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Texas Instruments 15TK - Class Set Teachers Manual Download Page 85

© 2000 T

EXAS 

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NSTRUMENTS 

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NCORPORATED

TI-15: A Guide for Teachers

78

Converting between fractions and mixed numbers

Convert the improper fraction 

6

4  

to

a mixed number.

Numerator Key

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Denominator Key

P r e s s

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¥

¢

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Fraction Modes

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¢

 6 

ž

 4

®

6

2

4

4

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    2

1

    4

2

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3
2

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Summary of Contents for 15TK - Class Set

Page 1: ...Front TI 15 A Guide for Teachers ...

Page 2: ...TI 15 A Guide for Teachers Developed by Texas Instruments Incorporated Activities developed by Jane Schielack ...

Page 3: ... materials Permission to Reprint or Photocopy Permission is hereby granted to teachers to reprint or photocopy in classroom workshop or seminar quantities the pages or sheets in this book that carry a Texas Instruments copyright notice These pages are designed to be reproduced by teachers for use in classes workshops or seminars provided each copy made shows the copyright notice Such copies may no...

Page 4: ...Value 29 Place value What s the Problem 34 Number sentences Problem solving How to Use the TI 15 38 1 Display Scrolling Order of Operations Parentheses 39 2 Clearing and Correcting 42 3 Mode Menus 45 4 Basic Operations 48 5 Constant Operations 55 6 Whole Numbers and Decimals 63 7 Memory 68 8 Fractions 71 9 Percent 80 10 Pi 84 11 Powers and Square Roots 88 CHAPTER PAGE How to Use the TI 15 continue...

Page 5: ...ers 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 an illustration of the TI 15 keyboard Things to Keep in Mind While many of the examples on the transparency masters may be used to develop mathematical concepts they were not designed specifically for that purpose For maximum flexibility each e...

Page 6: ...arency master in Chapter 1 Display Scrolling Order of Operations and Parentheses Because operations inside parentheses are performed first you can use X or Y to change the order of operations and therefore change the result Menus Two keys on the TI 15 display menus and Press or to move down or up through the menu list Press or to move the cursor and underline a menu item To return to the previous ...

Page 7: ...ttings to their defaults Standard notation floating decimal mixed numbers manual simplification Problem Solving Auto mode and Difficulty Level 1 addition in Problem Solving Clears pending operations entries in history and constants stored operations Automatic Power Down TM APD TM If the TI 15 remains inactive for about 5 minutes Automatic Power Down APD turns it off automatically Press after APD T...

Page 8: ...NTS INCORPORATED TI 15 A Guide for Teachers 1 Patterns in Percent 2 Fraction Forms 6 Comparing Costs 11 Number Shorthand 15 Related Procedures 20 In the Range 24 The Value of Place Value 29 What s the Problem 34 Activities ...

Page 9: ... make conjectures about percent based on the patterns they observe Students can then use manipulatives to verify their conjectures Examples Students may observe that for every item 10 of its price is twice as much as 5 of its price Students may observe that it is easy to estimate 10 of a whole number by using place value and looking at the digits to the right of the ones place Collecting and Organ...

Page 10: ... table like the amounts in the 10 table How does 5 of a 20 item compare to 5 of a 10 item How does 10 of a 20 item compare to 10 of a 10 item How does 10 of the cost of an item compare to the total cost of the item What conjectures can you make about finding 10 of a number What conjectures can you make about finding 5 of a number How can you use manipulatives to test your conjectures Continuing th...

Page 11: ...____________________ Date ___________________________ Collecting and Organizing Data Use your calculator to collect data about percent organize it in the table below and then look for patterns Cost of Item Amount of Tax in Metropolis West Tax Rate ____ Amount of Tax in Metropolis East Tax Rate ____ ...

Page 12: ...___ __________________________________________________________________________ 3 Repeat the activity with a different percent in the left column and compare your results __________________________________________________________________________ __________________________________________________________________________ 4 Repeat the activity changing the percents in the left column while keeping the...

Page 13: ...any ways to represent the solution as possible Examples By thinking of using a cup scoop to fill the bowls each bowl would receive 6 scoops or 6 4 cups of sugar By thinking of separating each cup into half cups there would be 12 half cups and each bowl would receive 3 half cups or 3 2 cups of sugar If a 1 cup measuring cup was used first each bowl would receive 1 cup of sugar then the last two cup...

Page 14: ...ions For example for 6 4 as a fraction enter 6 4 The displays in the different modes will look like the following n d man 6 4 n d auto 3 2 U n d man 1 2 4 U n d auto 1 1 2 Collecting and Organizing Data To guide students in creating data that will exhibit patterns in the fraction quotients ask questions such as What denominator did you choose to explore with Why What denominators do you get with t...

Page 15: ...her denominators seem to be related Example The pattern using a divisor of 6 is related to the patterns for 2 and 3 What pattern do you see in the related denominators Example They are related as factors and multiples Continuing the Investigation Have students brainstorm situations in which they would prefer to use each of the combinations of settings of fraction forms Example When working with pr...

Page 16: ... calculator to one of the following combinations of modes for fraction display Each person should choose a different setting improper manual simp improper auto simp mixed number manual simp mixed number auto simp 2 Select a denominator __________________ 3 Use this denominator with several numerators and record each person s results in the table below Numerator Denominator n d Man n d Auto U n d M...

Page 17: ...hat generalizations can you make __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 3 Try the activity again with a different denominator and compare your results with the two denominators _____________________________________...

Page 18: ...ch should each school contribute to the soccer field maintenance fund this year 2 Have students use the calculator to solve this problem in three ways Finding an integer quotient and remainder Finding the quotient in fraction form Finding the quotient in decimal form Collecting and Organizing Data Students should record their procedures and results on the Student Activity page To help them focus o...

Page 19: ...are yards in the soccer field they all involve multiplication and division How are they different You use different keys to tell the calculator in what form you want the answer displayed Analyzing Data and Drawing Conclusions To guide students in the analysis of their data ask questions such as How are your solutions in the three forms alike They all have a whole number component of 586 How are yo...

Page 20: ... 02 which does make sense As a school which form of the quotient would you want to use Responses may vary Some students may want to use the decimal form since it is the closest to the representation of money Some students may want to use the integer quotient and remainder form and suggest that the Central Office pay the 4 00 remainder Although the fraction form of the quotient describes the exact ...

Page 21: ...ict s soccer field each year The soccer field is 80 yards wide and 110 yards long The 6 schools that play on the field have decided to split the cost evenly How much should each school contribute to the soccer field maintenance fund this year 1 Use division with an integer quotient and remainder 2 Use division with a quotient in fraction form 3 Use division with a quotient in decimal form Analyzin...

Page 22: ...ave them record the resulting displays on the Student Activity page 4 When students reach the point where the left hand counter is no longer displayed ask them what they think has happened to the calculator The product has become so large that there is not room to display both the product and the counter so the counter has been dropped Have students continue to record the counter data even though ...

Page 23: ...present repeated multiplication by 10 with other starting factors For example using 2 as the starting factor the display 2x10 11 represents multiplying 2 by 10 eleven times or 2 x 1011 Collecting and Organizing Data To focus students attention on the relevant changes in the calculator s display ask questions such as What does the display 3 1000 mean When did the counter on the left disappear Why d...

Page 24: ...ct should be 100 000 000 000 The display 1x10 11 represents the product 1 x 10 11 What happens if you use 2 as the starting factor and multiply by 10 repeatedly The displays are the same except the first number in all the products is 2 The display 2x10 11 represents the product 2 x 10 11 Continuing the Investigation Students can use other powers of 10 as the repeating factor record the results in ...

Page 25: ...Name ___________________________ Date ___________________________ Collecting and Organizing Data Program the constant operation feature on your calculator to multiply by 10 Record the results in the table below for each time you press Number of Times ___ Used as a Factor Display 0 starting factor 1 2 3 4 ...

Page 26: ..._____________________________ 2 What does it mean when the right hand display changes For example 1x10 15 __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 3 Try the activity again with another multiple of 10 and compare your...

Page 27: ...hen read the output 1 8 which means subtracting 2 once from 10 gives 8 4 Have students continue this process with various numbers as their first input Discuss their results Pressing and then œ always gets you back to the first input number which means and œ are inverse procedures 5 Challenge students to find more pairs of procedures for and œ that will follow the same pattern and record their inve...

Page 28: ...e in your data Are the procedures inverses of each other How do you know If the output number for is used as the input number for œ and gives an output number equal to the original input number for then the procedures may be inverses of each other as in x 2 and 2 Does the pattern work with special numbers like 1 and 0 With fractions and decimals With positive and negative integers What happens if ...

Page 29: ... can investigate equivalent procedures such as dividing by a number and multiplying by its reciprocal For example if a student is exploring the relationship between x and 2 the tables might look something like this Table for Table for œ Input Procedure Output 1 P2 0 5 5 10 2 P2 1 3 P2 1 5 15 10 1 Input Procedure Output 1 x 2 x 1 3 x 1 5 1 ...

Page 30: ...output numbers in the appropriate table 4 Use the tables below to record and compare your results using and œ Table for Table for œ Input Procedure Output Input Procedure Output Analyzing Data and Drawing Conclusions 5 How do the two procedures compare __________________________________________________________________________ 6 What patterns do you see _____________________________________________...

Page 31: ...n be recorded as 1357 mm or as thousandths of meters 1 357 m Note that the measurement was rounded to 1357 mm because it fell somewhere between of a millimeter less than 1357 mm 1356 5 mm and of a millimeter more than 1357 mm 1357 5 mm 2 Have students then use rounding to record the same measurement to the nearest centimeter 136 cm or 1 36 m 3 Enter the original measurement on the calculator as 1 ...

Page 32: ...umber represents the measurement of a length of board to the nearest meter Ask students What could its measurement be if it had been measured to the nearest decimeter 2 5 m to 3 5 m 8 Round the original number to the nearest tenth 2 5 Ask students Does this lie within the range we identified 9 Repeat for measuring to the nearest centimeter hundredths and millimeter thousandths The range for centim...

Page 33: ...ing Analyzing Data and Drawing Conclusions To guide students in the analysis of their data ask questions such as What range is indicated by every measurement What patterns did you use in identifying the range of possible measurements How would you use these patterns to round 256 0295 to the nearest tenth Continuing the Investigation Have students replace the units of length with units of mass gram...

Page 34: ...t tenth _______________ Is that within the range you identified ______________________ 2 What is the measurement to the nearest tenth of a meter ________ a What could be the range of the measurement if it had been measured to the nearest hundredth of a meter centimeters _______________________________________________________________________ b Set Š to the nearest hundredth What is the measurement ...

Page 35: ...three measurements to the nearest millimeter that would be a 10 m when rounded to the nearest meter ___________________ b 9 0 m when rounded to the nearest tenth of a meter decimeter _______________________________________________________________________ c 9 05 m when rounded to the nearest hundredth of a meter centimeter _______________________________________________________________________ ...

Page 36: ... Ask them to count the jelly beans and observe the techniques they use counting one at a time making groups of 10 etc 3 Tell students you have run out of unit pieces and then ask How many rods groups of 10 would I need to use to make a pile of jelly beans the same size as yours 4 Have students explore the answer to this problem with their units or apply their knowledge of place value Then show the...

Page 37: ...m focus on the patterns ask questions such as How does the number of tens in 1314 compare to the number 1314 How about 567 2457 4089 etc If you cover the digit in the units place you see how many tens are in a number How does the number of hundreds in 1314 compare to the number 1314 How about 567 in 2457 in 4089 etc If you cover the digits to the right of the hundreds place you see how many hundre...

Page 38: ...s plus 14 more pennies or 1 dime and 4 pennies Older students can record the money and enter it into the calculator in decimal form 13 14 Then they can use the calculator to connect dimes to one tenth 0 1 of a dollar 13 14 has 131 dimes or tenths and pennies to one hundredth 0 01 of a dollar 13 14 has 1314 pennies or hundredths For older students connect the place value patterns to conversions bet...

Page 39: ... Record your observations in the table What patterns do you see Number Number of Thousands Number of Hundreds Number of Tens Analyzing Data and Drawing Conclusions Patterns 2 Write 5 numbers that have 15 tens __________________________________________________________________________ 3 Write 5 numbers that have 32 hundreds __________________________________________________________________________ 4...

Page 40: ...cord your observations in the table What patterns do you see Number Number of Tenths Number of Hundredths Number of Thousandths Analyzing Data and Drawing Conclusions Patterns 2 Write 5 numbers that have 15 tenths __________________________________________________________________________ 3 Write 5 numbers that have 32 hundredths _____________________________________________________________________...

Page 41: ...s 10 5 Have students brainstorm situations and related questions that this number sentence could be representing For example I had some money in my pocket and I spent 10 cents of it I only have 5 cents left How much money did I have in my pocket to begin with Have students practice the keystrokes necessary to display this equation and test the value they determine for 5 Over a period of time conti...

Page 42: ...and test what the solutions are Provide ideas for exploration by asking questions such as What actions could be happening in your story to go with addition subtraction multiplication or division How could you use these counters to act out this number sentence What could this number in the number sentence represent in your story What could the question mark in the number sentence represent in your ...

Page 43: ...partner s story Have students sort the number sentences they have made into categories e g those with 0 whole number solutions those with one whole number solution those with two whole number solutions those with infinite whole number solutions Have students try to find an equation or inequality with exactly 0 whole number solutions exactly 1 whole number solution exactly 2 whole number solutions ...

Page 44: ... Teachers 37 What s the Problem Name ___________________________ Date ___________________________ Write a number sentence using an operation and the Write a story that describes a situation and asks a question that can be represented by the number sentence ...

Page 45: ...olling Order of Operations Parentheses 39 Clearing and Correcting 42 Mode Menus 45 Basic Operations 48 Constant Operations 55 Whole Numbers and Decimals 63 Memory 68 Fractions 7 1 Percent 80 Pi 84 Powers and Square Roots 88 Problem Solving Auto Mode 94 Problem Solving Manual Mode 100 Place Value 106 ...

Page 46: ...monstrates the order in which the TI 15 completes calculations When using parentheses if you press before pressing Y Syn Error is displayed Operations inside parentheses are performed first Use X or Y to change the order of operations and therefore change the result Example 1 2 x 3 7 1 2 x 3 9 The first and second lines display entries up to 11 characters plus a decimal point a negative sign and a...

Page 47: ...de for Teachers 40 Equation Operating System EOS Priority Functions 1 first X Y 2 3 4 M 5 V W 6 T U 7 Ÿ 8 last Because operations inside parentheses are performed first you can use X Y to change the order of operations and therefore change the result ...

Page 48: ...AS INSTRUMENTS INCORPORATED TI 15 A Guide for Teachers 41 Order of Operations 1 2 x 3 Add T Press Display Multiply 1 T 2 V 3 1 Û 2 Ý 3 Ú 7 V Parentheses X Y 1 2 x 3 Press Display X 1 T 2 Y V 3 Å 1 Û 2 Æ Ý 3 Ú 9 ...

Page 49: ...entire number 3 clears the last entry all pending operations and any error conditions You can then enter a new number and continue your calculation Notes The examples on the transparency masters assume all default settings Pressing and simultaneously resets the calculator Resetting the calculator Returns settings to their defaults Clears memory and constants Pressing does not affect the mode setti...

Page 50: ...ers 43 Clearing entries 1 Enter 335 10 2 Clear the entry and pending operation 3 Enter 335 N 9 4 Complete the calculation Clear Press Display 335 T 10 3 3 5 Û 1 0 á clear the entry á 335 U 9 3 3 5 Ü 9 3 3 5 Ü 9 Ú 3 2 6 Note clears the screen but not the history ...

Page 51: ...I 15 A Guide for Teachers 44 Correcting entry errors using w 1 Enter 1569 3 2 Change the 9 to an 8 3 Add 3 4 Complete the calculation Backspace w Press Display 1569 T 3 1 5 6 9 Û 3 á w w w 8 1 5 6 8 á T 3 1 5 6 8 Û 3 á 1 5 6 8 Û 3 Ú 1 5 7 1 ...

Page 52: ...ons Setting Options Mode Auto Man Level of difficulty 1 2 3 Operation x P Display option 11 1 3 displays the Fractions menu from which you can select the following options Setting Options Display U n d n d Simplify Man Auto Notes The examples on the transparency masters assume all default settings You must be in Problem Solving to see its menu when you press Otherwise you will see the Calculator M...

Page 53: ...the constant operation 1 5 Clear OP1 When selected clears Op1 OP2 When selected clears Op2 Reset N No does not reset the calculator Y Yes resets the calculator Problem Solving Mode Menu Setting SubMenu Option Example Auto Level of difficulty 1 2 3 Operation x P add subtract multiply divide find the operation Manual Display option for Problem Solving Place Value only 11 Displays the number of ones ...

Page 54: ...Continued 3 Fractions Menu Setting Option Explanation Example Display U n d Displays results as mixed numbers 1 3 4 n d Displays results as improper fractions 7 4 Simplify Man Allows manual simplification 6 8 3 4 Auto Automatically simplifies to most reduced form of fraction 3 4 ...

Page 55: ...tive number Notes The examples on the transparency masters assume all default settings The result of Integer Divide always appears as quotient and remainder __ r __ The maximum number of digits for quotient or remainder r is 5 Quotient remainder and the r character cannot total more than 10 characters If you use the result of integer division in another calculation only the quotient is used The re...

Page 56: ...NSTRUMENTS INCORPORATED TI 15 A Guide for Teachers 49 Basic operations 2 54 N 6 Press Display Add Subtract T U Multiply Divide V W 2 T 54 U 6 2 Û 5 4 Ü 6 Ú 5 0 Equals 3 x 4 P 2 Press Display 3 V 4 W 2 3 Ý 4 P 2 Ú 6 ...

Page 57: ...TED TI 15 A Guide for Teachers 50 Entering negative numbers The temperature in Utah was N3 C at 6 00 a m By 10 00 a m the temperature had risen 12 C What was the temperature at 10 00 a m Negative M Press Display M 3 T 12 Ü 3 Û 1 2 Ú 9 ...

Page 58: ... for Teachers 51 Division with remainders Chris has 27 pieces of gum He wants to share the pieces evenly among himself and 5 friends How many pieces will each person get How many pieces will be left over Integer Divide Press Display 27 6 2 7 Þ 6 Ú 4 3 ...

Page 59: ...0 TEXAS INSTRUMENTS INCORPORATED TI 15 A Guide for Teachers 52 Division with decimal result Set the division display option to decimal and divide 27 by 6 Press Display Divide W Ù Ä ê á 27 W 6 2 7 Þ 6 Ú 4Ù5 ...

Page 60: ...RATED TI 15 A Guide for Teachers 53 Division with fractional result Set the division display option to fraction and divide 27 by 6 Press Display Divide W Ù Ä êêêê n d P á 27 W 6 n d P 5 1 0 n d P 5 1 1 0 2 4 êê 4 êêê 2 7 Þ 6 Ú 4 êêê ...

Page 61: ...RATED TI 15 A Guide for Teachers 54 Calculating equivalent units of time Sara ran 2 kilometers in 450 seconds Convert her time to minutes and seconds 450 seconds minutes seconds Integer Divide Press Display 450 60 4 5 0 Þ 6 0 Ú 7 3 0 ...

Page 62: ...a counter appears at the left and the total appears on the second line at the right of the display The counter shows how many times the constant has been repeated If the number at the right exceeds 6 digits the counter will not be shown The counter returns to 0 after it reaches 99 When you use with the constant function subsequent calculations are performed with the quotient portion of the result ...

Page 63: ... counting on There are 4 frogs in a pond If 3 more frogs jump into the pond 1 at a time how many frogs will be in the pond Constant Operations Add T Press Display T 1 stores operation Op1 Û 1 4 initialize using 4 Op1 4 add 1 one at a time Op1 4 Û 1 1 5 Op1 5 Û 1 2 6 Op1 6 Û 1 3 7 ...

Page 64: ...ile in her kitchen She made 4 rows with 5 tiles in each row Use repeated addition to find how many tiles she used Before you begin set the calculator to hide the constant operation Constant Operations Press Display hide constant operation 1 Ã Á êê á T 5 store the operation Op1 Û 5 0 initialize using 0 Continued Op1 0 á ...

Page 65: ... 2000 TEXAS INSTRUMENTS INCORPORATED TI 15 A Guide for Teachers 58 Multiplication as repeated addition Continued Press Display Op1 1 5 Op1 2 1 0 Op1 3 1 5 Op1 4 2 0 ...

Page 66: ...tiplication Use this formula and repeated multiplication to find the volume of a cube with a base of 5 meters V l x w x h 5 x 5 x 5 53 Constant Operations Multiply V Press Display V 5 store the operation Op1 Ý 5 1 initialize using 1 Op1 1 á Op1 1 Ý 5 1 5 Op1 5 Ý 5 2 2 5 Op1 2 5 Ý 5 3 1 2 5 ...

Page 67: ...S INCORPORATED TI 15 A Guide for Teachers 60 Using as a constant Use this formula to find the volume of each cube V base3 Constant Operations Powers Press Display 3 Op1 É 3 2 Op1 2 É 3 1 8 3 Op1 3 É 3 1 2 7 4 Op1 4 É 3 1 6 4 ...

Page 68: ...ived5stickersforeach householdjobshecompleted Shegave herbrother2stickersforhelpingwith eachjob Iftheycompleted3jobs how manystickersdoesshehave Constant Operations œ Press Display T 5 Op1 Û 5 œ U 2 œ Op1 Op2 Ü 2 0 Op1 Op2 0 á Op1 Op2 0 Û 5 1 5 œ Op1 Op2 5 Ü 2 1 3 œ Op1 Op2 8 Ü 2 1 6 œ Op1 Op2 1 1 Ü 2 1 9 ...

Page 69: ...ring constant operations Before entering a new operation in OP1 or OP2 you must clear the current values Mode Menu Press Display Ù ß Ä ê Þ Á Ï Á 2 êêêê ç clears OP1 Á Ï Á 2 êêêê ç clears OP2 Á Ï Á 2 ç êêêê exits Mode menu á Note Pressing does not clear constant operations ...

Page 70: ... results to the nearest hundred 5 Š rounds results to the nearest ten 6 Š rounds results to the nearest one 7 Š rounds results to the nearest tenth 8 Š rounds results to the nearest hundredth 9 Š š rounds results to the nearest thousandth Š r removes the fixed decimal setting You must press Š before a Place Value key each time you want to change the number of places for rounding Notes The examples...

Page 71: ...et the calculator You can set 0 through 3 decimal places If students are puzzled when they round 555 to the nearest whole number for example and the result is 1 you may need to remind them of the rules of rounding You can use r to enter decimal numbers regardless of the fixed decimal setting You must press before FIX takes effect You can apply the FIX setting to an individual value or to the resul...

Page 72: ...und 12 345 to the hundredth s place the tenth s place the thousandth s place and then cancel the Fix setting Fix decimal Š Press Display 12 r 345 1 2 Ù 3 4 5 Ú 1 2 Ù 3 4 5 Š Fix 1 2 Ù 3 4 5 Ú 1 2 Ù 3 5 Š Fix 1 2 Ù 3 4 5 Ú 1 2 Ù 3 Š š Fix 1 2 Ù 3 4 5 Ú 1 2 Ù 3 4 5 To cancel Fix Š r 1 2 Ù 3 4 5 Ú 1 2 Ù 3 4 5 ...

Page 73: ...I 15 A Guide for Teachers 66 Addition with money José bought ice cream for 3 50 cookies for 2 75 and a large soda for 99 How much did he spend Fix decimal Š Press Display Š Fix 3 r 50 T 2 r 75 T r 99 Fix 3 Ù 5 0 Û 2 Ù 7 5 Û Ù 9 9 Ú 7 Ù 2 4 ...

Page 74: ...5 A Guide for Teachers 67 Converting decimals to fractions Convert the decimal 5 to a fraction and then view the decimal again after the conversion Fix decimal Š Press Display r 5 Ù Ó Ú Ø Ù Ó Ÿ N D n d Ù Ó Ú Ó Ï Ø Ÿ Return to decimal Ø Ù Ó ííí ...

Page 75: ... the displayed value z Performs integer division on value in memory using the displayed value Only the quotient is stored and displayed 2 recalls the contents of memory to the display When pressed twice it clears the memory Notes The examples on the transparency masters assume all default settings Results are stored to memory and not displayed The display remains the same You can store integers fr...

Page 76: ... for each milk shake 3 20 Total cost Store to Memory z Memory Recall Press Display 2 V 1 r 19 2 Ý 1 Ù 1 9 Ú 2 Ù 3 8 z M 2 Ý 1 Ù 1 9 Ú 2 Ù 3 8 3 V 1 r 25 M 3 Ý 1 Ù 2 5 Ú 3 Ù 7 5 z T Add milk shakes to memory M 3 Ý 1 Ù 2 5 Ú 3 Ù 7 5 3 V r 20 M 3 Ý Ù 2 0 Ú 0 Ù 6 z U Deduct coupon from memory M 3 Ý Ù 2 0 Ú 0 Ù 6 Recall the total cost M 5 Ù 5 3 ...

Page 77: ...kly scores of 87 and 98 Find the average for each group of scores and the average of his averages together Store to Memory z Add T Press Display Memory Recall 96 T 85 9 6 Û 8 5 Ú 1 8 1 W 2 1 8 1 Þ 2 Ú 9 0 Ù 5 z M 1 8 1 Þ 2 Ú 9 0 Ù 5 87 T 98 M 8 7 Û 9 8 Ú 1 8 5 W 2 M 1 8 5 Þ 2 Ú 9 2 Ù 5 T M 9 2 Ù 5 Û 9 0 Ù 5 Ú 1 8 3 W 2 M 1 8 3 Þ 2 Ú 9 1 Ù 5 ...

Page 78: ...t of a mixed number 3 lets you enter the numerator of a fraction 4 lets you enter the denominator of a fraction 5 changes a mixed number to a fraction and vice versa 6 simplifies a fraction using the lowest common prime factor If you want to choose the factor instead of letting the calculator choose it press enter the factor an integer and then press You must be in Manual mode to use this function...

Page 79: ...e denominator or numerator first For operations you can enter 1 to 1000 for the denominator For conversions to decimal you can enter 1 to 100 000 000 for the denominator When you multiply or divide fractions and decimals the result is displayed as a decimal A decimal cannot be converted to a fraction if the result would overflow the display Clearing with w in fractions occurs from right bottom to ...

Page 80: ... mixed numbers A baby girl weighed 4 3 8 pounds at birth In the next 6 months she gains 2 3 4 pounds How much does she weigh Numerator Key Denominator Key Unit Key Press Display 4 8 3 T 3 8 2 3 4 3 3 1 8 4 8 5 7 8 ííí ííí ííí ííí ííííí 4 7 4 2 Û Mixed to Improper Conversion ...

Page 81: ...ator Key Denominator Key Press Display 18 24 Enter the fraction 1 8 2 4 Simplify Prepare to simplify 1 8 S 2 4 Factorial Simplify the fraction N D n d 1 8 9 2 4 1 2 O p t i o n a l C h e c k f a c t o r Y o u m u s t b e i n M a n u a l m o d e 2 Return to the fraction N D n d 9 1 2 Continue simplifying 9 3 1 2 4 ííííí ííííí íííí ííííí íííí ííí íííí à á à à ...

Page 82: ...g fractions Method 2 You choose a common factor Simplify 18 24 Numerator Key Denominator Key Press Display 18 24 Enter the fraction 1 8 2 4 Simplify Prepare to simply 1 8 2 4 6 Enter a common factor 1 8 2 4 Simplify the fraction 1 8 3 2 4 4 íííí á íííí íííí ííí íííí à à Ô á à Ô ...

Page 83: ...ns to decimals Convert the fraction 5 10 to a decimal and then view the original fraction after the conversion Numerator Key Denominator Key Press Display 5 10 N D n d 5 5 1 0 1 0 Fraction to Decimal Ÿ 0 Ù 5 Ÿ Ÿ Return to fraction N D n d 5 1 0 Ÿ Return to decimal 0 Ù 5 íííí íííí íííí Ú ...

Page 84: ...rs 77 Converting decimals to fractions Convert the decimal 5 to a fraction and then view the decimal again after the conversion Numerator Key Denominator Key Press Display r 5 Ù 5 Ú 0 Ù 5 Fraction to Decimal Ÿ N D n d Ù 5 Ú 5 1 0 Ÿ Ÿ Return to decimal 0 Ù 5 íííí ...

Page 85: ...de for Teachers 78 Converting betweenfractionsandmixednumbers Convert the improper fraction 6 4 to a mixed number Numerator Key Denominator Key Press Display Ä Ä êêêêêê Fraction Modes è æ êêêê 6 4 6 2 4 4 2 1 4 2 3 2 íííí ííí íííí íííí 1 1 1 Ú à ííí ...

Page 86: ... minutes Juan swims 20 laps in 5 minutes Who swims faster Compare the time as decimals and fractions To compare the times as decimals Numerator Key Denominator Key Press Display 5 3 4 3 3 4 4 Ÿ 5 Ù 7 5 Ÿ N D n d 7 5 1 0 0 Continue to compare as fractions 5 r 72 5 Ù 7 2 Ú 5 Ù 7 2 Ÿ N D n d 7 2 1 0 0 ííí íííííí ííííí 5 5 5 5 ííí ...

Page 87: ...00 TEXAS INSTRUMENTS INCORPORATED TI 15 A Guide for Teachers 80 Percent 9 Keys 1 y converts to a percent 2 ª enters a percent Notes The examples on the transparency masters assume all default settings 2 1 ...

Page 88: ... Teachers 81 Converting with percent Convert 25 to a decimal Percent Press Display ª 25 ª 2 5 ã Ú 0 Ù 2 5 Convert to Percent y Convert 25 100 to a percent Press Display 25 100 y 2 5 1 0 0 Convert 3 to a percent Press Display 3 y 3 à ã 3 0 0 ã íííí àã 2 5 ã ...

Page 89: ...mals and percent Convert 25 to a fraction simplify to lowest terms and then convert the fraction to a decimal Percent ª Press Display Fraction to Decimal 25 ª 2 5 ã Ú 0 Ù 2 5 Ÿ Ÿ N D n d 2 5 1 0 0 N D n d 2 5 5 1 0 0 2 0 N D n d 5 1 2 0 4 Ÿ 0 Ù 2 5 y 0 Ù 2 5 à ã 2 5 ã íííííí íííííí à íííí ííí à ííí ...

Page 90: ...aurant for dinner Their bill was 31 67 How much was the tip if they left 15 of their bill How much was the total including the tip Percent ª Convert to Percent Press Display y 31 67 3 1 Ù 6 7 Ú 3 1 Ù 6 7 Š Fix 3 1 Ù 6 7 Ú 3 1 Ù 6 7 V 15 ª Fix 3 1 Ù 6 7 Ý 1 5 ã Ú 4 Ù 7 5 31 67 T 4 75 3 1 Ù 6 7 Û 4 Ù 7 5 Ú 3 6 Ù 4 2 ...

Page 91: ...4 Pi 10 Keys 1 enters p Notes The examples on the transparency masters assume all default settings Internally pi is stored to 13 digits 3 141592653590 Only 9 decimal places are displayed To convert from p to a decimal value press Ÿ Nine decimal places are displayed 1 ...

Page 92: ...sing pi to find circumference Use this formula to find the amount of border you need to buy if you want to put a circular border around a tree at a distance of 3 meters from the tree C 2pr 2 x p x 3 Pi Press Display 2 V 2 Ý ß V 3 2 Ý ß Ý 3 Ú Ô ß Ÿ 1 8 Ù 8 4 9 5 5 5 9 2 ...

Page 93: ...e for Teachers 86 Using pi to find area Use this formula to find how much of the lawn would be covered by a sprinkler with a radius of 12 meters A pr2 p x 122 Pi Press Display V ß Ý 12 2 ß Ý Ï Ð É Ð ß Ý Ï Ð É Ð Ú S 1 4 4 ß Ÿ 4 5 2 Ù 3 8 9 3 4 2 1 12 m ...

Page 94: ... TI 15 A Guide for Teachers 87 Using pi to find volume Use this formula to find how much space a ball occupies V 4pr3 3 Pi Press Display 4 V V Ò Ý ß Ý 5 3 Ò Ý ß Ý Ó É Ñ W 3 Ò Ý ß Ý Ó É Ñ Þ Ñ Ò Ý ß Ý Ó É Ñ Þ Ñ Ú 5 2 3 Ù 5 9 8 7 7 5 6 5 cm ...

Page 95: ...ots 11 Keys 1 lets you specify a power for the value entered When you press the value is displayed if it is within the range of the calculator 2 calculates the square root of positive values including fractions Notes The examples on the transparency masters assume all default settings 1 2 ...

Page 96: ...NTS INCORPORATED TI 15 A Guide for Teachers 89 Finding the area of a square Use this formula to find the size of the tarpaulin needed to cover the entire baseball infield A x2 902 Powers Press Display 90 2 Ø É Ð Ú 8 1 0 0 ...

Page 97: ... 15 A Guide for Teachers 90 Finding the square root Use this formula to find the length of the side of a square clubhouse if 36 square meters of carpet would cover the floor L x 36 Square Root Press Display 36 Y â Å 3 6 Æ Ú 6 36 m2 of carpet ...

Page 98: ...A Guide for Teachers 91 Calculating powers Fold a piece of paper in half in half again and so on until it is not possible to physically fold it in half again How many sections are there after ten folds Powers Press Display 2 10 2 É Ï Ø Ú 1 0 2 4 ...

Page 99: ...for Teachers 92 Calculating negative powers Find the standard numerals for the following powers 2 3 2 3 2 3 1 2 3 Powers Negative M Press Display 2 M 3 2 É Ü Ñ Ú Ø Ù Ï Ð Ó M 2 M 3 Ü 2 É Ü Ñ Ú Ü Ø Ù Ï Ð Ó r 2 M 3 Ù 2 É Ü Ñ Ú Ï Ð Ó 1 2 M 3 1 2 êÉ Ü Ñ Ú Ö ...

Page 100: ...TEXAS INSTRUMENTS INCORPORATED TI 15 A Guide for Teachers 93 Using powers of 10 1 3 x 103 Powers Press Display 1 r 3 V 10 3 1 Ù 3 Ý Ï Ø É Ñ Ú 1 3 0 0 1 3 x 10L3 1 r 3 V 10 M 3 1 Ù 3 Ý Ï Ø É Ü Ñ Ú 0 Ù 0 0 1 3 ...

Page 101: ...me all default settings In Auto mode default the TI 15 presents problems with one element missing for example 5 2 or 5 7 or 5 2 7 If the answer is not correct the TI 15 displays no and gives a hint in the form of or After you enter three incorrect answers the TI 15 provides the correct answer After every fifth problem the TI 15 displays a Scoreboard that tallies the student s correct and incorrect...

Page 102: ...ENTS INCORPORATED TI 15 A Guide for Teachers 95 Select level of difficulty Choose the level of difficulty Problem Solving Mode Press Display Auto æ è êêêêê Auto 1 2 3 ê ê ë ì Auto 1 2 3 ê to exit Auto 8 Û Ã Ú 8 0 8 ê ë ì ...

Page 103: ... Teachers 96 Select type of operation Choose the type of operation addition subtraction multiplication division find the operator Problem Solving Mode Press Display Auto æ è êêêêê Auto 1 2 3 ê ê ë ì Auto Û Ü Ý Þ Ã ê Auto Û Ü Ý Þ Ã ê to exit Auto 4 Ý 1 Ú Ã ...

Page 104: ...ers 97 Test your skills Enter solutions to the problems that the calculator presents Problems are random Press Display Problem Solving Mode Auto æ è êêêêê Auto 8 Û 3 Ú Ã 11 Auto 8 Û 3 Ú 1 1 À s Auto 2 Û Ã Ú 7 4 Auto 2 Û 4 Ú 7 N Auto 2 Û 4 Ç 7 5 Auto 2 Û 5 Ú 7 À ...

Page 105: ... for Teachers 98 View the Scoreboard After every fifth problem the calculator displays a score board that tallies your right and wrong solutions You can also display the scoreboard at any time by pressing Problem Solving Mode Press Display Auto À s 5 0 ...

Page 106: ...or Teachers 99 Find the operator Change the type of operation to find the operator and solve the problems the calculator presents Problem Solving Mode Press Display Auto æ è êêêêê Auto Û Ü Ý Þ Ã ê Auto Û Ü Ý Þ Ã ê Auto 8 Ã 6 Ú 4 8 V Auto 8 Ý 6 Ú 4 8 À s ...

Page 107: ...iew previous problems When you first press the display shows the Scoreboard for a moment before showing the menu In Manual mode for all operations except inequalities the calculator accepts only integers You can enter no more than 11 characters on the display You can enter a problem that has one solution multiple solutions or no solution For example 1 solution 2 5 2 7 2 5 7 Multiple solutions 1 6 ...

Page 108: ...tion Problems with one solution are equations with one missing element for example 7 2 or 7 9 Enter a problem and find a solution Problem Solving Mode Press Display Auto æ è êêêêê Missing element Auto æ è êêêê á 5 U 3 5 Ü 3 Ú Ã 1 º 2 5 Ü 3 Ú 2 À 5 T 9 5 Û Ã Ú 9 1 º 3 5 Û 3 Ç 9 4 5 Û 4 Ú 9 À ...

Page 109: ... with more than one solution Problems with two missing elements may have more than one solution Enter a problem find the number of solutions and then find a solution Press Display Problem Solving Mode Missing element Auto æ è êêêê á T 3 Ã Û Ã Ú 3 4 º 2 2 Û Ã Ú 3 1 2 Û Ï Ú 3 À S ...

Page 110: ...s 103 Problems with no solution The TI 15 calculator is not designed to handle certain types of problems These will result in a 0 SOL no solution response from the calculator Problem Solving Mode Missing element Press Display Auto æ è êêêê á 1 U 2 1 Ü 2 Ú Ø 0 º á ...

Page 111: ...04 Less than greater than equals You can test inequalities and equalities using Problem Solving Press Display Problem Solving Mode Auto æ è êêêê á 2 T 1 1 T 2 5 T 4 10 2 Û 1 Ú 1 Û 2 À 5 Û 4 Ç 1 0 À S r 5 r 50 Ù 5 È Ù 5 0 Ù 5 Ú Ù 5 0 À S Equals Greater Than Less Than ...

Page 112: ...Guide for Teachers 105 View Scoreboard After every fifth problem the calculator displays a scoreboard that tallies your right and wrong solutions You can also display the scoreboard at any time by pressing Press Display Problem Solving Mode À 5 0 ...

Page 113: ...tivates the place value function in Manual mode It also works in conjunction with these keys Key Displays Number of thousands Number of hundreds Number of tens Number of ones Number of tenths Number of hundredths š Number of thousandths Example Enter 1 23 45 6 Press Œ 4 _ _ _ 4_ _ 4 01 Notes The examples on the transparency masters assume all default settings The Place Value features work only if ...

Page 114: ...represents 123 456 hundredths in the number 1234 567 When a number includes a repeated digit the calculator first analyzes its occurrence in the right most position To find the place value of other instances press the digit again See page 109 for an example Once Πis active it is not necessary to press this key before each digit To enter a new number however you must press enter the number and the...

Page 115: ...mine place value Enter 1234 567 Determine the place value of 7 and 4 Problem Solving Place Value Œ Press Display æ è êêêê á 1234r567 Œ ƒ 1 2 3 4 Ù 5 6 7 7 ƒ 1 2 3 4 Ù 5 6 7 ííííÙ í í 7 ƒ 1 2 3 4 Ù 5 6 7 7 Ü È 0 Ù 0 0 1 4 ƒ 1 2 3 4 Ù 5 6 7 ííí4 Ù ííí ƒ 1 2 3 4 Ù 5 6 7 4 Ü È 1 ...

Page 116: ...chers 109 Repeated digits Enter 123 43 Determine the place value of each 3 Problem Solving Place Value Œ Press Display æ è êêêê á 123 r43 Œ ƒ 1 2 3 Ù 4 3 3 ƒ 1 2 3 Ù 4 3 í í í Ù í 3 ƒ 1 2 3 Ù 4 3 3 Ü È 0 Ù 0 1 33 ƒ 1 2 3 Ù 4 3 í í 3 Ù í í ƒ 1 2 3 Ù 4 3 3 Ü È 1 ...

Page 117: ... for Teachers 110 How many How many hundreds are in 1234 567 How many hundredths Problem Solving Place Value Œ Press Display Hundreds æ è êêêê á Hundredths 1234r567 Œ ƒ 1 2 3 4 Ù 5 6 7 ƒ 1 2 3 4 Ù 5 6 7 1 2 í í Ù í í í ƒ 1 2 3 4 Ù 5 6 7 1 2 3 4 5 6 Ù í ...

Page 118: ...D TI 15 A Guide for Teachers 111 What s the digit What digit is in the hundreds place in 1234 567 Problem Solving Place Value Press Display Œ æ è êêêê 1 1 Ü Ù Ü Ï Ü Ù êêêêê á 1234r567 Œ ƒ 1 2 3 4 Ù 5 6 7 ƒ 1 2 3 4 Ù 5 6 7 í 2 í í Ù í í í ...

Page 119: ...ly so you can scroll the entry line or select a menu item Moves the cursor up and down respectively so you can see previous entries or access menu lists w Deletes the character to the left of the cursor before is pressed Displays menu to select format of results of division n d Displays menu to show or hide in Op1 or Op 2 1 Op Displays menu to clear Op1 or Op2 Op1 Clear Op2 Displays menu to reject...

Page 120: ...00 or if the results of a calculation yield a denominator greater than 1000 the TI 15 will convert and display the results in decimal format Separates a whole number from the fraction in a mixed number Displays a menu of settings that determine how fraction results are displayed U n d default displays mixed number results n d displays results as a simple improper fraction If N d n d is displayed a...

Page 121: ...se in a calculation when pressed once When pressed twice clears memory œ Each can store one or more operations with constant value s which can be repeated by pressing only one key as many times as desired To store an operation to Op1 or Op2 and recall it Press or œ enter the operator and the value and press or œ to save the operation Press or œ to recall the stored operation To clear the contents ...

Page 122: ...wice to enter Œ While in function you can determine the place value of a particular digit of given number or in conjunction with place value keys can determine how many thousands hundreds etc a number contains or what digit is in a given place Œd Determines the place value of digit d of given number Œ Tells how many thousands a given number contains or what digit is in the thousands place Œ Tells ...

Page 123: ... operator and operand is stored Auto In calculator mode Auto simplification of fractions to lowest terms is selected In Problem Solving function is in Auto mode I Integer division function has been selected appears only when cursor is over division sign n d P Division results will be displayed as fractions N d n d The fraction result can be further simplified Previous entries are stored in history...

Page 124: ...arameter for example L5 Syn Error Syntax error You entered an invalid or incorrect equation for example 5 2 or missing parenthesis P 0 Error Divide by 0 error You attempted to divide by 0 Op Error Error following steps for using Op1 or Op2 Overflow Error Overflow The result is too large to fit within the boundaries of the display Underflow Error Underflow Result is too small ...

Page 125: ...17 8324 Customers outside the U S Canada Puerto Rico and the Virgin Islands Contact TI by e mail or visit the TI Calculator home page on the World Wide Web e mail ti cares ti com Internet www ti com calc Product Service Customers in the U S and Canada Only Always contact Texas Instruments Customer Support before returning a product for service All Customers outside the U S and Canada Refer to the ...

Page 126: ...s provinces do not allow the exclusion or limitation of implied warranties or consequential damages so the above limitations or exclusions may not apply to you Legal Remedies This warranty gives you specific legal rights and you may also have other rights that vary from state to state or province to province Warranty Performance During the above one 1 year warranty period your defective product wi...

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