Texas instruments CBR GETTING STARTED

ETTING ETTING

5 5

TARTED WITH TARTED WITH

INCLUDINGINCLUDING

STUDENT ACTIVITIESSTUDENT ACTIVITIES

CBR™CBR™

CBR

)

TRIGGER

85-86

Calculator-Based Rangeré (CBRé) calculator-to-CBR cable

clamp 4 AA batteries

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Table of contents

CBR

)

NTRODUCTION

What is CBR? 2

Getting started with CBR — It’s as easy as 1, 2, 3 4

Hints for effective data collection 6

Activities with teacher notes and student activity sheets

TRIGGER

85-86

Activity 1 — Match the graph linear 13

Activity 2 — Toy car linear 17

Activity 3 — Pendulum sinusoidal 21

Activity 4 — Bouncing ball parabolic 25

Activity 5 — Rolling ball parabolic 29

Teacher information 33

Technical information

CBR data is stored in lists 37

RANGER settings 38 Using CBR with CBL or with CBL programs 39 Programming commands 40

Service information

Batteries 42

In case of difficulty 43

TI service and warranty 44

RANGER menu map inside back cover

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

ETTING STARTED WITH

CBR

What is CBR?

bring real-world data collection and analysis into the classroom

MATCH and BOUNCING BALL programs are built into RANGER

What does CBR do?

With

CBR

without tedious measurements and manual plotting.

lets students explore the mathematical and scientific relationships between distance,

CBR

velocity, acceleration, and time using data collected from activities they perform. Students can explore math and science concepts such as:

CBRCBRé ((Calculator-Based RangerCalculator-Based Rangeré

))

sonic motion detector

use with TI-82, TI-83, TI-85/

CBL

, TI-86, and TI-92

easy-to-use, self-contained

no programming required

Includes the RANGER programIncludes the RANGER program

the versatile RANGER program is one button away

primary sampling parameters are easy to set

and a TI graphing calculator, students can collect, view, and analyze motion data

motion: distance, velocity, acceleration

graphing: coordinate axes, slope, intercepts

functions: linear, quadratic, exponential, sinusoidal

calculus: derivatives, integrals

statistics and data analysis: data collection methods, statistical analysis

What’s in this guide?

Getting Started with CBR

calculator or programming experience. It includes quick-start instructions for using on effective data collection, and five classroom activities to explore basic functions and properties of motion. The activities (see pages 13–32) include:

teacher notes for each activity, plus general teacher information

step-by-step instructions

a basic data collection activity appropriate for all levels

explorations that examine the data more closely, including what-if scenarios

suggestions for advanced topics appropriate for precalculus and calculus students

a reproducible student activity sheet with open-ended questions appropriate for a wide

range of grade levels

is designed to be a guide for teachers who don’t have extensive

CBR

, hints

ETTING STARTED WITH

CBR

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

What is CBR?

(cont.)

to initiate sampling

battery door (on bottom)

port to connect to CBL (if desired)

port to connect to TI graphing calculators using the included

2.25-meter (7.5-foot) cable

reen light to indicate when data collection is occurring (sound also available)

button

CBR

)

red light to indicate

pecial conditions

onic sensor to record up to 200 samples per second with a range between

0.5 meters and 6 meters (1.5 feet and 18 feet)

TRIGGER

85-86

pivoting head to aim

ensor accurately

tandard threaded socket to attach a tripod or the included mounting clamp

buttons to transfer RANGER program to calculators

(on back)

includes everything you need to begin classroom activities easily and quickly — just add

CBR

TI graphing calculators (and readily available props for some activities).

sonic motion detector

RANGER

OPYING PERMITTED PROVIDED

program in the

EXAS INSTRUMENTS INCORPORATED

CBR

calculator-to-

4 AA batteries

CBR

cable

mounting clamp

5 fun classroom activities

ETTING STARTED WITH

CBR

Getting started with CBR—It’s as easy as 1, 2, 3

With

, you’re just three simple steps from the first data sample!

CBR

Connect

Connect using the calculator-to-

Push in connection.

The short calculator-to-calculator

Note:

cable that comes with the calculator also works.

to a TI graphing calculator

CBR

cable.

CBR

firmly

at both ends to make the

Transfer

RANGER

transfer the appropriate program from the

First, prepare the calculator to receive the program (see keystrokes below).

, a customized program for each calculator, is in the

to a calculator.

CBR

. It’s easy to

CBR

TI-82 or TI-83 TI-85/CBL or TI-86 TI-92

LINK

[

Next, open the pivoting head on the program-transfer button on the

During transfer, the calculator displays transfer is complete, the green light on and the calculator screen displays on

Once you’ve transferred the won’t need to transfer it to that calculator again unless you delete it from the calculator’s memory.

Note:

You may need to delete programs and data from the calculator. You can save the programs and data first by transferring them to a computer using TI-Graph Linké or to another calculator using a calculator-to-calculator cable or the calculator-to-

flashes twice and

CBR

The program and data require approximately 17,500 bytes of memory.

›

]

beeps twice.

CBR

RANGER

cable (see calculator guidebook).

CBR

LINK

CBR

DONE

[

]

, and then press the appropriate

CBR

RECEIVING

CBR

. If there is a problem, the red light

program from

Go to the Home screen.

(except TI-92). When the

flashes once,

CBR

beeps once,

CBR

to a calculator, you

ETTING STARTED WITH

CBR

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

Getting started with CBR—It’s as easy as 1, 2, 3

(cont.)

Run

Run the

RANGER

program (see keystrokes below).

For quick results, try one of the classroomready activities in this guide!

TI-82 or TI-83 TI-85/

Press Choose Press

RANGER

›

^ A

Press Choose

›

Press

or TI-86 TI-92

CBL

RANGER

Press L [ Choose Press ¨

VAR-LINK

RANGER

›

The opening screen is displayed.

Press

›. The

MAIN MENU

SETUPàSAMPLE SET DEFAULTS APPLICATIONS PLOT MENU TOOLS QUIT

From the Press

MAIN MENU

› to choose

MAIN MENU

& & & & &

choose

is displayed.

view/change the settings before sampling change the settings to the default settings

DISTANCE MATCH, VELOCITY MATCH, BALL BOUNCE

plot options

GET CBR DATA, GET CALC DATA, STATUS, STOPàCLEAR

SET DEFAULTS

START NOW

. The

. Set up the activity, and then press › to

screen is displayed.

SETUP

begin data collection. It’s that easy!

Important information

This guide applies to all TI graphing calculators that can be used with so you may find that some of the menu names do not match exactly those on your calculator.

When setting up activities, ensure that the

is securely anchored and

CBR

that the cord cannot be tripped over.

Always exit the

RANGER

program performs a proper shutdown of ensures that

Always disconnect

is properly initialized for the next time you use it.

CBR

program using the

CBR

from the calculator before storing it.

CBR

option. The

QUIT

when you choose

RANGER

QUIT

]

CBR

. This

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

ETTING STARTED WITH

CBR

Hints for effective data collection

Getting better samples

How does CBR work?

Understanding how a sonic motion detector works can help you get better data plots. The motion detector sends out an ultrasonic pulse and then measures how long it takes for that pulse to return after bouncing off the closest object.

, like any sonic motion detector, measures the time interval between transmitting the

CBR

ultrasonic pulse and the first returned echo, but

much more. When the data is collected,

using a speed-of-sound calculation. Then it computes the first and second derivatives of

CBR

the distance data with respect to time to obtain velocity and acceleration data. It stores these measurements in lists

L1, L2, L3

, and L4.

calculates the distance of the object from the

CBR

has a built-in microprocessor that does

CBR

Performing the same calculations as

Collect sample data in

➊

Use the sample times in

➋

REALTIME=NO

in conjunction with the distance data in L2 to calculate the

is an interesting classroom activity.

CBR

mode. Exit the

RANGER

program.

velocity of the object at each sample time. Then compare the results to the velocity data in

(

Use the velocity data in L3 (or the student-calculated values) in conjunction with the

➌

sample times in

n+1

to calculate the acceleration of the object at each sample time. Then

)à2 N (

n+1

compare the results to the acceleration data in

Object size

Using a small object at a far distance from the

decreases the chances of an accurate

CBR

n-1

)à2

reading. For example, at 5 meters, you are much more likely to detect a soccer ball than a ping-pong ball.

Minimum range

When the

the

CBR.

be misidentified by

sends out a pulse, the pulse hits the object, bounces back, and is received by

CBR

If an object is closer than 0.5 meters (1.5 feet), consecutive pulses may overlap and

. The plot would be inaccurate, so position

CBR

at least 0.5 meters

CBR

away from the object.

Maximum range

As the pulse travels through the air, it loses its strength. After about 12 meters (6 meters on the trip to the object and 6 meters on the trip back to the weak to be reliably detected by the the

ETTING STARTED WITH

. This limits the typical reliably effective distance from

CBR

to the object to less than 6 meters (19 feet).

CBR

), the return echo may be too

CBR

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

Hints for effective data collection

The clear zone

(cont.)

The path of the

beam is not a narrow, pencil-like beam, but fans out in all directions up

CBR

to 10° in a cone-shaped beam.

To avoid interference from other objects in the vicinity, try to establish a clear zone in the path of the recorded by

Reflective surfaces

beam. This helps ensure that objects other than the target do not get

CBR

CBR. CBR

records the closest object in the clear zone.

Some surfaces reflect pulses better than others. For example, you might see better results with a relatively hard, smooth surfaced ball than with a tennis ball. Conversely, samples taken in a room filled with hard, reflective surfaces are more likely to show stray data points. Measurements of irregular surfaces (such as a toy car or a student holding a calculator while walking) may appear uneven.

A Distance-Time plot of a nonmoving object may have small differences in the calculated distance values. If any of these values map to a different pixel, the expected flat line may show occasional blips. The Velocity-Time plot may appear even more jagged, because the change in distance between any two points over time is, by definition, velocity. You may wish to apply an appropriate degree of smoothing to the data.

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

ETTING STARTED WITH

CBR

Hints for effective data collection

RANGER settings

Sample times

is the total time in seconds to complete all sampling. Enter an integer between 1

TIME

second (for fast moving objects) and 99 seconds (for slow moving objects). For

REALTIME=YES, TIME

is always 15 seconds.

(cont.)

When

TIME=1 SECOND

Starting and stopping

The

SETUP

is a lower number, the object must be closer to the

TIME

, the object can be no more than 1.75 meters (5.5 feet) from the

screen in the

RANGER

program provides several options for starting and stopping

. For example, when

CBR

sampling.

BEGIN ON: [ENTER]

. Starts sampling with the calculator’s

key when the person

›

initiating the sampling is closest to the calculator.

BEGIN ON: [TRIGGER]

. Starts and stops sampling with the

person initiating the sampling is closest to the In this option, you also can choose to detach the

disconnect the cord from the sample, reattach the

, and press

CBR

, take the

CBR

to transfer the data. Use

›

CBR

. This lets you set up the sample,

CBR

where the action is, press

CBR

button when the

BEGIN ON: [TRIGGER]

when the cord is not long enough or would interfere with data collection. This is not available in

BEGIN ON: DELAY

REALTIME=YES

. Starts sampling after a 10-second delay from the time you press

mode (such as the

MATCH

application).

It is especially useful when only one person is doing an activity.

Trigger button

The effect of

varies depending on the settings.

CBR

›

ETTING STARTED WITH

starts sampling, even if

BEGIN ON: [ENTER]

BEGIN ON: DELAY

is selected. It also

stops sampling, but usually you will want to let a sample complete. In

REALTIME=NO

, after sampling has stopped,

automatically repeats the most recent sample, but does not transfer the data to the calculator. To transfer this data, from the

MAIN MENU

sample by choosing

choose

TOOLS

REPEAT SAMPLE

, and then choose

from the

PLOT MENU

GET CBR DATA

START NOW

. (You also can repeat a

from the

SETUP

screen.)

CBR

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

Hints for effective data collection

Smoothing

(cont.)

Smoothing capabilities built into the

RANGER

program can reduce the effect of stray signals or variations in the distance measurements. Avoid excessive smoothing. Begin with no smoothing or

smoothing. Increase the degree of smoothing until you obtain

LIGHT

satisfactory results.

For an activity with a higher-than-average likelihood of stray signals, you may wish to

increase the smoothing on the For already-collected

REALTIME=NO

calculator must be connected to the choose

Noise—what is it and how do you get rid of it?

When the

SMOOTH DATA

receives signals reflected from objects other than the primary target, the plot

CBR

, and then choose the degree of smoothing.

screen before sampling (see page 38).

SETUP

data, you can apply smoothing to the data. The

. Choose

CBR

PLOT TOOLS

from the

PLOT MENU

shows erratic data points (noise spikes) that do not conform to the general pattern of the plot. To minimize noise:

Make sure the

viewing a

REALTIME=NO

Try to sample in a clutter-free space (see the clear zone drawing on page 7).

Choose a larger, more reflective object or move the object closer to the

REALTIME=YES

is pointed directly at the target. Try adjusting the sensor head while

CBR

sample until you get good results before collecting a

sample.

CBR

(but farther

than 0.5 meters). When using more than one

in a room, one group should complete a sample before

CBR

the next group begins their sample. For a noisy

REALTIME=YES

obtain satisfactory results. (You cannot change the smoothing in the

VELOCITY MATCH

For a noisy

, or

REALTIME=NO

sample, repeat using a higher degree of smoothing until you

DISTANCE MATCH

BALL BOUNCE

applications.)

sample, you can apply a higher degree of smoothing to the

original data.

Speed of sound

The approximate distance to the object is calculated by assuming a nominal speed of sound. However, actual speed of sound varies with several factors, most notably the air temperature. For relative-motion activities, this factor is not important. For activities requiring highly accurate measurements, a programming command can be used to specify the ambient temperature (see pages 40–41).

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

ETTING STARTED WITH

CBR

Hints for effective data collection

REALTIME=YES

(cont.)

Use

REALTIME=YES

for slower objects

to see the results as they are collected

when you need to collect or plot only one type of data (distance, velocity, or acceleration)

mode:

for a sample

REALTIME=YES

mode, the

processes the requested plot data (distance, velocity, or

CBR

acceleration), which is transferred to the calculator following each individual distance measurement. Then

RANGER

plots a single pixel for that pulse.

Because all of these operations must be completed before the next sample can be requested, the maximum rate at which data can be sampled in

REALTIME=YES

mode is

limited.

It takes approximately 0.080 seconds just to sample, process, and transfer the data for a single data point. Additional time is required for operations such as plotting the point, which slows the effective sample rate to approximately 0.125 seconds in

REALTIME=NO

Use

REALTIME=NO

for faster objects

when smoothing is required (see page 9)

to operate the

when you need to collect or plot all types of data (distance, velocity, and acceleration) for

mode:

in detached mode (see page 11)

CBR

RANGER

a sample

In after all sampling is completed. The sample rate can be as fast as once every 0.005 seconds for close objects. Data for time, distance, velocity, and acceleration is transferred to the calculator.

Because the data is stored in the

and again.

ETTING STARTED WITH

REALTIME=NO

mode, data is stored in the

, you can transfer it from the

CBR

Each time you change smoothing, the

CBR

and not transferred to the calculator until

CBR

to a calculator again

CBR

applies the new smoothing factor, transfers

the adjusted data to the calculator, and stores the smoothed values in the lists. Choosing a domain changes the lists stored in the calculator. If you need to, you can

recover the original data from the choose

TOOLS

. From the

menu, choose

TOOLS

. From the

CBR

MAIN MENU

GET CBR DATA

in the

RANGER

program,

You also can share the same data with many students, even if they are using different types of TI graphing calculators. This allows all students to participate in data analysis activities using the same data (see page 11).

CBR

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

Hints for effective data collection

Using CBR in detached mode

(cont.)

Because the settings are required. On the

The special procedures are required.

Sharing data

What if you want the entire class to analyze the same data at the same time? With can disseminate

➊ ➋ ➌

➍

➎

cannot send data to the calculator immediately in detached mode, certain

CBR

screen:

SETUP

Set

REALTIME=NO

Set

BEGIN ON=[TRIGGER]

RANGER

program prompts you when to detach the

Transfer the

Collect the data with the

REALTIME=NO

RANGER

program to all students’ calculators prior to data collection.

data quickly within a classroom.

CBR

REALTIME=NO

mode.

Have the first student attach his or her calculator to the to-

From the choose

Press › to return to the

cable or the calculator-to-calculator cable.

CBR

MAIN MENU

GET CBR DATA. TRANSFERRING...

in the

RANGER

PLOT MENU

program, choose

is displayed and the plot appears.

, and then choose

and when to reattach it. No

CBR

using either the calculator-

CBR

. From the

TOOLS

QUIT

. Detach the cable.

TOOLS

you

CBR

menu,

Connect another calculator (of the same type) to the calculator with the data. On the

➏

receiving calculator, from the the

menu, choose

TOOLS

MAIN MENU

GET CALC DATA

set the sending calculator. When it is ready, press

in the

RANGER

program, choose

. Instructions are displayed telling you how to

›, and lists

L1, L2, L3, L4

are transferred automatically.

Transfer the data to another student’s calculator from

➐

while other students

CBR

continue the calculator-to-calculator transfers.

Once all students have the same data, they can analyze the data in

or outside

RANGER

To share data on the TI-85, use the

using the calculator’s list and graphing features.

feature outside of

LINK

RANGER

to transfer the lists.

using the

TOOLS

, and

. From

PLOT

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

ETTING STARTED WITH

CBR

Hints for effective data collection

Beyond simple data collection

(cont.)

Once you’ve collected and plotted data in

RANGER

, you can explore the data in relationship to a function. Because the data is collected as lists and displayed as a statistical plot, you can use

, , and œ to explore this relationship.

Inside RANGER

Explore plots using

, which is set automatically. (On the TI-85, use the free-moving

TRACE

cursor.) Manipulate the data set, including smoothing the data or selecting the domain of

interest.

Outside RANGER

Explore data using the calculator’s list editor.

Manually model a function to the data using the calculator’s Y= editor.

Automatically determine the equation that best fits the data using the calculator’s

regression capabilities.

Other relationships can be explored beyond those represented by the plot options in

RANGER

as statistical plots. From the

Plot1

. For instance, simultaneous plots of Distance-Time and Velocity-Time can be viewed

as L1 versus L2 and

MAIN MENU

as L1 versus L3. (You may also need to adjust the Window.)

Plot2

in the

RANGER

program, choose

, and then set

QUIT

Data and plots can be sent to a computer using TI-Graph Link. This is especially useful when students generate more involved reports of their activity findings.

Using CBR without the RANGER program

You can use

For information on using

For information on obtaining programs and activities, see page 36.

For information on programming commands to write your own programs, see pages

as a sonic motion detector with

CBR

with

CBR

40–41.

, see page 39.

CBL

or with programs other than

CBL

RANGER

ETTING STARTED WITH

CBR

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

Activity 1—Match the graph notes for teachers

Concepts

Function explored: linear. MATCH introduces the real-world concepts of distance

and time—or more precisely, the concept of distance versus time. As students attempt to duplicate graphs by walking while seeing their motion plotted, the concept of position can be explored.

In Explorations, students are asked to convert their rate of walking in meters per second to kilometers per hours.

Once they have mastered the Distance-Time match, challenge your students to a Velocity-Time match.

Materials

Ÿ calculator Ÿ CBR Ÿ calculator-to-calculator cable

A TI ViewScreené allows other students to watch— and provides much of the fun of this activity.

Hints

Students really enjoy this activity. Plan adequate time because everybody will want to try it!

This activity works best when the student who is walking (and the entire class) can view his or her motion projected on a wall or screen using the TI ViewScreen.

Typical answers

1. time (from start of sample); seconds; 1 second; distance (from the CBR to the object); meters; 1 meter

2. the y-intercept represents the starting distance

3. varies by student

4. backward (increase the distance between the CBR and the object)

5. forward (decrease the distance between the CBR and the object)

6. stand still; zero slope requires no change in y (distance)

7. varies by graph; @yà3.3

8. varies by graph; @yà1

9. the segment with the greatest slope (positive or negative)

10. this is a trick question—the flat segment, because you don’t move at all!

11. walking speed; when to change direction and/or speed

12. speed (or velocity)

13. varies by graph (example: 1.5 meters in 3 seconds)

14. varies by graph; example: 0.5 metersà1 second

Guide the students to walk in-line with the CBR; they sometimes try to walk sideways (perpendicular to the line to the CBR) or even to jump up!

Instructions suggest that the activity be done in meters, which matches the questions on the student activity sheet.

See pages 6–12 for hints on effective data collection.

Typical plots

example: (0.5 meters à 1 second) Q (60 seconds à 1 minute) = 30 meters à minute

example: (30 meters à 1 minute) Q (60 minutes à 1 hour) = 1800 meters à hour

example: (1800 meters à 1 hour) Q (1 kilometer à 1000 meter) = .18 kilometers à hour.

Have students compare this last number to the velocity of a vehicle, say 96 kilometers à hour (60 miles per hour).

15. varies by graph; sum of the @y for each line segment.

OPYING PERMITTED PROVIDED

EXAS INSTRUMENTS INCORPORATED

ETTING STARTED WITH

CBR

+ 32 hidden pages

Texas instruments CBR GETTING STARTED

Specifications and Main Features

Frequently Asked Questions

User Manual