent form of the amount of cake eaten to justify your answer.
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13 Statistics StatVars menu: Keys 1. v lets you enter data points (x for 1-Var stats; x and y for 2-Var stats). (See Chapter 12, Data editor and list conversions, for more details on v.) n Ï or Ð Sx or Sy 2. %t displays a menu from which you can select 1-Var, 2-Var or StatVars. Îx or Îy 1-Var Analyzes data from 1 set of data with 1 measured variable—x. 2-Var Analyzes paired data from 2 sets of data with 2 measured variables—x, the independent variable, and y, the dependent variable.
Entering 1-var stat data Five students took a math test. Using their scores, enter the data points: 85, 85, 97, 53, 77. v Use L1 for the scores and L2 for the frequency of the scores.
Viewing the statistics Find the number of data points (n), the mean (Ï), the sample standard deviation (Sx), the population standard deviation (Îx), the sum of the scores (Òx), and the sum of the squares (Òx2).
Removing data points Drop the lowest test score by editing the data in L1 in the data editor. Make sure you update the frequency list, L2, if needed. Find the new mean (Ï). Finally, clear the data from all of the lists.
Entering 2-var stat data The table below shows the number of pairs of athletic shoes sold by a small shoe store. The table shows the total number of pairs of shoes sold for two months and the total number of pairs of Brand A shoes sold during the same months. Enter this data in the data editor. Month April May Total No.
Viewing the statistics Assuming that the rate of shoe sales is a constant, you can use two data points to predict the June sales of Brand A if you know the total June sales. Use a line of best fit to find the June sales of Brand A if the store sells a total of 32 pairs in June. Hint: Find y'(32).
Viewing the statistics (Continued) %t %s %t 3 $ (scroll down to y') < 32 E < You can predict that 18 pairs of Brand A will be sold in June if the total sales are 32 pairs. Extra: Graph the two data points (58, 35) and (47, 28) on graph paper. Graph y' = ax' + b. (Find a and b that you calculated for this problem in the StatVars menu.) Next plot (32, 18).
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14 Probability Keys 1. H displays two submenus, PRB and RAND. PRB menu: nPr Calculates the number of possible permutations of n items taken r at a time. nCr Calculates the number of possible combinations of n items taken r at a time. ! Calculates the factorial of a number. RAND menu: rand Generates a random number between 0 and 1. Notes • The examples on the transparency masters assume all default settings. • A permutation is an arrangement of objects in which the order is important, as in a race.
Combination (nCr) You have space for 2 books on your bookshelf. You have 4 books to put on the shelf. Use this formula to find how many ways you could place the 4 books in the 2 spaces. H 4C2 A B C AB AB and BA count as only 1 BA CA combination DA Press D AC BC CB DB AD BD CD DC Display 4H$ <2< There are 6 unique combinations of 2 books chosen from 4 different books.
Permutation (nPr) Four different people are running in a race. Use this formula to find how many different 1st place and 2nd place outcomes can occur. 4P2 A B C AB and BA count as 2 permutations AB BA CA DA Press H D AC BC CB DB AD BD CD DC Display 4H <2< There are 12 different permutations for the 1st and 2nd place results of the race.
Factorial (!) State license plates contain different numbers and letters to create a unique identification number for each car. Make your own license plates each containing a 4-digit number. Using the digits 1, 3, 7, and 9 without repetition, how many 4-digit numbers can you form? You can use a tree diagram to create the following list of license plates.
Random (rand) H Generate a sequence of random numbers. Press Display H" << < Results will vary.
Random (rand) Set 1 as the current seed and generate a sequence of random numbers. Press H Display 1LH "< < H"< < < Note: Your results will be the same as this example if you use the same number to store to random seed.
Random integer (randint) Create your own calculator spinner. Your spinner will pick numbers from 2 through 10. H Hint: Generate a random integer from 2 through 10. Press Display H"$ < 2 %` 10 E < Results will vary.
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Logarithms and exponential functions 15 Keys Notes 1. %A displays the choice of two submenus, LOG and LN. • The examples on the transparency masters assume all default settings. The LOG menu has the following two choices: log( calculates the common logarithm (base 10). 10^ calculates 10 raised to the power of the value entered as the exponent (common antilogarithm). The LN menu has the following two choices: ln calculates the natural logarithm (base e, where e ≈ 2.718281828459).
Common logarithm and antilogarithm Illustrate the inverse relationship of log and 10^ by finding log(23) and then raise 10 to the result. Notice that 23 returns as the answer.
Natural logarithm and antilogarithm Illustrate the inverse relationship of ln and e^ (antiln or exp) by finding ln(23) and then raise e to the result. Notice that 23 returns as the answer.
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16 Pi Keys Notes 1. g displays the value of pi rounded to 10 digits (3.141592654). • The examples on the transparency masters assume all default settings. • In MathPrint mode™, include a decimal number inside the expression with pi to receive a decimal output. For example, if you enter 2À, the TI-34 MultiView™ calculator displays 2À. If you enter 2.0À, the calculator displays the decimal version, 6.283185307. • In MathPrint mode, you can use r to toggle the answer between decimal and pi formats.
Circumference Use this formula to find the amount of border you need if you want to put a circular border all the way around the tree. C = 2Àr = 2 × À × 1.5m Press g Display 2VgV 185< r The border length is 3À m. You will need apprxomiately 9.4 m for the border.
Area Use this formula to find how much of a lawn would be covered by the sprinkler. Round your answer to the nearest whole number, and then return to floating decimal mode.
Area (continued) g q$$ < -< The area that will be covered by the sprinkler is approximately 50 square meters.
Powers, roots, and reciprocals 17 Keys Notes 1. F squares the value. • The examples on the transparency masters assume all default settings. 3. %c calculates the specified root (x) of the value. • To use G, enter the base, press G, and then enter the exponent. 4. %a calculates the reciprocal. • In Classic mode, exponentiation using G is evaluated from left to right. The expression 2^3^2 is evaluated as (2^3)^2, with a result of 64.
Squares Use this formula to find the size of the tarpaulin needed to cover the entire baseball infield. F G A = x2 = 27.42 square meters Press Display 27 8 4 F< or 27 8 4 G 2< The area of the tarpaulin is 750.76 square meters.
Square roots Use this formula to find the length of the side of a square clubhouse if 3m2 of carpet would cover the floor. Round your answer to 0 decimal places. x = L = x b 3 meters 3m2 of carpet Press Display b3< q$$ "< -< The length of a side of the square clubhouse is 2 meters rounded to 0 decimal places.
Cubes Use this formula to find the volume of a cube with sides 2.3 meters long. Change your answer to a fraction. G V = L3 = 2.33 cubic meters L Press Display 283G 3< r The volume of the cube is 12.167 cubic meters.
Powers Fold a piece of paper in half, in half again, and so on until you cannot physically fold it in half again. How many sections would there be after 10 folds? After 15 folds? Press G Display 2 G 10 < 2 G 15 < Fold the paper in half once and you will see two sections. Fold the paper in half again and you will see four sections. Folding again yields 8 sections, and so on. After 10 folds there will be 1,024 sections.
Roots If the volume of a cube is 125 cm3, what is the length of each side? %c L = 3 125 cm L Press Display 3 %c 125 < The length of each side is 5 cm.
Reciprocals The chart below shows the amount of time spent building model ships. Ships Sailing Steam Luxury Time Spent Building 10 --1- hrs. 2 53 --- hrs. 4 5 --1- hrs.
Reciprocals (Continued) %a Steam ship: 5@3$4 " %O < %a < Luxury liner: 5@1$3" %O < %a < Ships Sailing Steam Luxury 134 Time Spent Building 10 --1- hrs. 2 53 --- hrs. 4 5 --1- hrs.
Angle settings and conversions If you specify an angle unit modifier from the Angle menu, the calculation is performed in that angle type, but the result will be given in the angle mode setting. Keys 1. %= displays the choice of two submenus that enable you to specify the angle unit modifier as degrees (º), minutes ('), seconds ("), or radians (r); or convert units using ´DMS. You can also convert between rectangular coordinate form (R) and polar coordinate form (P).
Degrees, minutes, and seconds to decimal Find the measure of the third angle of a triangle if one angle measures 45Ä 30' and the other angle measures 36Ä 15".
Degrees, minutes, and seconds to decimal (Continued) 180 %= 1 U %i < %= 5< %= The measure of the third angle is 98Ä 15'.
Decimal to degrees, minutes, and seconds You are visiting Beijing, China. Your GPS gives your location (latitude and longitude) as 39.55Ä N 116.20Ä E. Change your location information to degrees, minutes and seconds. Press %= Display 39 8 55 %= < %= # << 116 8 20 %= < %= # << Your location in Beijing, China is 39Ä 33' N 116Ä 12' E.
Degrees and radians Calculate the following: %= cos(180 degrees) cos(À radians) Remember: 180 degrees = À radians.
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Polar and rectangular conversions Keys 1. %= displays a choice of two submenus that lets you convert rectangular coordinates (x,y) to polar coordinates (r, Á) or vice versa. You can also specify the angle unit modifier. (See Chapter 18, Angle settings and conversions, for more information.) R ¶P Menu 19 2. %` enters a comma. Notes • The example on the transparency master assumes all default settings. • Before starting calculations, set the angle mode as necessary.
Polar to rectangular Convert the polar ordered pair (7, 30Ä) to rectangular coordinates. Press %= Display %= " 3 7 %` 30 E< %= " 4 7 %` 30 E< The rectangular ordered pair is (x, y) = (6.062177826, 3.5).
20 Trigonometry Keys Notes 1. %B displays a menu of all trigonometric functions (sin, cos, tan, sin-1, cos-1, tan-1). • The examples on the transparency masters assume all default settings. • Before starting a trigonometric calculation, be sure to select the appropriate angle mode setting (degree or radian—See Chapter 18, Angle settings and conversions). The calculator interprets values according to the current angle-unit mode setting. • E ends a trig function. sin calculates the sine.
Sine Use this formula to find the length of the ramp, D. Round your answer to the nearest whole number, and then return to floating decimal mode. %B 1.
Sine (Continued) %B -< q$$ << The length of the ramp is D = 7 m rounded to the nearest whole number.
Cosine Use this formula to find the distance, D, from the base of the ladder to the house. Round your answer to the nearest whole number, and then return to floating decimal mode.
Cosine (Continued) %B -< q$$ << The distance is approximately 1 meter.
Tangent Use this formula to find the distance, D, from the lighthouse to the boat. Round your answer to the nearest whole number, and then return to floating decimal mode.
Tangent (Continued) %B -< q$$ <-< The distance from the lighthouse to the boat is approximately 153 m.
Inverse sine Use this formula to find the angle of the conveyor belt, x. Round your answer to the nearest tenth, and then return to floating decimal mode.
Inverse sine (Continued) %B -< q$$ << The angle of the conveyer belt is x = 40.5Ä rounded to the nearest tenth.
Inverse cosine Use this formula to find the angle of the ski jump, x. Round your answer to the nearest tenth, and then return to floating decimal mode.
Inverse cosine (Continued) %B -< q$$ << The angle of the ski jump is x = 25.0Ä rounded to the nearest tenth.
Inverse tangent Use this formula to find the angle of depression, x. Round your answer to the nearest tenth, and then return to floating decimal mode.
Inverse tangent (Continued) %B -< q$$ << The angle of depression is x = 13.5Ä rounded to the nearest tenth.
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A Quick reference to keys KEY FUNCTION !" ! " move the cursor left and right so you can scroll an entry on the Home screen. #$ Press % ! or % " to scroll to the beginning or end of a current entry. # $ move the cursor up and down to navigate menu items, view entries in the Data editor and function table, and view previous entries on the Home screen. % # moves the cursor to the oldest entry on the Home screen, and to the top entry of the active column in Data editor.
A Quick reference to keys (continued) KEY FUNCTION %= Displays the following menus. DMS lets you specify the unit of an angle. R ¶P lets you convert rectangular coordinates to polar coordinates, or vice versa. DMS R ¶P 1: Ä 1: R ´Pr( 2: ' 2: R ´PÁ( 3: " 3: P ´Rx( 4: r 4: P ´Ry( 5: ´DMS C C is a shortcut key to enter a number in scientific notation format b Calculates the square root. _ Appends the % sign to a number. Results display according to the decimal notation mode setting.
A Quick reference to keys (continued) KEY FUNCTION %{ Clears all memory variables. v Lets you enter the statistical data points for 1-Var stats and 2-Var stats. vv Press v once to display the data editor screen. Press again to display the Clear and Conversion menus. Lets you access list names when in the Conversion menu. J Deletes the character at the cursor. < Completes the operation or executes the command. %f Lets you insert a character at the cursor.
A Quick reference to keys (continued) KEY FUNCTION z Accesses variables. Press this key multiple times to choose x, y, z, t, a, b, or c. You can also use z to recall the stored values for these variables. In the Data editor, z is a shortcut that takes you straight to the author line to enter or edit a conversion. %' Turns off the calculator and clears the display. & Turns on the calculator. H Displays the following menus. PRB lets you calculate permutations, combinations, or factorials.
Quick reference to keys (continued) A KEY FUNCTION %t Displays the following menu from which you can select 1-Var, 2-Var, or StatVars. 1-Var Stats Analyzes data from 1 set of data with 1 measured variable–x. 2-Var Stats Analyzes paired data from 2 sets of data with 2 measured variables–x, the independent variable, and y, the dependent variable. StatVars After choosing 1-Var or 2-Var stats, displays data values. StatVars displays the following menu of stat variables with their current values.
A A-6 Quick reference to keys (continued) TI-34 III Explorer Plus: A Guide For Teachers © 2007 TEXAS INSTRUMENTS INCORPORATED
B Display indicators INDICATOR MEANING 2ND 2nd function. FIX Fixed-decimal setting. (See the Mode section in Chapter 1, TI-34 MultiView basic operations, and Chapter 8, Decimals and decimal places.) SCI Scientific notation. (See the Mode section in Chapter 1, TI-34 MultiView basic operations.) DEG, RAD Angle mode (degrees or radians). (See the Mode section in Chapter 1, TI-34 MultiView basic operations.) L1, L2, L3 Displays above the lists in data editor.
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C Error messages When the TI-34 MultiView™ calculator detects an error, it returns an error message with the type of error. To correct the error, note the error type and and determine the cause of the error. If you cannot recognize the error, use the following list, which describes error messages in detail. Press - to clear the error message. The previous screen is displayed with the cursor at or near the error location. Correct the expression.
C Error messages (continued) MESSAGE MEANING MEMORY LIMIT The calculation contains too many pending operations (more than 23). If using op1 or op2, you attempted to enter more than four levels of nested functions using fractions, square roots, exponents with ^, xÑ, and x2 (MathPrint™ mode only). LOW BATTERY Replace the battery. Note: This message displays briefly and then disappears. Pressing does not clear this message.
Texas Instruments support and service D For general information Home Page: education.ti.com KnowledgeBase and e-mail inquiries: education.ti.com/support Phone: (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only International Information: education.ti.com/international For technical support KnowledgeBase and e-mail inquiries: Phone (not toll-free): education.ti.com/support (972) 917-8324 For product (hardware) service Customers in the U.S.
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E Battery information Battery precautions Battery disposal • Do not leave batteries within the reach of children. • Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. • Do not mix rechargeable and non-rechargeable batteries. • Install batteries according to polarity (+ and -) diagrams. • Do not place non-rechargeable batteries in a battery recharger. • Properly dispose of used batteries immediately. • Do not incinerate of dismantle batteries.
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