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.
ii Using the TI-73: A Guide for Teachers © 1998 TEXAS INSTRUMENTS INCORPORATED
iii About the Development Team Texas Instruments would like to acknowledge the following individuals who worked as a team in developing and evaluating these materials.
iv 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.
v Table of Contents About the Development Team About the Activities iii iv Number Sense The Cookie Caper Dice Digits How Do You Measure Up? 1 5 9 Patterns, Relations, and Functions Stadium Walls The Twin’s Towers Major Martian Headache 13 23 31 Measurement and Geometry The Dolphin Drip, Drip, Drip Only the Height Has Been Changed 35 41 49 Probability and Statistics Give Me 5! A Foot is a Foot–Or is It? Which Brand is Best? TI-73 Index Activity Content Index 55 63 69 79 80 © 1998 TEXAS INSTRUMENTS
1 Activity 1 Number Sense The Cookie Caper ♦ equivalent fractions ♦ fractions to decimals Materials Students learn about equivalent fractions by sharing their favorite cookies. ♦ 7cm (2¾ in.) poster board circles for cookies ♦ copies of fractional circles (provided) ♦ shapes of colored paper to represent chocolate chips, nuts, raisins etc.
2 Using the TI-73: A Guide for Teachers Number Sense 3. Give students a set time period to trade cookie “bites” (slices) with each other. Tell them they must trade equal-sized pieces, so they will need to know what fractional parts are equal to each other. Example A ½ slice may be traded for two ¼ slices. At the end of the trade time, each student should still have a whole cookie, but now it is made of a variety of cookie ingredients. 4. Discuss the results with your students.
Number Sense Activity 1: The Cookie Caper 3 Wrap-up ♦ 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 > (fraction-to-decimal function). Discuss why these equivalent fractions also have the same decimal value. Example Press Y = Q > b. The display shows .25 as the decimal equivalent for ¼. Then enter [ = Y Z > b. The display again shows .25 as the decimal equivalent.
4 Using the TI-73: A Guide for Teachers © 1998 TEXAS INSTRUMENTS INCORPORATED Number Sense
5 Activity 2 Number Sense Dice Digits Students use 4 numbers, any operations, and grouping symbols to write mathematical expressions that are equal to each of the numbers 1 through 9.
6 Using the TI-73: A Guide for Teachers Activity—Part A Whole Class 1. Demonstrate to your students how to roll dice on the TI-73 to get 4 numbers. Record the 4 numbers. a. Go to the Home screen. -l b. Select dice from the MATH PRB menu, and paste it to the Home screen. 1""J c. Enter the number of dice you want to roll at one time. QEb You now have 4 numbers. d. Record the 4 numbers on the transparency. 2.
Number Sense Activity 2: Dice Digits 7 Activity—Part B Individual or Small Group 1. Have each student or pair of students roll dice on the TI-73 to get 4 numbers. 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. Wrap-up ♦ Students can exchange papers and check one another’s work.
8 Using the TI-73: A Guide for Teachers Number Sense Name __________________________ Date __________________________ Activity 2 Dice Digits Roll dice to get 4 numbers. Record numbers below.
9 Activity 3 Number Sense How Do You Measure Up? Students discover the ratio between their heights and the lengths of their intestines. This activity is a good introduction to using lists to find the mean and performing operations on lists.
10 Using the TI-73: A Guide for Teachers Number Sense 1. Measure the strings. 2. Enter the data in L1 on the TI-73. a. Display the List editor. 3 b. If necessary, clear L1. $ to highlight L1 :b c. Starting at the first line in L1, enter the string lengths. (You’ll get an error if L1 is still highlighted.) Press b after each list item. 3. Find the mean of L1. a. Return to the Home screen. -l b. Access the - v MATH menu and select mean. -v""[ c. Calculate the mean of L1. -vYEb 4.
Number Sense Activity 3: How Do You Measure Up? 11 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. Enter the data in L2. a. Display the List editor. 3 b. If necessary, clear L2. $ to highlight L2 :b c. Enter the heights in L2. Press b after each list item. 3.
12 Using the TI-73: A Guide for Teachers Number Sense 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’ average height to average intestine length. Extensions Investigate the length of the intestine for different animals. Compare the ratio of the height to intestine length to the ratio you discovered above.
13 Activity 4 Patterns and Relations Stadium Walls Students investigate real-life situations and find patterns by making concrete representations and making T-charts. Students then describe and generalize these patterns verbally, symbolically, and graphically. ♦ patterning ♦ graphing ♦ evaluating expressions ♦ equivalent math expressions Materials ♦ graph paper ♦ toothpicks ♦ TI-73 Setup Present the following problem to students.
14 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. Example length(X) 1 2 3 4 5 6 7 number of beams(Y) 4 7 10 13 16 19 22 3. Investigate the pattern in the tables and concrete models and predict how many beams are needed for a wall length of 7 and a length of 10. 4.
Patterns and Relations Activity 4: Stadium Walls 15 6. Now have students determine how many beams are needed for a length of 57. Discuss how they found their solutions. (Some students may find the solution by recognizing that each number in the right-hand column is obtained by adding 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. a.
16 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 Y. 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. For example, As the number of lengths change, what happens to the number of beams? Have students share rules in small groups, and then with the whole class. b.
Patterns and Relations Activity 4: Stadium Walls 17 10. Ask: What remains the same or constant? (1) What changes or varies? (L-number of lengths varies) 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. a. On each line where there is an entry, clear the Y= editor. &: b. Now enter the equation. [I\Y 12. View the window. ' 13. Discuss the possible values for X and Y.
18 Using the TI-73: A Guide for Teachers Patterns and Relations 14. Turn off STAT PLOTS, and then display the graph. -eQb* 15. Ask: What do you notice about the graph on the screen? What is the value of Y when X is 57? How can you find out? (Press ) to see the values on the graph. If you are not tracing whole number values for X, estimate the value of Y by rounding the decimal.) What will Y equal when X is 57? (To find the whole number value, press R J b.
Patterns and Relations Activity 4: Stadium Walls 19 20. Change the graph style of Y2. & # to Y2 ! so the cursor is blinking on top of the little diagonal line on the far left b Notice that the diagonal line has changed to a darker line. 21. To see the second line graph over the first, press *. Ask: What is true about the graph of the second equation compared to the first? (same line) 22. Explain that another way to determine that the two equations are graphing the same line is from the graph screen. 23.
20 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. ♦ Have students substitute X = 57 in the equations to find a value for Y. This will also show the equivalency of the equations.
Patterns and Relations Activity 4: Stadium Walls 21 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. One student decided to sell granola bars. The predicted profit for every bar sold is $0.65.
22 Using the TI-73: A Guide for Teachers © 1998 TEXAS INSTRUMENTS INCORPORATED Patterns and Relations
23 Activity 5 Patterns and Functions The Twin’s Towers Students develop the concept of a variable while solving problems using the b key and the - ¢ key. ♦ problem solving ♦ percents ♦ adding fractions Materials ♦ blocks or cutouts ♦ student activity sheet (provided) ♦ TI-73 ³ Setup the towers with ➪ Build blocks as you discuss this Discuss the following situation with your class. My twin brother and sister are building towers with blocks. They built them in the following ways.
24 Using the TI-73: A Guide for Teachers Patterns and Functions Activity—Part A 1. Ask students: Look at the row for the number of blocks. What pattern do you see? (The first number is 3 and then increases by 1.) 2. Demonstrate along with your class how to put the pattern into the TI-73. a. Explain that this whole scenario starts with a 1-level tower that needs 3 blocks. So the first entry is 3. [b b.
Patterns and Functions Activity 5: The Twin’s Towers 25 3. Now have students generate this sequence on their TI-73s. [b\Yb 4. Working in groups of two, have students use their TI-73s to answer the following questions. How many blocks do you need for a 27-level tower? (29) How many blocks do you need for a 53-level tower? (55) A ___-level tower has 27 blocks? (25) A ___-level tower has 53 blocks? (51) Activity—Part B 1. Now the twins build the following towers. Have students build them, too.
26 Using the TI-73: A Guide for Teachers Patterns and Functions 4. Have students set up the counter for the second scenario. - t # #, and then " until { b Y ¡ Z " to } b # # to Done b b - t # #, and then " until { b # # to Done b - ¢ (above the a key) DYE\Y¡ -¢DZE\Z - t # #, and then " until } b # # to Done b b {} indicates a list of ➪ numbers. means the answer ➪ inAns(1) the first position of the list and Ans(2) means the answer in the second position of the list.
Patterns and Functions Activity 5: The Twin’s Towers 27 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. Wrap-up Discuss the power of Ans with your students. You could have solved all of the situations examined by making lists of each sequence, term after term.
28 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. Have them write the situations in story form, and then trade with another group. ♦ Give students the screen shot at the right. Ask them to create at least one situation that would fit this pattern.
Patterns and Functions Activity 5: The Twin’s Towers 29 Name __________________________ Date __________________________ Activity 5 The Twin’s Towers 1. Build the above pictures with blocks or cutouts. 2. How many blocks total will you need to build a 6-story building? a. Build it and write the number here: ✏____________________________ b. Now develop a pattern for entering it into the TI-73. Write your pattern here: ✏____________________________ c.
30 Using the TI-73: A Guide for Teachers Patterns and Functions Name __________________________ 1. Build the above pictures with pattern blocks or cutouts. 2. How many blocks total will you need to build a boat with 5 puffs of smoke? a. Build it and write the number here: ✏____________________________ b. Now develop a pattern for entering it into the TI-73. Write your pattern here: ✏____________________________ c. Now check your pattern by entering it into the TI-73 and pressing b 4 times.
31 Activity 6 Major Martian Headache Patterns ♦ patterning ♦ writing simple rules Materials Students learn about patterning and writing simple rules as they explore a hypothetical situation about Martians. ♦ large marshmallows (heads) ♦ small marshmallows (antenna ends) ♦ toothpicks (antennas) ♦ paper and pencil ♦ TI-73 ³ Setup ♦ Divide the class into groups and distribute 5 large marshmallows to each student. ♦ Provide each group with a tray of toothpicks and a dish of small marshmallows.
32 Using the TI-73: A Guide for Teachers Patterns 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. 2. Starting with one Martian head, make a T-chart to show how many heads and how many antennas. An example of the start of a T-chart follows. # Martian Heads 1 2 . . 5 # Antennas 2 4 . . 3.
Patterns Activity 6: Major Martian Headache 4. Guide students to see that the rule for making antenna muffs is heads ¦ 2 = number of antenna muffs. Show students how this also can be written as X ¦ 2 =Y. 33 ➪ The TI-73 displays the multiplication symbol as an asterisk ¦. 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. &IMZ 7.
34 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. Have them enter their rules in the Y= editor (&) and use the table as before. Wrap-up Have students draw their Martians with a different number of antennas and show how they adapt to their environment.
35 Activity 7 Geometry The Dolphin ♦ plotting ordered pairs ♦ connecting line graphs (xyLine) Materials ♦ dolphin picture overlayed on a grid (provided) ♦ transparency of provided dolphin picture ♦ grid paper ♦ TI-73 ³ 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. ♦ Have students draw and label the x- and y-axes on their papers.
36 Using the TI-73: A Guide for Teachers Geometry Activity Have students perform the steps unless otherwise indicated. 1. On the transparency of the dolphin picture, label the xand y-axes using whole numbers. Have students label their copies, too. on the level of ➪ Depending your students, the dolphin may be in the first quadrant only or it may be in more than one quadrant. 2. Lead the class in a discussion of selecting the first few key points to make a dot-to-dot outline of the dolphin.
Geometry Activity 7: The Dolphin 37 7. Set up the xyLine plot (connected line graph). a. Access the STAT PLOTS menu. - e (above the & key) b. Select Plot 1. b c. With the cursor blinking on the word On, select it. b d. Move to Type and select the xyLine plot (first row, second from left Ó). #"b e. Move to Xlist and select L1. #-vb f. Move to Ylist and select L2. #-v#b g. Move to Mark and select the . (dot) as the mark for the xyLine plot. #""b h.
38 Using the TI-73: A Guide for Teachers Geometry 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. Assessment Suggestions ♦ Ask: What was represented by the numbers in L1 and L2? ♦ Have students write a journal entry explaining what they learned. Extensions ♦ Have students draw their own picture and label the ordered pairs.
Geometry Activity 7: The Dolphin 39 3. Access the VARS menu and select Picture. -}4 4. At PICTURE, select where you want to store your picture. b to select Pic1 or 2 to select Pic2 or 3 to select Pic3 ♦ To recall the picture, 1. Turn off the axes. -g##"b 2. Starting at the Home screen (- l), go to DRAW STO and select RecallPic. 2""2 3. Go to VARS and select Picture. -}4 4. Select where your picture is stored (Pic1, 2 or 3). 5. Press *.
40 Using the TI-73: A Guide for Teachers © 1998 TEXAS INSTRUMENTS INCORPORATED Geometry
41 Activity 8 Measurement and Geometry Drip, Drip, Drip Students collect data from a dripping faucet. Then, using the TI-73, they produce data on the Home screen. Afterwards, they view the same data using a table, a graph, and the Trace feature.
42 Using the TI-73: A Guide for Teachers Measurement and Geometry 7. Ask students: Why did we count for 2 minutes? (Ten minutes is a long time to count. Counting for 2 minutes allows you to get an average for 1 minute. Counting for 3 or 4 minutes might give a more accurate average per minute, but it might be too long for your students.
Measurement and Geometry Activity 8: Drip, Drip, Drip 43 11. View and trace the graph. *) ! or " to trace until X=0 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. - i (above the * key) 13. Scroll down (#) in the X column to 24.
44 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. Tell students to predict what the graph of this equation would look like compared to the graph in Part A, step 11. 3. Use the Manual-Fit function to plot these data points for 1 hour and 2 hours. a. First, change the settings for the viewing window.
Measurement and Geometry Activity 8: Drip, Drip, Drip 45 f. Now select the first point on the line. " until X=1 $ until Y=4 b to select the first point on the line g. Select the second point on the line. " until X=2 $ until Y=8 b to select the second point The screen shows the expression for the line. h. Save the line. b 4. Turn on Trace. * ). Ask: Was your prediction correct? 5. Investigate if the drip were half as fast.
46 Using the TI-73: A Guide for Teachers Measurement and Geometry Name _______________________ Date _______________________ 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. What did you calculate for number of drips in 1 minute? ✏__________________________ 5.
Measurement and Geometry Activity 8: Drip, Drip, Drip 47 Name _______________________ 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. Sketch the graph on the screen at the right. Use Manual-Fit to plot these data points. 3.
48 Using the TI-73: A Guide for Teachers © 1998 TEXAS INSTRUMENTS INCORPORATED Measurement and Geometry
49 Activity 9 Measurement Only the Height Has Been Changed Students collect data and examine variables that may cause a change in the distance a toy car will travel on the floor when it is rolled down a ramp.
50 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. (For example, if the ramp is 24cm, the intervals would be 4cm, 8cm, 12cm, 16cm, and 20cm. Zero cm would be flat and 24cm would be straight up. If you wish to use inches, for example, a 12-inch ramp, the intervals would be 2 in., 4 in.
Measurement Activity 9: Only the Height Has Been Changed 51 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 L1, enter the ramp heights from 0 to the straightup position. (1) Display the List editor. 3 (2) If necessary, clear L1. $ to highlight L1 :b (3) Enter each ramp height. Press b after each entry. b. Now follow the same procedure to enter in L2 the group data showing the distance the car traveled.
52 Using the TI-73: A Guide for Teachers Measurement 9. Before graphing, set up the viewing window for each TI-73 ('). • Xmin will be 0. • Xmax will be the height of the ramp straight up plus 5 (so you can see the full graph). • Ymin will be 0. • Ymax will be the longest distance a car traveled plus 5. For more information, see “Setting the Window Format” and “Defining Window Values” in the Function Graphing chapter of the TI-73 Guidebook Xmax and Ymax values ➪ The shown here are just examples.
Measurement Activity 9: Only the Height Has Been Changed 53 Name __________________________ Date __________________________ Activity 9 Only the Height Has Been Changed L1 L2 Height of the Ramp Distance the Car Traveled (flat) 0 0 (straight up) 0 Height of ramp Straight up Flat Distance the car traveled © 1998 TEXAS INSTRUMENTS INCORPORATED
54 Using the TI-73: A Guide for Teachers © 1998 TEXAS INSTRUMENTS INCORPORATED Measurement
55 Activity 10 Probability Give Me 5! ♦ order of operations ♦ mental math ♦ basic computation Materials Students investigate the results of tossing 5 coins. They compare what happens to what is expected to happen. ♦ student activity sheets (provided) ♦ TI-73 ³ Setup ♦ If your TI-73s have not been used for any random numbers prior to this activity, you and your students need to store an integer “seed value” to rand in each TI-73.
56 Using the TI-73: A Guide for Teachers Probability Activity—Part A Have students perform the steps unless otherwise indicated. 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. -l b. Access the Math menu and select coin. 1""S c. Toss 5 coins. REb 3. Explain to students that 1 means heads, and 0 means tails. Heads are worth 1 point each.
Probability Activity 10: Give Me Five 57 10. Discuss with students: How many total trials did you and your partner have? Raise your hand if you had a 5-point toss. Raise your hand if you had a 0-point toss. Which score on a single trial would you predict is more likely to occur, 0 or 5? Out of the 50 trials, how many trials would you predict to be worth 5 points? 11. Record group data in the Coin-Toss Trials Small Group Data table provided.
58 Using the TI-73: A Guide for Teachers Probability c. Starting from the first line in L1, enter the possible points as shown in the screen at the right. (You’ll get an error if L1 is still highlighted.) Press b after each list item. d. Follow the same procedure to enter the class data into L2. 17. Now graph a histogram. a. Access the STAT PLOTS menu. - e (above the & key) b. Make sure the other plots are off. Qb c. Select Plot 1. -eb d. With the cursor blinking on the word On, select it. b e.
Probability Activity 10: Give Me Five 59 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 equally likely (have the same probability)? ♦ Have students list the ways to get a sum of 1.
60 Using the TI-73: A Guide for Teachers Probability 3. Compare the group experimental probabilities with the theoretical probabilities from the tree diagram. a. Go to L3 and calculate the group probabilities by dividing each entry in L3 by the total number of trials (sum of L2 ). 3 " $ to highlight L3 (See screen at the right.) -vZF-v""J -vZEb b. In L4 enter the frequencies from the tree diagram. (See screen at the right.) " to the first line of L4 Enter the frequencies from the tree diagram.
Probability Activity 10: Give Me Five 61 Name __________________________ Activity 10 Date __________________________ Give Me 5! Get Ahead With More Heads Score Sheet Trial # A B A B Student A B A B A B 1 2 3 4 5 Total Coin-Toss Trials Small Group Data Points each roll Frequency Probability-fraction Probability-decimal 0 (0 H, 5 T) 1 (1 H, 4 T) 2 (2 H, 3 T) 3 (3 H, 2 T) 4 (4 H, 1 T) 5 (5 H, 0 T) Total number of trials—50 © 1998 TEXAS INSTRUMENTS INCORPORATED
62 Using the TI-73: A Guide for Teachers Probability Name __________________________ Coin-Toss Trials Class Data Points each toss Frequency Probability fraction Probability decimal Percent equivalent 0 1 2 3 4 5 Totals Theoretical Probability of Tossing 5 Coins H5 T5 H5 T< 5 T H5 H< 5 T H5 T< 5 T H5 H< 5 T H5 < T T5 H5 H< 5 T H5 T< 5 T H< H H T H H T T H H T T H T T H, H, H, H, H = 1 + 1 + 1 + 1 + 1 = 5 H, H, H, H, T = 1 + 1 + 1 + 1 + 0 = 4 H, H, H, T, H = 1 + 1 + 1 + 0 + 1 = 4 H, H, H, T, T = 1
63 Activity 11 Probability and Statistics A Foot is a Foot–Or is It? Students investigate how their own foot measurements compare to the customary measurement of a foot (12 inches). ♦ mean ♦ conversion of fractions to decimals ♦ measurement Materials ♦ ruler ♦ student activity sheet (provided) ♦ TI-73 ³ Setup ♦ Tell students that the dictionary defines foot, as it relates to measurement, as a measure of length equal to 12 inches based on the average length of a human foot.
64 Using the TI-73: A Guide for Teachers ♦ Demonstrate to students how to measure a foot, from heel to toe, so that everyone is measuring the same. Ask: What unit should we use to measure? (inches) What if there are parts of an inch left? Will we record it as a decimal or fraction? (Fraction would probably be easiest for this part.) Do we need to measure both feet or just one foot? Should we measure with the shoe on or off? Activity Have students perform the steps unless otherwise indicated. 1.
Probability and Statistics Activity 11: A Foot is a Foot–Or is It? 65 4. Now enter the data into a list (L1), and then find the mean. a. Display the List editor. 3 b. If necessary, clear L1. $ to highlight L1 :b c. Starting from the first line in L1, enter each length. (You’ll get an error if L1 is still highlighted.) Remember to press b after each entry. d. Find the mean of the data in L1. (1) Return to the Home screen. -l (2) Access the - v MATH menu and select mean.
66 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). 7. Now enter the combined data into a list (L2), and then find the mean. a. Display the List editor. 3 b. If necessary, clear L2. $ to highlight L2 :b c. Starting from the first line in L2, enter each length.
Probability and Statistics Activity 11: A Foot is a Foot–Or is It? 67 Wrap-up Ask students: Was the mean of the combined data from L2 the same as 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? Do you think average foot sizes differ around the world? How could we find
68 Using the TI-73: A Guide for Teachers Probability and Statistics Name __________________________ Date __________________________ Activity 11 A Foot is a Foot–Or is It? Name (indicate child or adult) Length of foot in inches (use fractions for leftovers) Convert fractions to decimals Mean of my data __________________ Mean of class data ________________ Does our class data support the statement that the average human foot is 12 inches long?____ © 1998 TEXAS INSTRUMENTS INCORPORATED
69 Activity 12 Probability and Statistics Which Brand Is Best? In this real-world activity, students comparison shop in their community. Then they produce consumer reports to share their findings with their class.
70 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. a. First, enter the prices into List 1 (L1) on the TI-73, and set the decimal to the hundredths place. (1) Display the List editor. 3 (2) If necessary, clear L1.
Probability and Statistics Activity 12: Which Brand is Best? 71 ➪ One way to find the range 2. Calculate the range. is shown in the screen below. 3. Now make a box plot on the TI-73. a. Access the STAT PLOTS menu. - e (above the & key) b. Make sure the plots are off. 4b c. Select Plot 1. -eb d. With the cursor blinking on the word On, select it. b e. Move to Type and select the box plot (second row, third from left Ö). #""""""b f. Move to Xlist. If L1 is not already set, set it to L1. #-vb g.
72 Using the TI-73: A Guide for Teachers Probability and Statistics nice connection is to ➪ Acompare the trace values 5. Move around the graph and see the data. ) ! and " to view data for Xmin, median, and Xmax with their calculated values. 6. Have students sketch and label their plot on paper for their report. (If you have TI-73 TI-GRAPH LINKé, students may print their graphs to color and label.) 7.
Probability and Statistics Activity 12: Which Brand is Best? 73 9. Now enter the surveyed information into the TI-73. a. Enter the brand names in L2. (In this example, we use the brand names from the example table.) 3 " to L2 - t # #, and then " until " b $ $, and then ! until A b # # # # to Done b b (Because " is only needed for the first element of a categorical list, you can enter the rest of the elements from the Text editor without it.) b.
74 Using the TI-73: A Guide for Teachers Probability and Statistics g. Move to Data List. If L3 is not already set, set it to L3. #-v[b h. Continue setting up the plot. Your screen should look like the screen at the right. Press b at Vert and at the $ icon. Scale tells the TI-73 the ➪ value or quantity each icon represents. The display shows a maximum of 7 icons. Choose your scale based on the largest number in your data list, or you can select ( 7:ZoomStat and the TI-73 will select a scale for you.
Probability and Statistics Activity 12: Which Brand is Best? 75 d. Select the bar graph Ð (first row, last from left) and continue setting up the plot as in the picture at the right. (DataList2 and DataList3 allow you to do a double or triple bar graph. They are not relevant to this activity, and whatever is listed is okay.) 15. Display the graph. (J 16. Now move around the graph and see the data. ) ! and " to view data 17.
76 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 to print their 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.
Probability and Statistics Activity 12: Which Brand is Best? 77 Name __________________________ Date __________________________ 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: Brand Name Price 1. $ 2. $ 3. $ 4. $ 5. $ 2. Record the following information. Show all calculations.
78 Using the TI-73: A Guide for Teachers Probability and Statistics Name __________________________ 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. Product Type: Brand Name Price 1. $ 2. $ 3. $ 4. $ 5. $ Tally for each choice 4.
79 TI-73 Index ACTIVITY PAGE NO.
80 Using the TI-73: A Guide for Teachers Activity Content Index ACTIVITY PAGE NO. PATTERNS FRACTIONS DECIMALS OPERATIONS x x Add.
81 Activity Content Index (continued) ESTIMATION RATIO x Percent MEASUREMENT GEOMETRY PROBABILITY STATISTICS x x x Mean x Rounding Graphing Percent x Rate of Change, Volume x Percent Collecting Data Mean, Graphing, Collecting Data x x Percent x x x © 1998 TEXAS INSTRUMENTS INCORPORATED
