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Texas Instruments TI-73 Teachers Manual

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Using the TI-73:
A Guide for Teachers
Table of Contents
Developed by
Cathy Cromar, Stephen Davies, Pamela Patton Giles,
Gary Hanson, Pamela Weber Harris, Rita Janes,
Ellen Johnston, Jane Martain, Linda K. McNay, Melissa Nast,
Louise Nutzman, Aletha Paskett, Claudia Schmitt, and Karen Wilcox
Edited by
Brenda Curry
Design by
Susan Gullord
With contributions by
Eddy Frey, Doug Harnish, Guy Harris,
Gay Riley-Pfund, and Dianna Tidwell

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   Summary of Contents for Texas Instruments TI-73

  • Page 1

    Using the TI-73: A Guide for Teachers Table of Contents Developed by Cathy Cromar, Stephen Davies, Pamela Patton Giles, Gary Hanson, Pamela Weber Harris, Rita Janes, Ellen Johnston, Jane Martain, Linda K. McNay, Melissa Nast, Louise Nutzman, Aletha Paskett, Claudia Schmitt, and Karen Wilcox...

  • Page 2: Using The Ti

    Using the TI-73: A Guide for Teachers © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 3: About The Development Team

    Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this book. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

  • Page 4: About The Activities

    Using the TI-73: A Guide for Teachers About the Activities This guide consists of 12 activities designed to be teacher-directed. They are intended to help develop mathematical concepts while incorporating the TI-73 as a teaching tool. Organization Each activity is self-contained and includes: The mathematical strands with which the activity is most closely associated: Number Sense;...

  • Page 5: Table Of Contents

    Drip, Drip, Drip Only the Height Has Been Changed Probability and Statistics Give Me 5! A Foot is a Foot – Or is It? Which Brand is Best? TI-73 Index TI-73 Activity Content Index Activity Content Index Index © 1998 T...

  • Page 6: Number Sense

    7cm (2¾ in.) poster board circles for cookies copies of fractional circles (provided) shapes of colored paper to represent chocolate chips, nuts, raisins etc. (optional) glue or glue sticks scissors markers or crayons TI-73  © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 7

    What kinds of trades could they have made to end up with a whole cookie? 5. Use the TI-73 to verify equivalent fraction trades and to count or add up fractions to see if they equal a whole cookie.

  • Page 8

    Have students make a list of the fractions they think are equivalent to each other. Have students enter their equivalent fractions into the TI-73 and change each to a decimal using > function). Discuss why these fraction-to-decimal equivalent fractions also have the same decimal value.

  • Page 9

    Using the TI-73: A Guide for Teachers Number Sense © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 10: Dice Digits

    “seed value” to With each rand execution, the TI-73 generates the same random-number sequence for a given seed value. The TI-73 factory-set seed value for different random-number sequence, store any non-zero...

  • Page 11

    4. Repeat this procedure to write an expression equal to 5. Continue the demonstration until students understand what to do. Students may use the TI-73 to find the expression or to check the value of the expression. Example If the 4 numbers are...

  • Page 12

    2. Instruct students to use all 4 numbers, any operations, and grouping symbols to write an expression for each of the numbers 1 through 9. 3. Have students check their work on the TI-73 and record each expression on the student activity sheet provided.

  • Page 13

    Using the TI-73: A Guide for Teachers Activity 2 Dice Digits Roll dice to get 4 numbers. Record numbers below. ________ ________ ________ ________ Expression Can you find more than one expression for each number? © 1998 T EXAS NSTRUMENTS...

  • Page 14: How Do You Measure Up

    TI-73  You may want to do this part of the setup in the hall or some place with a large area of floor space.

  • Page 15

    Using the TI-73: A Guide for Teachers 1. Measure the strings. 2. Enter the data in on the TI-73. a. Display the List editor. b. If necessary, clear $ to highlight c. Starting at the first line in lengths. (You’ll get an error if Press b after each list item.

  • Page 16

    Number Sense Activity — Part B In this part, students discover the ratio of the average height of a student to the average length of an intestine. Have students perform the steps unless otherwise indicated. 1. Measure height in centimeters or inches. 2.

  • Page 17

    Using the TI-73: A Guide for Teachers Assessment Suggestions The average length of the small intestine of an ostrich is 1372cm (45 ft.). Three ostriches have heights of 314cm (10 ft. 3 in.), 308cm (10 ft. 1 in.), and 299cm (9 ft. 8 in). Have students find the ratio of the ostriches’...

  • Page 18: Stadium Walls

    The length of each wall is measured by the number of beams along the bottom of the wall. length 1 length 2 length 3 Patterns and Relations patterning graphing evaluating expressions equivalent math expressions Materials graph paper toothpicks TI-73  © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 19

    Using the TI-73: A Guide for Teachers Activity Have students perform the steps unless otherwise indicated. 1. Model the wall using toothpicks to represent the beams to a length of 6. 2. As each length of the wall is modeled, record the total number of beams in a T-chart.

  • Page 20

    3 to the previous term, starting with 4.) 7. Show students how the TI-73 may be used to find the solution in the same manner. You can do this in one of two ways, with the @ key or with the b key.

  • Page 21

    Using the TI-73: A Guide for Teachers 8. Using the TI-73, lead students to alternative methods by reading the T-chart as a relationship between X and a. Tell students to look at the numbers in their T-chart and describe the rule that relates the number of lengths to the total number of beams.

  • Page 22

    What will the graph of the line represented by these equations look like? 11. The TI-73 uses X and Y when graphing, so change the equation B = 3L + 1 to Y = 3X + 1 using the Y= editor.

  • Page 23

    ( TblStart=0, @Tbl=1, Indpnt: Auto, Depend: Auto 17. Use the TI-73 to show a table of values for the equation. - i (above the * key) 18. Compare the table on the TI-73 with the T-chart in the first part of the activity.

  • Page 24

    Patterns and Relations 20. Change the graph style of & # to ! so the cursor is blinking on top of the little diagonal line on the far left Notice that the diagonal line has changed to a darker line. 21.

  • Page 25

    Using the TI-73: A Guide for Teachers Wrap-up Ask: Based on your observation of the graphs of the equations, what conclusions would you draw about the equations you graphed? Have students report findings. This could lead to a discussion of equivalent expressions and simplifying expressions.

  • Page 26

    Patterns and Relations Activity 4: Stadium Walls Extensions Assign the following problem and have students answer the questions. A group of students from a jazz choir want to attend an international competition. They need to raise money to help pay for the expenses. Each student decided to investigate a scheme and present their findings at the next meeting of the group.

  • Page 27

    Using the TI-73: A Guide for Teachers Patterns and Relations © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 28: The Twin's Towers

    7 ..29 © 1998 T problem solving percents adding fractions blocks or cutouts student activity sheet (provided) TI-73 ³ Build the towers with blocks as you discuss this activity or have the students build them with you. EXAS...

  • Page 29

    2-level tower.) c. Press \ Y. Ask the class to tell you what (Explain that just pressing \ indicates to the TI-73 that it needs two things to add, so it grabs the answer (in this case, above and calls it d.

  • Page 30

    1-story tower 2-story tower 2-story tower 2. Ask students how they would enter this scenario into the TI-73. Z b \ Z b 3. Have students answer the following questions. How many blocks do you need for an 8-story tower? A ____-story tower has 28 blocks.

  • Page 31

    Using the TI-73: A Guide for Teachers 4. Have students set up the counter for the second scenario. - t # #, and then " until Y ¡ Z " to # # to Done - t # #, and then " until...

  • Page 32

    Patterns and Functions 3. Explain to students that the process they have been using to find successive terms in a sequence of numbers is called recursion. Recursion means that each term is built from the term before it. This recursive process allows students to solve more complicated, real-life problems.

  • Page 33

    Using the TI-73: A Guide for Teachers Give students a situation like in the last question. Then give them the screen shot shown at the right. Ask students to discuss what the screen means. In groups, have students come up with their own situations that can be solved recursively.

  • Page 34

    TI-73 and pressing b 5 times. Did you get the right number of blocks? 3. Using your TI-73 pattern, how many blocks will you need to build a 13-story building? 4. How many stories will you have if you use 53 blocks? 5.

  • Page 35

    TI-73 and pressing b 4 times. Did you get the right number of blocks? 3. Using your TI-73 pattern, how many blocks will you need to build a boat with 17 puffs of smoke? 4. How many puffs of smoke will you have if you use 37 blocks? ©...

  • Page 36: Major Martian Headache

    Ask students: If each Martian has two antennas, how many antenna muffs will be needed for the entire community of Martians? Patterns patterning writing simple rules Materials large marshmallows (heads) small marshmallows (antenna ends) toothpicks (antennas) paper and pencil ³ TI-73 © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 37

    Using the TI-73: A Guide for Teachers Activity Have students perform the steps unless otherwise indicated. 1. Make each large marshmallow into a Martian head by poking 2 toothpicks on it and adding 2 small marshmallows to the tops of the toothpicks for antennas.

  • Page 38

    5. Ask students: If there are 67 Martians in a community, how many antenna muffs would be needed? 6. On the TI-73, enter X ¦ 2 =Y into the Y= editor. & I M Z 7. Explore for any given Martian community size by first setting up a table of values.

  • Page 39

    Using the TI-73: A Guide for Teachers 12. Tell students: Digging deeper, the Rover found evidence of other communities that had different numbers of antennas. 13. Have your students repeat the above activity using other numbers of antennas per Martian. See if they can write a rule for each.

  • Page 40: The Dolphin

    Activity 7 The Dolphin Students use ordered pairs to reproduce a picture of a dolphin on the TI-73 screen, and then set up an appropriate viewing window. Setup On the grid paper, demonstrate how to draw the x- and y-axes.

  • Page 41

    Have students label their copies. 5. Record the coordinates of each of those points on a sheet of paper. 6. Using the TI-73, enter the x-coordinates of the dolphin outline into and the y-coordinates of the dolphin outline into a.

  • Page 42

    (( more information, see “Setting the Window Format” and “Defining Window Values” in the Function Graphing chapter of the TI-73 Guidebook . i. Turn on the grid. - g # " b j. Make sure the axes are turned on.

  • Page 43

    Using the TI-73: A Guide for Teachers Wrap-up Have students compare their team’s picture graph with another team’s picture. Have them discuss with their partner and the other team whether or not the graphs are exactly alike and why or why not.

  • Page 44

    Geometry 3. Access the VARS menu and select 4. At , select where you want to store your PICTURE picture. b to select Pic1 to select Pic2 to select Pic3 To recall the picture, 1. Turn off the axes. - g # # " b 2.

  • Page 45

    Using the TI-73: A Guide for Teachers Geometry © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 46: Drip, Drip, Drip

    Drip, Drip, Drip S tudents collect data from a dripping faucet . Then, using the TI-73, they produce data on the H ome screen . Afterwards, they view the same data using a table , a graph , and the Trace feature.

  • Page 47

    Enter the numbers as shown in the screen at the right. Use # to move down the fields. (For more information about the viewing window, see “Setting the Window Format” and “Defining Window Values” in the Function Graphing chapter of the TI-73 Guidebook .) © 1998 T EXAS...

  • Page 48

    Measurement and Geometry 11. View and trace the graph. ! or " to trace until Ask: What is the value of Y? What does this point represent? (When time = 0, there is no water.) 12. Now look at this same information in a table. - f (above the ' key) The screen should look like the one at the right.

  • Page 49

    Using the TI-73: A Guide for Teachers Activity — Part B Have students perform the steps unless otherwise indicated. 1. Ask students: If the faucet were dripping twice as fast, what would be the volume after 1 hour? After 2 hours? 2.

  • Page 50

    Measurement and Geometry f. Now select the first point on the line. " until $ until b to select the first point on the line g. Select the second point on the line. " until $ until b to select the second point The screen shows the expression for the line.

  • Page 51

    Using the TI-73: A Guide for Teachers Activity 8 Drip, Drip, Drip Activity — Part A 1. Record start time. 2. How many drips did you count in 2 minutes? 3. How much water did you collect in 10 minutes? 4.

  • Page 52

    Measurement and Geometry Activity — Part B 1. If the faucet were dripping twice as fast, what would be the volume after 1 hour? After 2 hours? Write these as data points. 2. Predict what the graph of this equation would look like compared to our graph.

  • Page 53

    Using the TI-73: A Guide for Teachers Measurement and Geometry © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 54: Only The Height Has Been Changed

    Measurement length mean collecting data graphing Materials ruler yardstick, meterstick, or measuring tape ramp (cardboard or wood) - length should be divisible by 6 toy car student activity sheet (provided) TI-73 ³ © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 55

    Using the TI-73: A Guide for Teachers Activity Have students perform the steps unless otherwise indicated. 1. As a class, measure the ramps. They should all be the same length. 2. Divide the length by 6 so students have 5 different intervals to test their ramp height.

  • Page 56

    Measurement 8. Now using the TI-73, create a horizontal bar graph, and then compare it to the graph made on the activity sheet. a. In , enter the ramp heights from 0 to the straight- up position. (1) Display the List editor.

  • Page 57

    For more information, see “Setting the Window Format” and “Defining Window Values” in the Function Graphing chapter of the TI-73 Guidebook . 10. Display the graph and discuss the data. Have students compare this graph to the graph they made on their activity sheets.

  • Page 58: Only The Height Has Been Changed

    Measurement Activity 9 Only the Height Has Been Changed Straight up Flat Distance the car traveled Activity 9: Only the Height Has Been Changed Name __________________________ Date Height of the Ramp Height of the Ramp Distance the Car Distance the Car Traveled Traveled (flat) 0...

  • Page 59

    Using the TI-73: A Guide for Teachers Measurement © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 60: Give Me 5

    TI-73 generates the rand same random-number sequence for a given seed value. The TI-73 factory-set seed value for generate a different random-number sequence, store any non-zero seed value to 1. Enter the number you want for your seed value.

  • Page 61

    Have them play the game “Get Ahead with More Heads.” The instructions follow. 1. Group students into pairs. 2. Using the coin-toss function of the TI-73, toss 5 coins. a. Return to the Home screen. b. Access the Math menu and select 1 "...

  • Page 62

    Is one less probable? 15. Collect the class data and have students record it in the Class Data table. 16. Enter the class data into the TI-73 using lists. Use for the points and for the frequencies. a. Display the List editor.

  • Page 63

    Using the TI-73: A Guide for Teachers c. Starting from the first line in points as shown in the screen at the right. (You’ll is still highlighted.) Press b get an error if after each list item. d. Follow the same procedure to enter the class data into 17.

  • Page 64

    Probability 18. Turn on trace. ! and " to move along the histogram Discuss the following questions. In our class data, which outcomes are least likely? Which outcomes are most likely? Compare this to your small group data. Is it the same? If not, what makes the difference? (sample size) Wrap-up for Part A Ask students: Which scores on a single toss are...

  • Page 65

    Using the TI-73: A Guide for Teachers 3. Compare the group experimental probabilities with the theoretical probabilities from the tree diagram. a. Go to and calculate the group probabilities by dividing each entry in trials (sum of 3 " $ to highlight - v Z F - v "...

  • Page 66

    Probability Activity 10 Give Me 5! Get Ahead With More Heads Trial Total Total Points each roll Points each roll Frequency Frequency 0 (0 H, 5 T) 0 (0 H, 5 T) 1 (1 H, 4 T) 1 (1 H, 4 T) 2 (2 H, 3 T) 2 (2 H, 3 T) 3 (3 H, 2 T)

  • Page 67

    Using the TI-73: A Guide for Teachers Points each Frequency toss Totals Theoretical Probability of Tossing 5 Coins H 5 H, H, H, H, H = 1 + 1 + 1 + 1 + 1 = 5 < T 5 H, H, H, H, T = 1 + 1 + 1 + 1 + 0 = 4 H 5 H, H, H, T, H = 1 + 1 + 1 + 0 + 1 = 4 <...

  • Page 68: A Foot Is A Foot - Or Is It

    How many people should we survey? Could we find out this information without a survey? Where could we find it? Probability and Statistics mean conversion of fractions to decimals measurement Materials ruler student activity sheet (provided) TI-73 ³ © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 69

    How will we add the fractional parts? (If you wish, you can convert them to decimals using the TI-73. See the example in the next step.) 3. Find the averages from the data.

  • Page 70

    Probability and Statistics 4. Now enter the data into a list ( mean. a. Display the List editor. b. If necessary, clear $ to highlight c. Starting from the first line in (You’ll get an error if Remember to press b after each entry. d.

  • Page 71

    Using the TI-73: A Guide for Teachers 6. Combine the class data by either combining the individual foot lengths and finding the mean or by averaging the individual means. (It may be beneficial for students to do it both ways so students can see if the same answer comes up both ways).

  • Page 72

    Probability and Statistics Wrap-up Ask students: Was the mean of the combined data from the mean from the Home screen? What does our combined class data show? Is the statement true that the average length of a human foot is 12 inches, or a foot? Do you think our class data is accurate? How could we make it even more accurate? Where could we find data without measuring feet?

  • Page 73

    Using the TI-73: A Guide for Teachers Activity 11 A Foot is a Foot – Or is It? Name (indicate child or adult) Mean of my data __________________ Mean of class data ________________ Does our class data support the statement that the average human foot is 12 inches long?____ ©...

  • Page 74: Which Brand Is Best

    (box plot, pictograph, bar graph, pie chart) tables Materials student activity sheets (provided) ³ TI-73 Make sure that the 5 prices the students list are not all the same. © 1998 T EXAS NSTRUMENTS NCORPORATED...

  • Page 75

    Using the TI-73: A Guide for Teachers Activity Have students perform the steps unless otherwise indicated. 1. On the activity sheets provided, have students use their information to report the minimum and the maximum prices of the product they selected, the mode, the mean, the median, and the range of prices.

  • Page 76

    Probability and Statistics 2. Calculate the range. 3. Now make a box plot on the TI-73. a. Access the STAT PLOTS - e (above the & key) b. Make sure the plots are off. c. Select Plot 1 - e b d.

  • Page 77

    Using the TI-73: A Guide for Teachers 5. Move around the graph and see the data. ! and " to view data 6. Have students sketch and label their plot on paper for their report. (If you have students may print their graphs to color and label.) 7.

  • Page 78

    Probability and Statistics 9. Now enter the surveyed information into the TI-73. a. Enter the brand names in use the brand names from the example table.) 3 " to - t # #, and then " until " $ $, and then ! until...

  • Page 79

    13. Have students sketch their graphs on paper for their report. (If you have TI-73 may print their graphs to color and label.) 14. Make a bar graph on the TI-73 showing the frequency results of the polls. a. Access the STAT PLOTS - e (above the &...

  • Page 80

    17. Have students sketch their graphs on paper for their report (or use TI-73 TI-GRAPH LINKé graphs to color and label). 18. Make a pie chart on the TI-73 showing the percents from the polls. a. Access the STAT PLOTS - e (above the &...

  • Page 81

    Using the TI-73: A Guide for Teachers 21. Have students sketch their graphs on paper for their report (or use TI-73 TI-GRAPH LINKé graphs to color and label). 22. Have students write analyses of their information. Here are some things you may want them to address: Do you think that packaging, advertising, shipping, etc.

  • Page 82

    Probability and Statistics Activity 12 Which Brand Is Best? 1. Choose a product that is distributed in at least 5 different brands. List the product type, the different brands, and the price for each brand. Product Type: Product Type: Brand Name Brand Name 2.

  • Page 83

    Using the TI-73: A Guide for Teachers 3. Record the results of your poll of 50 people (students, teachers, and other adults). Try to poll those who would actually be doing the buying. Be sure to ask why they chose that brand and include their responses with your analysis.

  • Page 84: Index Ti-73 Index

    Only the Height Has Been Changed Give Me 5! A Foot is a Foot–Or is It? Which Brand is Best? PAGE TI-73 FUNCTIONS IN ACTIVITY Fraction-to-Decimal Random, Store, Dice, Probability List, Mean, Sum Constant, Y=editor, Window, Graph, Trace, Table Last Answer (Ans), Text...

  • Page 85: Activity Content Index Activity Content Index

    Using the TI-73: A Guide for Teachers Activity Content Index ACTIVITY The Cookie Caper Dice Digits How Do You Measure Up? Stadium Walls The Twin’s Towers Major Martian Headache The Dolphin Drip, Drip, Drip Only the Height Has Been Changed Give Me 5! A Foot is a Foot–Or is It?

  • Page 86

    Activity Content Index ESTIMATION RATIO Percent Rounding Percent Percent Percent (continued) (continued) MEASUREMENT GEOMETRY Rate of Change, Volume © 1998 T PROBABILITY STATISTICS Mean Graphing Collecting Data Mean, Graphing, Collecting Data EXAS NSTRUMENTS NCORPORATED...

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