ELEMENTARY SCIENCE PROGRAM MATH, SCIENCE & TECHNOLOGY EDUCATION

A Collection of Learning Experiences

Roamer Revised August 2007

CATTARAUGUS-ALLEGANY BOCES

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TABLE OF CONTENTS

Background Information ..........................................................................................3-6 User’s Guide ...........................................................................................................7-9 Getting Acquainted ..................................................................................................10-18 Pen Pack ..........................................................................................................18 Sound ..............................................................................................................19 Software ..........................................................................................................20 Sensors ...........................................................................................................21-25 Beginner Activities Estimating Distance ..........................................................................................26 Estimation and Non-Standard Units of Measurement ......................................27-28 Addition and Subtraction on the Number Line ..................................................29-36 Intermediate Activities Introduction to Angular Units ............................................................................37-40 Using Roamer to Turn Angles ..........................................................................41-42 Locations on the Cartesian Coordinate Plane ..................................................43-50 Navigation Amazement ....................................................................................51-55 Creating Symmetry with the Roamer ................................................................56-59 Roamer Olympics I ...........................................................................................60-63 Roamer Mission to Mars ..................................................................................64-70 Additional Activities Miscellaneous .................................................................................................71-72 Using the Repeat Function ...............................................................................72 Using the Procedure Function ..........................................................................73 Using Sounds and Roamer Music ....................................................................73-74 Using the Pen Pack ..........................................................................................74-75 Beginner – The Three Billy Goats Gruff, Roamer Style ....................................76 Beginner – Traveling With the Grouchy Ladybug .............................................77 Beginner – Linear Units of Measurement I .......................................................78 Beginner – Estimations of Linear Measurements II ..........................................79 Intermediate – Scaling Up ................................................................................80 Intermediate – Using Roamer for Linear and Angular Movement ....................81 Advanced – Ice Cream Roamer Route .............................................................82-94 Roamer Music .................................................................................................94 Advanced – Orthographic Roamer Projections ...............................................95-96 Integrating Roamer Into Lessons Introduction to Linear Units ..............................................................................97 Introduction to Angular Units ............................................................................98

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Exploring Perimeter and Area ..........................................................................99-100 Geometric Shapes and Forms .........................................................................101 Programming Roamer to Make Shapes ...........................................................102 Roamer Equations ............................................................................................103-104

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ROAMER

What is Roamer? Roamer is an easy to use floor robot that can fire the imaginations of students and entice them to solve problems in math, science, ELA and technology. Roamer is programmed with logo-like commands, which are simple enough for preschoolers and sophisticated enough for high school students to write complex procedures. Roamer is a visual, kinesthetic tool that students can program and manipulate to explore their world. Roamer uses control technology to enable students to make decisions that can give immediate results or achieve long-term goals depending on the level (see control technology).

Why use Roamer in the classroom?

• Roamer supports brain-based instruction

• Hands-on

• Meaningful

• Novel

• Gives immediate feedback and evaluation

• Improves retention of content Students are given the opportunity to teach the robot, thereby enhancing the students’ own understanding of the material. Roamer takes abstract concepts and makes them concrete when dealing with new material. An example would be having students experience inside and outside angles of a triangle by having them program the roamer to draw various triangles. Roamer supports the New York State Learning Standards in:

• ELA by helping students read, write, listen and speak for information and understanding; literary response and expression; critical analysis and evaluation and social interaction.

• Math by developing conceptual understanding, procedural fluency and problem solving. It also successfully intertwines the new New York State mathematical content and process strands at all levels.

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• Roamer successfully integrates technology into all subject areas.

Seymour Papert, a mathematician who co-founded the MIT Artificial Intelligence Laboratory with Marvin Minsky, worked with the team that created the first version of Logo in 1967. He felt that knowledge was created and constructed by learners themselves as they interact with their environment. The Logo Programming Language was designed as a tool for learning. Its features - modularity, extensibility, interactivity, and flexibility -follow from this goal.

Logo puts the child in control of the computer. Rather than passively consuming digital content, Roamer tasks demand that children are actively involved in controlling the movements of the Roamer. In this regard children learn to teach the Roamer how to think and in doing so become aware of their own thinking. This approach allows children to develop and grow from their own mistakes and successes in the use of Logo, thus becoming aware of themselves as learners. Roamer promotes and encourages problem solving and investigative approaches. Roamer tasks can be embedded in problem-solving activities that may require the application of a range of strategies. Process of enquiry is an integral part of engagement with Roamer tasks. Roamer is not all about getting the correct answer all the time. By its very nature, engagement with the Roamer means that mistakes will appear in the commands that children program into the Roamer. The process of looking at the command procedure to find out where the error might be is a vital part of working with Roamer. Activities should encourage children to observe, hypothesis, test and readdress their thinking without fear of failure or negative feedback. Roamer fosters a collaborative philosophy. It is argued that we learn by doing things, but theorists such as Vygotsky take this a stage further by arguing that we learn even better by interacting with others and talking about what we have done and learned as they engage with Roamer/Logo activities. This collaboration philosophy can be further cemented by encouraging children to reflect and report on what they have learned to their peer group, teacher or any other appropriate audience. This can be seen as a celebration of achievement, but will more importantly allow children the opportunity to ensure that they have understood what they have learned in their engagement with the Roamer/LOGO task.

How can Roamer enrich and enhance learning? Roamer is highly motivational and student friendly. Roamer helps students to develop key skills such as counting, estimating and sequencing. More advanced or older students can learn about angles and to refine problem solving and thinking skills. As part of the industry’s expectations for new employees, workers will need the ability to set and solve problems as part of a team. Most Roamer activities involve students

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working collectively as part of a “think tank”. At other times the problem is sub-divided into individual tasks whose outcomes are integrated into a final solution. Workers will also need a broad understanding of mathematics and how it can be used to solve problems. Roamer is an object to think with. Students program it to solve problems that contain mathematical challenges and design. Activities that reflect an every day problem reveal the practicality of math and how relevant it is to our society. Future citizens will need to be flexible and constantly learning. Mathematical skill is a key ingredient in their ability to do this. Roamer develops life skills: problem solving, synthesis, and communication in a group-working environment. It is also an interdisciplinary tool that highlights the mathematical aspects of many different subjects. Students should become mathematical problem solvers. Activities should vary from simple tasks solvable in an hour to projects that can take days or weeks to complete. Problems with more than one right answer should be included. Roamer activities can be tailored to meet the specific needs of the teacher, student and timetable. Students should be encouraged to communicate mathematically by reading, writing and discussing the subject and their ideas about it. Roamer activities can present children with a first knowledge of a concept. Sometimes they do not have the language or knowledge to describe the situation, but readily express themselves in a language they find meaningful. Other aspects of Roamer work involve writing problem statements, discussing possible solutions and recording the progress to a solution. It is important that students develop mathematical reasoning and thinking skills. The attributes should be rewarded even more than “finding a right answer.” Roamer offers opportunities to develop an understanding of mathematical methods and fosters the fundamental mathematical thinking skills. With Roamer, children can try and see what happens, analyze results and see the consequences. They can have a theorem and test it, modify it, etc… Students mathematical literacy denotes their ability to explore, conjecture, reason logically, refine and develop ideas using a variety of mathematical consequences. The Roamer offers interesting opportunities to develop an understanding of mathematical methods. Many Roamer problems are solved by making an estimate and adopting a systematic method of adjustment to arrive at a satisfactory answer. The content and approach to mathematics should be appropriate to all students, irrespective of gender or race. Roamer is a creative tool that can be used in many different contexts. The same mathematical activity can be approached in many different ways. The activity can be defined by the teacher or by students as a means of self-expression or relevant to their circumstance. An important factor in achieving acceptance of math amongst a diverse populace is the ability of individuals to engage with the subject. Roamer is very successful at this. In

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many Roamer activities, students can set their own goals and decide when they’ve achieved them. Children can get a great thrill from controlling a robot and a real sense of achievement when they attain their objective. Mathematical knowledge often emerges from experience of problem solving. The essence of Roamer’s usefulness is the easy way a large range of problems can be set. The same problem can be presented in a simple or complex manner. Often the complexity grows the further the student explores the activity as they discover more mathematical problems. Sending Roamers on journeys is a typical problem enabling children to explore ideas of geometry, measurement and estimation. Once they’ve completed the journey, could they use Roamer to draw a map of it? This offers opportunities to explore the ideas of scale and similarity. The way mathematics is taught should include opportunities for appropriate project work; group work; discussion between teacher and students and among students; practice of mathematical methods; and exposition by the teacher. The many examples cited illustrate how Roamer can be used to meet the first three of these criteria. The last one is a matter for the teacher.

Areas of Concern When it comes to using Roamer in the classroom, there are three major obstacles to overcome depending on the age of the students. Many children don’t really understand directional language. Most know forward and back, but many get their right and their left mixed up and will need to learn the meaning of clockwise and counter-clockwise. Seeing the world from another perspective can also be a challenge. Imagine if you’re facing a student, your right is their left, and their right is your left. To program the Roamer successfully you have to be able to de-center. Students need to think of Roamer programming as though they are the Roamer. The shape of the Roamer can also be a source of confusion. As a hemispherical shape, it is difficult to tell the front from the back. Left and right only have meaning if you know which is the front and which is the back. The Roamer could be decorated with stickers such as eyes and a nose, in an effort to distinguish this. When the student is at the Roamer key pad and the numbers are in the upright position, the arrow pointing away from the student is pointing forward.

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HELPFUL START UP HINTS

Batteries A Roamer comes equipped with two (2) six volt rechargeable batteries with spring terminals only. Any other terminals will not work.

Warning When inserting and removing batteries be sure spring terminals are not caught under Roamer battery contact strips. To open Roamer only use a coin. Screwdrivers or knives will damage fasteners. Fasteners were especially designed for use with a coin. To replace the battery cover, turn and push fasteners using your thumb until they click into place. NEVER leave batteries in the Roamer when not in use or when transporting, remove the batteries. Roamer has a high amp shut down which is activated after the Roamer is sitting idle for five minutes. However, this does not shut the Roamer completely off and if left in this state, can (and will) run batteries down. You must turn the Roamer switch off by hand to prevent this from happening. Due to the weight of the batteries, if they are left in while transporting, they can (and will) damage the battery cover door. Also removing the batteries will prevent damage to the Roamer should the batteries leak.

Rechargeable Batteries: *Charge batteries after each full day of use and before first use. Never leave them in a discharged state.

Programming Hints: The natural response when first meeting a Roamer is to prod a few keys and see what happens. The Roamer’s keyboard, sound cues and simple programming structure support this exploratory process. With a minimum of teacher intervention children can achieve remarkable success. They quickly learn how to make the Roamer move about and make sounds.

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CM =Cancel Memory 90 = a quarter turn, or right angle

Δ = Forward GO = go

∇ = Backward R = repeat W = wait P= procedure

= Right [ ] = brackets

= Left CE = Cancel the last entry The exploratory work can lead to more purposeful work, where children program the Roamer to behave in a particular way; for example, teaching the Roamer to move through an obstacle course. As their expertise and confidence grows, children are able to tackle more substantial projects. Again, with its “Repeat” and “Procedure” facilities, the Roamer supports these developments. Your Roamer comes with a built in Demonstration Program, which is activated when the Roamer is turned on. However, to bypass the demo for instant programming, after turning your Roamer on just press Clear Memory (CM,CM) twice and you are ready to do your own programming without having to run the demo first.

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Demonstration Program If you press GO after you switch on the Roamer, it will carry out the Demonstration Program. This can be used to show beginners the basic Roamer functions. Remember to clear the Demonstration Program from the GO Memory before programming.

Teaching the Roamer The Roamer moves forward and back, turns left and right, waits and makes sounds. You teach the Roamer to do this by pressing keys on the top of its body. There is a key for each of these functions, and a set of number keys. To enter an instruction press a key followed by a number. This tells the Roamer how far to move, how much to turn, how long to wait or what sound to make. There are three other function keys: Sense, Two-State Outputs and Stepper Motor. These are more advanced functions covered in another section. It is advisable to write programs down on paper first, then to key them into the Roamer. With young students or with complex programs, it is advisable to have students walk through the Roamer program before entering the program codes into the Roamer. There are several positive results to be gained from this disciple:

1. It develops planning and thinking skills. 2. It develops the important skill of recording information. 3. It provides the child and the teacher with a record of their programs and the

processes involved in achieving their objectives.

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Ready to GO Switch on your Roamer and press GO. What did it do? Roamers remember what you tell them to do. They do it when you press GO. They forget when you press CM, CM. Try making your Roamer move forward. (You must tell it how far.) Try to discover how to make it turn.

Ready to Learn What do you want the Roamer to do? Tell the Roamer to do three or four things, one after the other. Add a couple more things to what it’s already done. What happens if your press CE? And then press GO? Clear the memory (CM CM) and teach the Roamer something else.

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Roamer Programs There are two types of programs, the GO Program and Procedures. The GO Program is a list of instructions carried out when you press GO. A Procedure is a list of instructions with a name. Once you have defined the list, its name (e.g. P1) is used like any other instruction. When you enter its name in the GO program, the Roamer will carry out the whole procedure list.

What is the GO program? This is a term that you will see from time to time when you are setting up the different programs for the Roamer. It simply means that after you setup a program you must run it before the instructions you gave it become effective or locked into place in the GO memory. This will become clearer to you as we will be using our Changing the Units of Distance, Units of Turn and so on.

Memory The Roamer has two types of memory, GO Memory and Procedure Memory. The Roamer will remember up to 59 instructions, and its powerful programming facilities enable it to carry out hundreds of actions. When its memory is nearly full the Roamer will sound a warning, similar to the sound you hear when you press CM.

GO Memory Instructions in the GO Memory are carried out when you press GO. If you add more instructions after executing the GO program, they will be added to the GO Program and carried out the next time you press GO. The Roamer waits for two seconds after you press GO before executing the GO Program.

Clearing the GO Memory Pressing CM CM clears the GO Memory and allows you to enter a new GO Program. It does not clear the Procedure Memory. The first time you press CM a warning is sounded. Pressing CM a second time clears the GO Memory.

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If you press CM by mistake, press another key, or wait 10 seconds. The Roamer will then carry on with its GO Memory intact.

Δ Forward and ∇ Back

Pressing Δ or ∇ followed by number from 1 to 99 tells the Roamer to move forward or

back that number of units.

Right and Left Turn

Pressing or followed by a number up to 999 turns the Roamer to the right (clockwise) or left (counterclockwise) that number of units.

Wait Pressing W followed by a number from 1 to 99 tells the Roamer to be still and quiet for that number of seconds.

Units of Distance and Turns When you switch the Roamer on it moves forward and back in units equal to its body length (30 cm) and turns in angular units of 1 degree. You can change the units of distance and turn. This allows the teacher to set the most appropriate units for each teaching period. Once the units are set, they remain unchanged until you redefine them, or switch the Roamer off. Clearing the GO Memory does not change the last unit setting. Changing the Units of Distance

To change the unit of distance, press Δ or ∇ followed by [ ].

Then press a number between 1 and 99. The number determines how many centimeters will be in each unit of distance. Then press [ ] again. The GO Program must run before the change becomes effective.

i.e. Δ1 Moves the Roamer forward 30 cm (the default setting).

Δ [10] Sets the units of distance to 10 cm.

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∇ 2 Moves the Roamer back 20 cm.

∇ [1] Sets the units of distance to 1 cm.

Δ 5 Moves the Roamer forward 5 cm.

GO, GO When GO is pressed a second time, the first instruction Δ 1

moves the Roamer forward 1 cm, in accordance with the last setting ∇1. Changing units of Turn

To change the units of Turn, press or followed by [ ]. Then press a number from 1 to 999. This number determines how many degrees will be in each unit of turn. Then press [ ] again. The GO Program must run before the change becomes effective.

i.e. [90] Sets the unit of turn to 90.

2 Turns the Roamer 180 to the left. GO

Sound Cues When you press a key, the Roamer makes a sound. If the instruction is valid the sound is positive. Invalid instructions produce a negative sound.

i.e. Δ1Gives two positive sounds.

9 Gives a positive, a negative then a positive sound. The Roamer turns right 9 units.

90 Gives three positive sounds. GO Gives a positive sound, followed by a 2 second pause, the Roamer moves forward 1 unit, turns right 9 and then left 90 units.

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Stopping the Roamer If the Roamer is carrying out a list of instructions and you want to stop it before it has finished, hold down any key until it completes the current instruction. This feature allows children to stop the Roamer if it is not doing what they wanted it to.

CE – Cancel Entry Pressing CE cancels the last instruction or part instruction from the GO Program.

i.e. 40

∇ Back key pressed in error.

CE Cancels the last entry, ∇.

Δ3

90 GO The Roamer turns left 40, moves forward 3 and turns right 90.

CE Cancels the last entry, 90. GO The Roamer turns left 40 and moves forward 3.

CE Cancels the last entry, Δ3.

GO The Roamer turns left 40.

R – Repeat Pressing R, followed by a number up to 99, will make the Roamer repeat a following list of instructions, that number of times. The list must be enclosed in a “box” by placing [ ] before and after the list. Repeat lists can contain other repeat lists. This is like putting one box inside another. You can place up to five “boxes” within “boxes”. I.e. Nest repeats 5 deep. i.e. R 6 [ Start the first repeat.

60 R 4 [ Start second repeat.

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81 ] End second repeat. ] End first repeat. GO The Roamer turns through 360 units. Every 60 units it stops

and plays 2 notes, 4 times.

Procedures A procedure is a list of instructions named P, plus a number from 1 to 99. The list is enclosed in brackets [ ]. Roamer Procedures have four distinct advantages. Procedures support “Bottom Up” programming. The “Bottom Up” programming approach is to solve new programs using existing knowledge. If the Roamer has been taught a procedure, it can be used in the performance of new tasks. Procedures facilitate “Top Down” problem solving. The “Top Down” approach of dividing a complex program into smaller, more manageable problems is an important life skill. The Roamer’s Procedure facility encourages this approach. Procedures increase the Roamer’s action capacity. By entering procedures into the GO Memory, the Roamer can carry out each procedure while only taking up a single instruction. Procedures simplify the process of changing a program. To change a GO Program, the GO Memory must be cleared and the whole list must be re-keyed with the modified instructions. If instructions are entered as procedures, only the procedures need to be redefined. i.e. P 4 [ Starts the definition of Procedure 4.

Δ3 First instruction of P4.

90 Second instruction of P4. ] Ends the definition of P4. GO Nothing happens. P4 is not yet part of the GO Program. P4 Enters P4 in the GO Program. GO P4 is executed: forward 3 left 90. CM, CM Removes P4 from the GO Program but leaves it in the

Procedure Memory.

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When keying in instructions in a procedure definition, sound cues for valid and invalid instructions are still made. However a different pitch is used to inform the programmer that the instructions are part of a procedure, not part of a GO Program. Putting a Procedure Inside Another Procedure A procedure can be part of another procedure. i.e. P1 [ Starts definition of Procedure 1.

P4 Procedure 4 (already defined) is the first instruction in P1.

P9 Procedure 9 (as yet undefined), is the second instruction in P1.

Δ3 The third instruction in P1.

] Ends the definition of Procedure 1. P1 Puts Procedure 1 in the GO Memory GO The Roamer executers P4. Since P9 is undefined, the

Roamer will ignore it before executing the last instruction Δ3.

P9 [ Starts definition of Procedure 9. R4 [

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18 ] Ends the Repeat list. ] Ends the definition of Procedure 9. GO The Roamer executes P4, then P9, and finally moves

forward 3 units.

Procedures can be nested to any depth – memory permitting.

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Changing a Procedure To change a procedure, simply redefine it. i.e. P6 Starts definition of P6.

Δ50

W10

20

]

P6 Enters P6 into the GO Program.

GO The Roamer moves forward 50, waits 10 seconds, and turns right 20.

P6 [ Redefines P6.

∇7 ] GO P6 is still in the GO Program and executes the new

definition: back 7.

Erasing a Procedure To erase a procedure from the Procedure Memory, enter P and the procedure number, followed by [ ] and [ ]. i.e. P12 [

R4[

Δ10

90

] P12

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GO The Roamer moves in a square pattern. P12 [ ] Erases the definition of P 12. GO Nothing happens because P12 in now undefined. Rules about Using Procedures 1. A procedure cannot use itself. Roamer procedures are not recursive. 2. You can only define one procedure at a time. 3. A procedure cannot include a procedure with a lower number. This means that Procedure 1 can call all other procedures, and Procedure 99 cannot call any.

Pen Pack Your Roamer comes with 4 penholders, 12 Stick pens, 3 pen brackets, 6 M3 x 12 pozi-drive screws for fitting the Pen Brackets to the Roamer, and a Roamer Pen Pack Activity Book. To fit a pen into a Roamer, push it into a Pen Holder and drop it into the hole in the center of the Roamer. If you want the Roamer to draw with more than one pen, screw the brackets to brass bushes on the underside of the Roamer.

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Sound The Roamer has a programmable sound facility. You need to specify how long each note will last (duration) and how high or low the note will be (pitch).

The play a note, press followed by a number from 1 to 8 for its duration, and another number from 1 to 13 for its pitch. If you want a rest (silent note), enter 14 for the pitch. Changing the tempo and octave Roamer sounds may be played at one of five tempos and one of three octaves. To

change the tempo or octave press then press [ ]. Press a number between 1 and 5 for the tempo. 1 is the fastest, 5 is the slowest. Press a number between 1 and 3 for the octave. 1 is lowest, 3 is highest. Press [ ] again.

i.e. [11] Sets the fastest tempo and the lowest octave.

11 Plays the Roamer’s lowest, shortest note.

[53] Sets the slowest tempo and the highest octave.

813 Plays the Roamer’s highest, longest note. When you press GO, the Roamer starts with the tempo set at 3 and the octave set at 2.

Musical equivalents When defining the pitch, 1 = C, 2 = C#, 3 = D, 4 = D#, 5 = E, 6 = F, 7 = F#, 8 = G, 9 = G#, 10 = A, 11 = A#, 12 = B, 13 = C, 14 = REST. C# = D flat D# = E flat F# = G flat G# = A flat A# = B flat When defining the duration, 1 is equivalent to a sixteenth note (semi-quaver), 2 is equivalent to a eighth note (quaver), 3 is equivalent to a quarter note (crochet), 6 is equivalent to a half note, and 8 is equivalent to a whole note. Setting the tempo at 1 produces 170 beats per minute; 2,3,4 and 5 produce 140, 100, 80 and 60 beats per minute respectively.

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Roamer World Software

As students develop their programming skills, they soon realize the limitations of the Roamer. They can’t review what they’ve entered. They can’t correct errors or insert commands without starting all over again. Worst of all, they can’t print or save their work. In fact, all is not lost. These are precisely the things computers allow us to do with its display, hard drive and printer. Roamer World is the software that enables students to view, change, print and store their “GO Programs”. Roamer World is an educational software package based on the programming of a floor Roamer. The students control the movement of the onscreen Roamer by a sequence of commands. It has been produced to give students their first experience of writing a computer program. Before using this program students will need to have had experiences with simple directions and measurement. Remember that Roamer World is a simulation of programming the Roamer itself. The keyboard cannot be used. Click on the Roamer control panel to enter instructions. To insert an instruction, select the line ABOVE where you want the new line to appear. After making changes, send the GO Program back to the Roamer. In addition to the software, you can use a connecting lead to transfer GO Programs between the computer and the floor Roamer. Both have been provided for you in this kit. Once you are connected, the process is simple. Click on Roamer and select the menu option you wish to use - Copy Go Program from Roamer or Send Go Program to Roamer.

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SENSORS (These items must be requested, they do not come standard in the Roamer kit)

Roamer and Control Technology Control Technology provides many educational opportunities. With the Roamer, Control Technology becomes a natural extension of design work. Again, it is important to have a design brief, which will be altered and appraised from time to time in the development of solving the problem posed. The Control Technology accessories include a control box (which is a necessity), a light pack, sensor and motor pack. This section will include designing using the control accessories as well as how they work in the development of control procedures, which are recommended at level 5 and above. However, some younger students who have a knowledge and experience of lights and motors may find the work easy to understand. About the Control Packs The Roamer control box – is a small flat box that attaches underneath the Roamer. This allows you to control up to 4 Outputs (for motors, bulbs, LED’s, etc.), a Stepper Motor drive (for use with moving an arm, etc.), an Input control for sensors and a Power line for sensors. Obviously, using all of these will decrease dramatically the battery charge, so it is wise to have spare batteries on hand or on charge. The Light pack – consists of 8 bulb units, a flasher unit, two lamps and an activity book. The Sensor pack – consists of a light sensor, sound sensor, 2 touch sensors, a push button sensor and 2 suction pads plus an activity book. The Motor unit –attaches through wires from the control box. A standard electrical motor will work as well. The pack also has a Stepper motor that is useful when wanting a pulsing type action. This also comes with an activity book. The Roamer and Control Once you have attached the Control Box to the Roamer, the robot can take on a totally different appearance. It can become a sophisticated control device capable of introducing control work to primary age children and also giving valuable challenges to children from secondary schools. To introduce children to using control mechanisms is not as daunting as many feel. It is a lot easier than logo or using a buffer box. The Roamer control language uses very basic terms, “High and Low”.

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For example: - to turn a light on, the procedure would be T 1 2 -- T = turn on control 1 = specifies which Output on the Control Box 2 = High meaning ON T 1 1 – T = turn on control 1 = Output 1 2 = Low meaning OFF The order must always be T + Output number + High or Low To develop this further – program the Roamer to move then turn a light on then off before moving again. To make the motor turn in either direction it must be connected to 2 Output terminals (for example 2 and 4). Stepper Motors

Stepper motors are an invaluable aid with the Roamer. Whereas the DC Motor will move only clockwise or counter-clockwise, the stepper motor can be programmed to move in “pulses”. Each pulse turns the motor 1 step. The Roamer can be programmed to drive the “pulsing” for this. When the stepper motor is not turning, it is help in place by a braking force, but this tends to use quite a lot of battery power, so beware! To program the stepper motor: M1 – will move the stepper motor clockwise M2 – will move the stepper motor counterclockwise Once you have chosen which way you wish to turn it needs to be told the number of steps required. Enter a number between 1 and 999 for the number of steps. Important: The Roamer cannot move, turn or make a sound while it is using the stepper motor, but the Outputs for lights still work. Using the Stepper motor you can have a lot of fun with the Roamer – 3 examples Valiant suggest in their activity book are as follows: - Changing the Roamer into a Strong Man with Stepper motor “lifting” the dumb bells attached via an arm. - Using Meccano to build a crane model which can be attached to the Roamer.

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- Similar to the first model would be an arm which has a hat attached that the stepper motor could raise up and down as the Roamer meets new people. Let’s look at the Strong Man Procedure: R 4 – repeat 4 times [ M 1 4 5 – stepper motor switches on and moves 45 steps clockwise. Strong Man raises dumb bells. W 3 – waits 3 seconds M 2 4 5 – Stepper motor turns 45 steps counterclockwise. Strong Man lowers dumb bells. ] GO Important: Should you wish to move continuously, omit W 3 Writing programs with Outputs and Stepper instructions can be used anywhere in the GO program including a repeat instruction or in a procedure instruction. Sensors Using the Sensor control unit, children can program Roamer to react to its environment, by switching the lights on when moving into a darkened area. For children to understand how and what sensors are they could look at how animals, humans and plants use senses and sensors to live. For example, bats have a near radar sense to detect things in the dark, whereas a bird or prey can detect small mammals at great distances. Sensors in inanimate objects are a little different. Children could be encouraged to look at things around them. (Automatic doors, remote controls, timers on microwaves, etc.) The Roamer’s sensor system can recognize a signal and will respond by executing a “sense procedure”. A sense instruction tells the Roamer which Input signal to recognize and which sense procedure to execute.

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The Roamer can be programmed to recognize – A high to low change (light to dark) A low to high change (dark to light) Low to high or high to low (either light to dark to dark to light change) A sense procedure is likely any other Roamer procedure, except it is referred to in sense instruction and should not be used as part of the normal program you want the Roamer to perform. When the Roamer executes a sense instruction, it remembers what type of signal to recognize, and which procedure to execute if the signal occurs. It will then continue to perform the rest of the program. Likewise, if it receives the correct signal, it will immediately stop the GO program and execute the sense procedure. It will then continue with the GO program when sense procedure stops. To try and put the above in some sort of context, imagine the Roamer is a dog you are training to respond to whistles. Get the children to write a simple GO program that moves the Roamer around. Attach a sound sensor. Now enter the following - S 3 1 – Program the Roamer to recognize either a high to low signal or low to high signal and respond executing sense procedure 1 W 10 – wait 10 seconds (This is the sense instructions) now enter the GO program The Roamer “dog” should respond the a whistle and stop whenever you want it, but after 10 seconds return to its original GO program. Another activity that you could suggest to children would be to transform the Roamer into a car using two lights for headlights and attaching a Light sensor to it. The children could then be asked to write a program to move around a darkened room with the lights on, but when an electric light is switched on (daylight) the sensor would react and turn the headlights off.

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The sense instruction might be like this:

Δ 3

T 12 T 22

Δ 4

T 11 T 21

Δ 3

GO S 13 R 4

[ Δ 3

90] Sense Procedure P 3 [T 12] Alternatives could be to use a “Touch sensor” which can be programmed so that if the Roamer touched a wall or object it will stop and alter its tracks. The more you experiment with the Roamer control work the more interesting and wider ranging the possibilities become.

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Beginner: Estimating Distance Objective: To have students come to an accurate conclusion on how far Roamer must move to travel different distances.

How far must Roamer travel before he pops a balloon? Rather than having students measure precisely to achieve accurate results, estimation is often a useful skill. Estimation is using the information available and any prior knowledge to make a sensible approximation or guess. With the balloons in place on the wall and paper clips attached to Roamer, place Roamer a distance away from the balloons. Ask students to estimate the number of steps Roamer must take in order to pop a balloon. Mark your starting point on the floor with a piece of masking tape. Now test the number by programming the Roamer. Did Roamer reach and pop the balloons? Or did he fall short? Or go to far? Adjust and start over making adjustments as needed until a correct answer is found. Now move Roamer to another starting point and mark the new position with tape on the floor. Make and test estimations until the second balloon pops. For the third balloon, position Roamer somewhere between the first two pieces of tape on the floor. Mark this new point with a piece of tape. With the prior knowledge now of how much it took from the more distant and closer points come up with an accurate estimation by only guessing numbers between those estimations. How many guesses did this take? Did you get the balloon to pop on your first try?

Materials: Roamer with batteries 2 paper clips 3 balloons masking tape Preparation: Read background information on how to use and program Roamer. Batteries should be charged so they are ready to be used. Inflate balloons and tape end to end. Attach balloons to wall near floor using masking tape. Straighten and attach the paper clips to front of Roamer side by side. Basic Skills Development: Estimating Distance Trial and Error

27

Beginner: Estimation and Non-Standard Units of Measurement

Objective: To provide students opportunities to make comparisons between estimated measurements using non-standard units of measure and to use the Roamer Robot to estimate distances.

For the first activities in this learning experience, it is preferred to have the Roamer batteries uninstalled. Mark out a distance of about 3 meters. Have students estimate how many Roamer lengths it would take to cover the distances versus how many of their own footsteps. Have students make the measurements in footsteps and Roamer lengths. Repeat the process with their paces versus Roamer units and compare the results. Lead a discussion on which method of measurement may be more accurate and why. (footsteps and paces will vary) Repeat the process with different distances, non-standard units (pencils, erasers), and the Roamer. Program the Roamer to move forward 1 to 5 Roamer units. Have students measure the distance in order to discover that the default setting for Roamer is one Roamer in length. Direct the students to sit in a circle and then estimate the distance from one student to another. Have them program the Roamer to go to a student sitting across from them using their estimations of the distance between themselves and the other student. Have the student receiving the Roamer send Roamer onto a different student. Change the Roamer unit distance setting. Program the Roamer to move forward 1 to 5 of the new Roamer distances. Again, have the class send the Roamer across the circle to another student using the new Roamer unit setting. Depending on the class, you may want to measure the error in the actual distance and the estimated distance. Record the data to discover who had the least error in their estimations.

Materials: For the class: Meter Stick* Roamer A variety objects from the classroom Pencils Erasers Any object that can be used as a non-standard measuring tool For each student: Journal* *provided by teacher Basic Skills Development: Analysis, Inquiry and Design Information Systems Mathematics Interdisciplinary Problem Solving Language for Literary Response and Expression Preparation: Number concepts and estimating Preliminary steps to programming Roamer. Space is needed in the classroom for this series of activities. If there is not enough classroom space consider moving this series of activities into the hallway. A review lesson on programming the Roamer may be needed. Student should be provide access to programming handouts.

28

Estimation and Non-Standard Units of Measurement continued Page 2

Extension: Use Roamer’s distance unit setting to allow Roamer to move in small units (footsteps). Use this distance (footsteps) setting to measure the distance between two objects. Program the Roamer to move between the two objects. Set Roamer’s distance setting to allow Roamer to move in large units (paces). Use this distance setting to measure the distance between two objects. Program the Roamer to move between the two objects. Compare the results from estimations of distances using various methods of measurement - Roamer movements, footsteps, paces, and standard units of measure.

Evaluation Strategy: Given various non-standard/ standard measurement tools and the Roamer Robot, students will be accurately record and present a measurement for each activity. Students will estimate various distances, program instructions for the Roamer and move the Roamer to pre-determined positions.

29

Beginner: Addition and Subtraction on the Number Line

Objective: To provide students hands-on experiences with graphing numbers, finding coordinates of points, and determining solutions to addition and subtraction problems on the number line. A Roamer size number line will be generated for program evaluation.

How does Roamer use the number line to do addition and subtraction? Numbers can be represented as points on a number line. We can program a Roamer to move along a number line and perform addition and subtraction problems. To construct a number line, you draw a line and mark the origin. Label this mark 0 (zero). Determine a unit length and mark off units to the right of the origin and label them consecutively 1,2,3,4,5,,,, Now do the same to the left of the origin and label them consecutively 1,2,3,4,5,,,,

The number line extends indefinitely in both directions, which are indicated by the arrowheads. Introduce the construction of the number line to the class. As a learning experience, determine the familiarity of the mathematics terminology of your class. For example, does anyone know what a negative number looks like? You may use the terms origin, number line, positive, negative, arrowheads and unit length as vocabulary words. Review these terms daily so the vocabulary becomes familiar to the students. The number line will be used in graphing numbers, and identifying the coordinates or locations of points. Each point on the number line (usually labeled with capital letters) is called a graph of the number that corresponds to it. The number itself is called the coordinate of the point. See copies provided for questions on the Number Line. You and your class will create a number line on the floor of your classroom, using masking tape and a measurement device that produces the proper scale for the Roamer to show-off its addition and

Now try writing another program

to make a smaller rectangle.

Write your program here.

Write your program here.

Now try writing another program

to make a larger triangle.

Write your program here.

Try out this program.

Materials: Roamer Number line transparency Masking tape Measurement Devices Number cards List of Addition/Subtraction Problems to Solve For each student: Number Line Copy Journal* *provided by the teacher Preparation: Students will scale and proportion, count in numeric order, comparison of numbers, addition of numbers, subtraction of numbers. New mathematics terminology include the number line, origin, positive numbers, negative numbers, graphs of numbers, coordinates of points. Clean space will be needed on the floor or table top so that an appropriate scaled number line can be created for use with the Roamer. Adaptive devices may be required for children with special needs.

30

Addition and Subtraction on the Number Line continued Page 2

subtraction skills. Remember the standard Roamer unit is 30 cm. For Kindergarten and first grade a number line from 0 to 10 will work well. For second and third grade, a number line from -10 to 10 is needed. And for grades four and up a number line with an x and y-axis is needed with each numbered –10 to 10.

Kindergarten and First Grade Once you have successfully created the Roamer number line, you can lead the class in a simple problem by programming the Roamer to move forward for adding numbers, and backward for subtracting numbers. Example: 2 + 3 – 4 =? Solution: Remember to always begin a problem with the Roamer on the origin of the number line, 0. Program the Roamer to move forward 2 units, forward 3 units, and backward 4 units. The Roamer should end up on 1. The solution to 2 + 3 – 4 = 1. A sheet of addition/subtraction problems with their solutions are available, but student developed problems are highly encouraged and could be used for assessment. Allow students to determine the solutions of the problems using their copied versions of the number line before actually programming the Roamer to perform the solutions. Have students show their solutions and programs to each other for feedback and critical analysis. Students can then evaluate the success of programs before the Roamer performs them. Students will keep a journal of the mathematics terminology and their interpretations that have been introduced and used. They may also wish to display their problems and solutions of Roamer programs used with the number line.

Evaluation Strategy: Students can be assessed with similar addition/subtraction problems, as well as encouraged to create and solve their own problems, or that of a friends.

31

Addition and Subtraction on the Number Line Continued Page 3

Second and Third Grade

Other than addition and subtraction, the number line can be used in graphing numbers and identifying the coordinates or location of points. Each point on the number line (usually labeled with capital letters) is called a graph of the number that corresponds to it. The number itself is called the coordinate of the point. Example:

Solution: The coordinate of point A is –4 and the coordinate of point B is 2.

Using Roamer as the coordinate, give students a point on the number line to travel to. Starting at 0 tell students to travel to –4. Now give students another point on the number line to travel to. Fourth Grade and Up For older students, a number line can be used to graph coordinates using an x-axis and a y-axis. When writing coordinates, they are written in parenthesis with the x -axis given first, followed by a comma, and then the y-axis. Example:

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Addition and Subtraction on the Number Line continued Page 4 Solution: 2 is the coordinate on the x-axis and –4 is the coordinate on the y-axis. So the coordinates for point A would be written as (2,-4). Using Roamer give students a point on the number line to travel to, beginning with the x-axis. Starting at 0 tell students to travel to 2. Now tell students the y-axis point, -4 to travel to. Their program should look like, Forward 2, Right 90, Forward 4. Another way to write this would also be Forward 2, Left 90, Backward 4. Give students coordinates and have them program Roamer to travel to those points. Or have students write programs to travel around the number line, and where they stop they must give their coordinates.

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0 1 2 3 4 5

6 7 8 9 10

-1 -2 -3 -4 -5

-6 -7 -8 -9 -10

34

Addition and Subtraction Problems For The Roamer On The Number Line

1) 2 + 3 - 4 = ? Program ___________________________________ Solution ___ 2) 3 - 6 + 8 = ? Program ___________________________________ Solution ___ 3) 1 + 5 - 3 = ? Program ___________________________________ Solution ___ 4) 4 - 9 - 2 = ? Program ___________________________________ Solution ___ 5) 8 + 1 - 4 - 4 = ? Program ___________________________________ Solution ___ 6) -2 + 3 - 4 + 5 = ? Program ___________________________________ Solution ___ 7) -4 + 3 - 4 + 3 = ? Program ___________________________________ Solution ___ 8) -3 + 2 - 4 - 2 = ? Program ___________________________________ Solution ___ 9) 5 - 6 - 2 + 3 = ? Program ___________________________________ Solution ___ 10) 9 - 2 - 7 - 6 + 5 - 4 = ? Program ___________________________________ Solution ___

35

Addition and Subtraction Answers For The Roamer On The Number Line

1) 2 + 3 - 4 = ? Program ∆2, ∆3, ∇4 Solution 1

2) 3 - 6 + 8 = ? Program ∆3, ∇6, ∆8 Solution 5

3) 1 + 5 - 3 = ? Program ∆1, ∆5, ∇3 Solution 3

4) 4 - 9 - 2 = ? Program ∆4, ∇9, ∇2 Solution -7

5) 8 + 1 - 4 - 4 = ? Program ∆8, ∆1, ∇4, ∇4 Solution 1

6) -2 + 3 - 4 + 5 = ? Program ∇2, ∆3, ∇4, ∆5

Solution 2

7) -4 + 3 - 4 + 3 = ? Program ∇4, ∆3, ∇4, ∆3 Solution -2

8) -3 + 2 - 4 - 2 = ? Program ∇3, ∆2, ∇4, ∇2 Solution -7

9) 5 - 6 - 2 + 3 = ? Program ∆5, ∇6, ∇2, ∆3 Solution 0

10) 9 - 2 - 7 - 6 + 5 - 4 = ? Program ∆9, ∇2, ∇7, ∇6, ∆5, ∇4 Solution -5

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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Origin Negative Numbers Positive Numbers

The Number Line

A B C D E

Questions for the Number Line: 1. What is the coordinate for point A? Answer: 3 2. What is the coordinate for point B?

Answer: 3. What is the coordinate for point C?

Answer: 4. What is the coordinate for point D?

Answer: 5. What is the coordinate for point E? Answer:

-5 -4 -3 -2 -1 0 1 2 3 4 5

Use the Number Line to the right to answer the following questions.

6. Show the graph of -5, and label the point F. 7. Show the graph of 5, and label the point G. 8. Show the graph of -2, and label the point H. 9. Show the graph of 3, and label the point I. 10. Show the graph of 1/2, and label the point J.

37

Intermediate: Introduction to Angular Units Objective: Students with gain concrete experience in determining the angles present in everyday objects.

What are the angles of various objects? Review with the class the various types of angles (90, 45, 60, 30). This may be a good time to review a history of measurement and degrees. Hand out the Angle Munchers and have students measure various angles within the classroom. Use the Pattern Blocks as an object that has angles to measure. Have them record the item and the degree of the angle. Have class measure both interior angles and exterior angles. Classify the angled items according to the degree of the angle. Using the circular protractors have the class estimate the degrees they would have to turn to turn a square corner. Le them refer back to the Angle Munchers once they have recorded their estimations to verify if they are close to the correct angle. Using the circular protractors have the class estimate the degrees they would have to turn to turn half the way around. Let the class test their estimates. Using the circular protractors have the class estimate the degrees they would have to turn to turn all the way around. Let the class test their estimates.

As a class, have students sit around in a circle. Students will estimate the central angle to get the Roamer to another person. Students will continue to keep journals of their experiences using angle measurement tools. They will respond to the question on what the thought processes was when trying to find and make angle measurements. Extension: Compare the results from estimations of angles using the various methods of measurement – angles between the fingers, bending body measurements, angle of the sun at various times.

Materials: For the class: Angle Munchers Items with Different Types of Angles Circular Protractors Pattern Blocks For each student: Journal* *provided by teacher Basic Skills Development: Analysis, Inquiry, and Design Mathematics Interdisciplinary Problem Solving Language for Literary Expression Preparation: Students will gain preliminary knowledge base on angles – estimating. Space will be needed in the classroom to allow for movement and to get to odd shaped angles and objects. Adaptive devices may be required for children with special needs. Evaluation Strategy: Given various non-standard/ standard measurement tools (e.g. Angle Munchers and Protractors), students will accurately record and present angle measurements for each learning experience.

38

Transversal

Two Parallel Lines cut by a Transversal.

These Corresponding angles are congruent.

Transversal

These Alternate Interior angles are also congruent.

Two Parallel Lines cut by a Transversal.

Two supplementary angles.

Their sum = 180°

Notice a straight line consists of a

straight angle = 180°

60° 120°

63°

63°

117°

117°

Supplementary Angles

Alternate Interior

Corresponding Angles

Acute angle, less than 90° Right angle, equal to 90° Obtuse angle, greater than 90°

39

1. There are four pairs of Corresponding angles in the figure above. Can you name them all? 2. Measure one Corresponding angle pair with a protractor, then measure another pair. What is true of each pair? 3. There are two pairs of Alternate Interior angles in the figure above. Can you name them? 4. Measure one Alternate Interior angle pair with a protractor, then measure another pair. What is true of each pair? 5. Can you find any supplementary angles in the figure above? If so, how many are there and can you name them all?

Transversal

Two Parallel Lines cut by a Transversal.

a b

c d

x z

w y

40

Transversal

Two Parallel Lines

cut by a Transversal.

a b

c d

x z

w y

1. There are four pairs of Corresponding angles in the figure above. Can you name them all?

∠b and ∠y, ∠z and ∠d, ∠a and ∠w, ∠x and ∠c 2. Measure one Corresponding angle pair with a protractor, then measure another pair. What is true of each pair?

∠b and ∠y both measure 45° ∠x and ∠c both also measure 45°

∠a and ∠w both measure 135° ∠z and ∠d both also measure 135° 3. There are two pairs of Alternate Interior angles in the figure above. Can you name them?

∠z and ∠w ∠x and ∠y 4. Measure one Alternate Interior angle pair with a protractor, then measure another pair. What is true of each pair?

∠z and ∠w both measure 135° ∠x and ∠y both measure 45° 5. Can you find any supplementary angles in the figure above? If so, how many are there and can you name them all? There are 8 adjacent (next to) supplementary angle pairs:

∠a and ∠b, ∠x and ∠z, ∠w and ∠y, ∠c and ∠d,

∠b and ∠z, ∠y and ∠d, ∠a and ∠x, ∠w and ∠c

But any angle combination that adds up to 180° are supplements to each other, therefore there are 8 more supplementary angle pairs:

∠a and ∠y, ∠a and ∠c, ∠c and ∠z, ∠y and ∠z,

∠w and ∠x, ∠b and ∠w, ∠b and ∠d, ∠d and ∠x

41

Intermediate: Using Roamer to Turn Angles Objective: To provide students opportunities to learn to use Roamer to estimate angles and distances.

Using Roamer and/or the computer and Roamer World software, program Roamer to turn half the way around clockwise. Then, turn half way around counter-clockwise. Finally, turn all the way around counter-clockwise. Have the class identify the kinds of angles being used in this programming. (They can refer back to the circular protractors for help.) For each of the following activities allow enough time for each student to have a turn at programming each of the steps. Send the Roamer to a friend. As part of the program have the Roamer turn clockwise one half the way around and return to the sender. Identify the angle that was programmed into Roamer. Program the Roamer to turn one quarter of the way clockwise. Send Roamer to another person. Identify the person the Roamer is supposed to reach. Identify the angle that was programmed into Roamer. Program the Roamer to turn one quarter of the way counter-clockwise. Send Roamer to another person. Identify the person the Roamer is supposed to reach. Identify the angle that was programmed into Roamer. Students will continue to keep journals of running records of their experiences using Roamer to estimate distances and angles. They will respond to the question of how the thought processes that went on when trying to adjust the distances and angles for Roamer to more closely match the distances between students. Extension: Compare the results from estimations of distances and angles using the various methods of measurement - Roamer Robot movements, footsteps, strides, and standard units of measure. Students will reflect in their journals about their experiences in attempting to get Roamer to go to the person they indicated.

Materials: For the class: Roamer Computer with Roamer Software Package Installed Navigation Compasses Angle Munchers Circular Protractors For each student: Journal* *provided by teacher Basic Skills Development: Analysis, Inquiry and Design Mathematics Interdisciplinary Problem Solving Language for Information and Understanding Language for Literary Response and Expression Preparation: Working knowledge of angles, programming knowledge of Roamer, understanding of directional terminology (clockwise / counter-clockwise) Space large enough in the classroom or other space to have the Roamer move various distances. There is also a need for enough space for the class to form one to two circles, depending upon the number of Roamer available to use in the classroom. Adaptive devices may be required for children with special needs.

42

Using Roamer to Turn Angles continued Page 2

Evaluation Strategy: Given various non-standard/ standard measurement tools and the Roamer Robot, students will be accurately record and present angle measurements for each activity. Students will estimate various distances and angles, program instructions for the Roamer and move the Roamer to determined positions.

43

Intermediate: Locations on the Cartesian Coordinate Plane

Objective: To provide students with hand-on experience in programming the Roamer to move from one precise location to another. Students become familiar with horizontal and vertical number lines and how they combine together to plot a specific location.

It is the graphing of points on the Cartesian or coordinate plane that allows us to draw graphs or pictures of algebraic equations. We can also use the coordinate system to identify a specific location, and therefore give a set of directions. The Cartesian plane is simply a grid, such as graph paper, with certain numbers naming certain lines and the intersections of the lines. The numbers that name the intersections are called ordered pairs. For example, the ordered pair (1,3) names the intersection of the first line across the graph and the third line up from the bottom. These intersections are called points. The ordered pair is always shown in parentheses. The Cartesian plane has a horizontal axis (across), which is numbered. There is also a vertical axis (Up and down) with numbers. The point at which the horizontal and vertical axes cross is called the origin, and its name is (0,0). If you and your class are familiar with the Number Line, the Cartesian coordinate system is simply a combination of two Number Lines. One that moves left and right, and another that moves up and down. Together they allow you to navigate anywhere! One very important concept to reinforce with your students is the order of movement. Mathematicians move across first, and then up or down to a particular point. Remember to move on the lines rather than the spaces. For some practice in the classroom, use the grid on the next page to answer the following questions.

Materials: For the class: Roamer First Quadrant Graph Paper Transparency For each student: First Quadrant Graph Paper Copy Four Quadrants Graph Paper Copy Roamer Stepping Stones Activity Scavenger Hunt Activity Journal* *provided by teacher Basic Skills Development: Language for Information Understanding Analysis, Inquiry and Design Mathematics Common Themes Connected to MST Interdisciplinary Problem Solving Preparation: Students will count in numeric order, positive and negative numbers, the Number Line, and gain simple programming experience with the Roamer. Negative numbers can be avoided for younger children by limiting your graphs to the First Quadrant and the Stepping Stone activity. Adaptive devices may be required for children with special needs.

44

Locations on the Cartesian Coordinate continued Page 2

What letter is at (4,2)? [This tells you to go over four lines and up two lines. It’s the letter A!] What letter is at (2,4)? [Go across two lines and up four lines. It’s the letter C!] What are the coordinates of the letter B? [Answer: (1,1)] Put a star at (2,0) [This point lies on the X-axis.] What are the coordinates of any point on the Y-axis? [Answers: (0,3) or (0,2) or (0,4) or (0,1)] Use the First Quadrant Graph Paper to make up your own questions! So far we have graphed points on the coordinate plane called Quadrant I. All of the points were positive and to the right and above the origin (0,0). There are also Second, Third and Fourth Quadrants. These Quadrants involve negative numbers. See the Four Quadrants Graph Paper for examples. If we start off at the origin (0,0) we can go up or down, left or right. You could also use the directions North, South, East and West to show you students that we can move to a specific location using this coordinate system. When everyone understands how to graph points in the four quadrants, we can then communicate directions to each other by speaking the same number “language”.

Evaluation Strategy: Students can be assessed with similar questions of point coordinates in either the First or all Four Quadrants. A first quadrant application assessment can be achieved by using the Stepping Stone Map, which requires students to program the Roamer so that it stops at each stone while crossing a stream. To make this assessment more competitive, you can make each stone like a target. There could be different point values associated with the target stone so that students who program the Roamer to land on a stones edge would get less points than the Roamer that lands directly in the center of the stone. Another assessment using all four quadrants is the Scavenger Hunt Map. This requires students to start at the origin, and move into each quadrant to succeed in the hunt. An even more difficult task for older children is the Roaming on Mars activity.

45

Locations on the Cartesian Coordinate continued Page 3

Use the graph above to answer the following questions. What are the coordinates of F? [You go 2 to the left and up 1. The coordinates are (-2,1)] What are the coordinates of G? [You go to the right 2 and down 2. The coordinates are (2,-2)] What point is at (-3,-2)? [ Answer: E ] What are the coordinates of point H? [The coordinates are (2,2)] Put a star at (0,-2). [This point lies on the Y-axis. It is not in any Quadrant.] Use the Four Quadrants Graph Paper to make up your own questions!

Another application of the graphing in four Quadrants is the relationship to the directions on a compass. North and south lie along the Y-axis, while east and west lie along the X-axis. Students can then see that in order to follow a set of directions to find items for the scavenger hunt, you need to move so many units in a specific direction. In addition northeast, southeast,

southwest, and northwest can also be introduced as directions 45° in between the main directions. Students will keep a journal of the new information they have learned about the Cartesian coordinate system and the techniques used to graph points and determine the coordinates of points. They may also wish to display their solutions of the Roamer program used in the Stepping Stone activity and/or the Scavenger Hunt activity.

46

Locations on the Cartesian Coordinate continued Page 4

Extension: Have the students record in their log/journal what prior knowledge they had of the Cartesian coordinate system before this learning experience. Can they see the correlation between it and directions of north, south, east and west? Investigate the Roaming on Mars activity for further discussion and challenges.

47

~ ~ ~ ~ STREAM ~ ~ ~ ~

S T A R T

F I N I S H

Stepping Stone Activity Navigate the Roamer from one side of the stream to the other by using a program

that takes it from one stone to the next. You must use all the stones in order to

successfully cross the stream.

Good Luck!

Stepping Stone Activity Navigate the Roamer from one side of the stream to the other by using a program

that takes it from one stone to the next. You must use all the stones in order to

successfully cross the stream.

Good Luck!

48

Stepping Stone Activity Navigate the Roamer from one side of the stream to the other by using a

program that takes it from one stone to the next. You must use all the

stones in order to successfully cross the stream.

Good Luck!

Roamer

Finish

Roamer

Start

~ ~ ~ ~ STREAM ~ ~ ~ ~

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Cow

Haven

Farms

General

Hospital

Bluebird

Baseball

Diamond

Lookout

Lake

Freedom

Library

County

SPCA

Finish

Start Scavenger

Hunt

50

Freedom

Library

Cow Haven

Farms

Lookout

Lake

Start Scavenger

Hunt

County

SPCA

Finish

Bluebird

Baseball

Diamond

General

Hospital

Roamer Scavenger Hunt Your challenge is to write a program that sends the Roamer on the Scavenger Hunt listed below.

The first stop on the Hunt is Cow Haven Farms to grab a handful of hay. Second stop is Lookout Lake to collect a water sample in a jar.

Third stop is Freedom Library to return a book. Fourth stop is General Hospital to drop off a get well card at the information desk. Fifth stop

is the Bluebird Baseball Diamond to tie a red ribbon onto the bleachers. The sixth and final stop is the County SPCA to give a dog a bone.

Good Luck !

N

S

E W

51

Intermediate: Navigation Amazement Objective: Students will experience the ability to perform measurements, make decisions, program the Roamer, and re-create a scaled up version of a maze. Several correct paths allow students to make evaluations on different routes and their possible advantages.

Several mazes are provided to suit the ability level of your students. Choose an appropriate one and let students work together in pairs. Each pair will decide the path to be taken by the Roamer, and take the appropriate measurements of length and/or angles from the copy maze in order to write a program for the Roamer. After the program is written, it can either be analyzed and evaluated by a different pair of students or a team of “inspectors” before it is allowed to be programmed into the Roamer. During the actual navigation, any Roamer crossing a maze barrier is disqualified, and sent back to the drawing board. Students should then re-create the maze so that the Roamer can navigate through it. This should be done on a clean floor in the Roamer scale of 1 unit = 30 cm or you may establish a different unit scale so that the maze can be re-created on a tabletop. See User Guide to change the unit scale using [ ]. Be certain to double-check all measurements as the maze is being re-created. It may be easier for the teacher to re-create the maze for younger children, or it can be a lesson in cooperative learning as different groups of students are responsible for different aspects of re-creating the maze. A simple way to do this is with masking tape representing the barriers, but this will not “catch” the Roamer in a mistake. However, if students are using a watchful eye as each team navigates the maze, they should catch a disqualification. A better way, but more time consuming would involve taping cardboard or poster board down to the floor to act as barriers. As a final activity, allow each team of students to program the Roamer and navigate the maze. You may even time each team run to collect data and make an evaluation of course decisions, number of program steps and their possible advantages or disadvantages. Students will keep a journal of the procedures used in measuring, documenting the measurements, scale

Materials: For the class: Roamer Maze Transparencies Masking Tape Measurement Devices Ruler Protractors Cardboard or Poster Board* (optional). For each pair of students: Maze Copies Journal* *provided by teacher Basic Skills Development: Language for Information Understanding Language for Critical Analysis and Evaluation Analysis, Inquiry and Design Transfer Information Mathematics Interdisciplinary Problem Solving Preparation: Students will learn linear measurement, scale and proportion, angle measurement, simple Roamer programming ability, and cardboard or poster board construction ability (optional). A clean, undisturbed space will be needed on the floor or tabletop so that an appropriate scaled maze can be created for use with the Roamer. Adaptive devices may be required for children with special needs.

52

Navigation Amazement continued Page 2

and proportion decisions, and maze re-creating techniques. They may wish to also assess better ways to establish the barriers than those given. They may also wish to display their mazes and solutions of Roamer programs used with the navigation of the maze. Extension: Any maze can be translated onto a Cartesian coordinate plane. This would incorporate more mathematical skills as students plot their course and identify maze barriers using ordered pairs. For an activity involving sensors, have the students program the Roamer to respond to different sound commands as a method to navigate it through the maze.

Evaluation Strategy: Students can be assessed with similar or more difficult maze problems. They should also be encouraged to create their own mazes. The correctness and craftsmanship of the maze re-creation, ability to work with others, and timed navigation can also be used as an assessment.

53

Finish

Start

Maze # 1

54

Finish

Start

Maze # 2

55

Finish

Start

Maze # 3

56

Intermediate: Creating Symmetry With The Roamer

Objective: To provide students with the knowledge and experiences of various symmetry and allow them to program the Roamer to produce finished images. The ability to visualize relationships between objects in space is important in everyday life as well as geometry. Reading and sketching maps, giving and following directions, understanding diagrams for toy and furniture assembly are some examples where spatial thinking skills are required.

The essential ideas of symmetry and proportion are woven into our lives through architecture, clothing, commercial designs, science, art, recreation, and natural phenomena. The term symmetry is defined as balance; proportion of parts or elements; harmony; correspondence of arrangement, and beauty of form. The snowflake is often cited as an example of perfect symmetry. Some letters of the alphabet are also symmetrical, as well as the wings of a butterfly. The Roamer can be programmed to draw a line that corresponds to a reflected image. It can also be programmed to create symmetrical shapes using translations. There are many classifications of symmetry, but we will limit our experiences to three main types; Reflections, Rotations, and Translations. See the attached copy that gives several examples of each. Rotation symmetry can be defined by taking a shape and simply turning it. As you can see on the copy this

rotation is 90°, but it could easily be 15°, 45°, 180°, etc. Rotation symmetry can produce unique shapes. Can your class find other examples of this form of symmetry? Mirror reflection or bilateral symmetry shows the same pattern arranged symmetrically on two sides of a center line or axis. You can create a reflection symmetry by folding a piece of paper in half, and cutting out a shape along the fold. When you open the paper the fold is the center line and the shape produced is symmetrical. Some capital letters of the alphabet also show reflection symmetry. How many symmetrical letters are there? What other objects have mirror reflection symmetry? The final type of symmetry we will create are translations. Here the object or pattern remains the

Materials: For the class: Several copies are provided which allow students to investigate different types of symmetry and create symmetrical shapes. The use of pens with the Roamer can be further detailed in the Valiant Roamer Pen Pack Activity Book. Paper and Roamer pens, as well as reference books or magazines showing symmetrical objects For each student: Journal* *provided by teacher Basic Skills Development: Information Understanding Mathematics Common Themes in MST Preparation: Simple programming experience with the Roamer. Pictures of symmetrical objects or patterns to reference. Space will be needed on the floor or table tops so students can check their programs for symmetry with the Roamer. Adaptive devices may be required for children with special needs.

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Creating Symmetry With The Roamer continued Page 2

same, but it is moved or translated a specific distance in a specific direction. The Olympic Rings are an example of translation symmetry. Footprints in the sand, as well as the keys on a piano are examples too! Can you find any others? Once you have discussed the three types of symmetry and you feel confident that your students have some experience with their differences, you can begin to write programs for the Roamer to draw lines of symmetry. There are several examples provided, but only your imagination can stop you and your class from creating your own symmetry. The pen placement in the Roamer is crucial for the type of line you wish the Roamer to draw. See the Valiant Roamer Pen Pack Activity Book for assistance. It may be helpful for the students to place the pens in both the center position as well as in the perimeter position and investigate the results when a specific shape is programmed into the Roamer. For example, when you program a route for an isosceles triangle

(all 60° angles), the center pen will draw it, but the perimeter pen creates something quite different. But this unique shape also has symmetry! Circles can only be produced using the perimeter position, so think before you insert the ink. Students will keep a journal of various types of symmetry objects or pictures that they have collected from magazines or from nature. Extension: Have the students record in their log/journal what prior knowledge they had of symmetry before this activity. Can they identify any other kinds of symmetry in nature, or how symmetry is used in advertising, design, architecture, construction of bridges, and in painting?

Evaluation Strategy: Students can be assessed with similar symmetry problems, as well as encouraged to create their own symmetrical drawings. They should be able to distinguish between the three types of symmetry introduced. They may also wish to display their knowledge in a collage or hanging mobile, which should also show some form of symmetry or balance.

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90°°°° Rotation Symmetry

Mirror Reflection Symmetry

Translation Symmetry

Different Types of Symmetry

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Hexagram

(Star of David)

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Intermediate: Roamer Olympics I

Objective: This learning experience provides a competitive environment experience that allows students to be creative as they work cooperatively. Groups of students will program the Roamer to perform specific skills as they compete to be the fastest, the most successful, and the most creative.

This Roamer Olympic learning experience introduces competition to the Valiant Roamer world. Several events are provided which require students to program the Roamer to push, pull, dance to music, race an obstacle course, and draw the Olympic rings. The competition for each learning experience can be timed so that events can be held at different times on different days without disturbing the quest for the Olympic gold medal. As indicated in the rules of the game, three stopwatches should be used to record the time of race events. Each group’s time will be the average of the three times. The teacher may also wish to time the event in case of a major time discrepancy with one of the stopwatches.

You may wish to divide students into several groups with an option for each group to enter each event, or designate specific groups for specific events. Student groups may wish to represent different countries, states, colors or even mascots in the competition to develop team spirit. Be sure to establish the judging criteria well before the Olympics begin so that each group knows how they will be evaluated. Each classroom is unique, so be creative but fair with the judging and scoring. A team of volunteer judges may also be used. A special creative award is added for each event and may be presented to any group who has decorated the Roamer in an appropriate way that corresponds to the event. For example in the dance routine, if the music chosen was “Raindrops Keep Falling On My Head”, the Roamer might have an umbrella. See Roamer Olympic Events ditto for Rules of the game and course layouts. Students will keep a journal on how this Roamer Olympic competition is similar/different to the real Olympics. They may also wish to record the process that their group went through as they participated in each event. How well did their group work together? What were some problems that their group had to over come? What did they like the best/ the least

Materials: For the class: Roamer 4 Stop Watches Inclined Plane Ramp Paper Cups Ribbon Cardboard Masking Tape Roamer with Pen Adapters Various Paper/Cloth Materials for Decorating the Roamer For each student: Journal* *provided by teacher Basic Skills Development: Language for Information Understanding Analysis, Inquiry, and Design Mathematics Interdisciplinary Problem Solving Creating, Performing, and Participating in the Arts Preparation: Olympic Games awareness, programming capabilities with the Roamer, music program ability, familiarity with Roamer pen drawing, design and attachment of paper or cloth material. Clean space will be needed on the floor or table top so that each Olympic event can be performed by the Roamer. Adaptive devices may be required for children with special needs.

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Roamer Olympics continued Page 2

about the learn experience? What are some other events they would like to do? Extension: Have the students record in their journal what prior knowledge they had of Olympic competition. Is competition always good? What are some examples when competition is not good? What might cause the Roamer to act differently from race to race? What role does the batteries play in the energy the Roamer has to compete? How would you measure the battery energy? What would maximize the energy level of the battery?

Evaluation Strategy: Successful participation in each event is an assessment in itself. Students can also be assessed by Gold, Silver and Bronze medals awarded in each event. Timed races will be an easy indicator of 1st, 2nd and 3rd, but judging criteria for creative Roamer decoration will have to be established for each event before the contest begins.

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Olympic Rings

Inclined Plane

Ramp

Start

Finis

Obstacle Course Track Design

Use a stack of

books to fill in this

area and form a

barrier.

Paper cups with

ribbon attached

to form barrier.

60cm

30cm

150cm

90cm

60cm

30cm

60cm

30cm

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Roamer Olympic Events “Cattle Guard” Push Rules of the Game: Each Roamer contestant will be required to push a wooden block a distance of 300 centimeters in a straight line. The block may not be attached to the Roamer, instead you must design a “cattle guard” and attach it to the Roamer. The “cattle guard” will be the only thing allowed to guide the wooden block along the straight course. If the wooden block gets away from the Roamer during the race, the Roamer must return to the starting line again, as the time continues to record. Each contestant will be timed using three stop watches. The average of the three times will be recorded for each group. You may decorate the Roamer to enhance this event for a special creativity award. Monster Roamer Pull Rules of the Game: Each Roamer contestant will be required to pull a wooden block a distance of 300 centimeters in a straight line. The block will be fastened to the Roamer’s perimeter pen attachment using any rubber band. Each contestant will be timed using three stop watches. The average of the three times will be recorded for each group. If at any time during the race the rubber band breaks, the Roamer will be disqualified. You may decorate the Roamer to enhance this event for a special creativity award. Roamer Dance Routine Rules of the Game: Each Roamer contestant will be required to play music as it performs a dance routine in a 150cm by 150cm square. Disqualification will occur if the Roamer moves outside of the designated area. Judges should look for a dance that matches the theme of the music. The entire dance routine should last between 30 to 60 seconds. You may decorate the Roamer to enhance this event for a special creativity award. Roamer Obstacles To Overcome Rules of the Game: Each Roamer contestant will be required to race an obstacle course for the fastest time. Each contestant will be timed using three stop watches. The average of the three times will be recorded for each group. See Obstacle Course Track Design ditto for specific details. You may decorate the Roamer to enhance this event for a special creativity award. Roamer Art and Accuracy Rules of the Game: Each Roamer contestant will be required to draw the Olympic rings, see ditto for design. Accuracy, precision and color presentation will be the main judging criteria. Students will be allowed to pick-up and move the Roamer to different locations. You may decorate the Roamer to enhance this event for a special creativity award.

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Roamer Mission to Mars

Cattaraugus Allegany BOCES Math, Science and Technology

Valiant Roamer

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Student Guide

The Roaming Spirit

You are part of a Mars Robotic Exploration Team that just successfully landed the robotic explorer craft Spirit, on the surface of Mars. Specifically, the Spirit landed near the middle of the Gusev Crater, a nearly 161 kilometer-wide (100-milewide) crater just south of the Martian Equator.

Radio data from the spacecraft has indicated that all systems within the craft are functioning properly, and you are now cleared for your first remote investigation.

Your mission is to extract clues from the rock and soil samples you obtain about the past environmental conditions within the crater. For example, sedimentary rocks may hold the information needed to determine whether or not there existed a wet environment capable of sustaining life.

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Mars is much smaller and has much less mass than the Earth. Therefore the gravitational force is almost 1/3 that of the Earth. The atmosphere on Mars is very thin, and the resulting low pressure on the surface prevents water from existing in a liquid state. However, at some point in time, the atmosphere may have been more substantial, and water may have been present in a liquid form. This may have allowed for the existence of living organisms.

Challenge

The robotic craft must obtain rock and soil samples from three various sites within the crater. Your team must prepare a map of the route your robotic craft will take to get to each of the three sites to be studied. You have been provided with a map showing the location of the Spirit, and the three sites. Topographic information has been provided to warn you of any obstructions that make cause the craft to get stuck or be damaged. Your team must plot a route for the Spirit to follow that will enable it to travel to all three sites in the most effective manner, in the shortest period of time. To be sure the path is safe and accurate, your team will use Roamers to simulate the path the Spirit will take. Your entire group will create a model of the surface of the Gusev Crater, according to the map you were given. You will then test the accuracy of the path for the Spirit by running the Roamer through the course first. Try to find the most direct and fastest route through the model.

Throughout this activity, you will use various scales of measurement. Your map will have a scale of 1:10, which means that every centimeter or unit on the map equals 10 centimeters on the model. This means that 3 units will equal 30 cm (the distance the roamer will travel when you program in direction 1) Enjoy the mission and good luck!

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Student Guide

Student Instruction Sheet for Roaming Spirit Mission

• On your map, draw out the best possible path for the Roamer to take. Remember, the Roamer must begin at the starting point and travel to each site in alphabetical order, and then back to the starting point. The Roamer cannot hit any of the boulders or other hazards during its journey. If it does, it must be reprogrammed. The real challenge lies in completing the full journey in the shortest period of time.

• Measure the length of each movement of the Roamer in centimeters (remember that I cm on the map = 10cm on the model AND for every unit programmed into the roamer it will move 30 cm). Record this information in the distance/angle column of the Roaming Spirit Program Sheet. Record the angles the Roamer must rotate to move to each site in the distance/angle column as well.

• Write your program on the Roaming Spirit Program Sheet.

• Test your program using the Roamer on the model. Place the Roamer directly over the Spirit Starting Point and execute the GO command. Use a stopwatch or a watch with a second hand to time how long the Roamer takes to travel the complete route. It is only necessary for the Roamer to cross over a part of each study site before going on to the next location. If the Roamer misses any study site, stop the simulation and analyze your program for errors. Correct your program and try the simulation again. You may also want to change the program to decrease the time necessary to complete the mission.

• When you have determined the program that you want the Roamer to follow, submit the following information to your teacher.

▪ Model Site Layout Map with the route Roamer drawn on it ▪ Roaming Spirit Program Sheet

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Teacher’s Guide Teacher Instruction Sheet for Roaming Spirit Mission

Objective The object of this activity is to facilitate the student groups to program their Roamers to follow a detailed model of the surface of Mars, just as the NASA craft, Spirit, is currently slated to do on Mars. They will create and scale the model according to the challenge, determine the correct configurations for the Roamer, and program it to follow the selected pathway.

Scheduling and Setup Depending on the number of Roamers you have, student teams may consist of 2 to 4 members. You may construct the model yourself, or your students may prefer to. In any case, the model needs to be a scaled up version (1:20) of the Model Site Layout Map you’ve received. The final floor model of Mars will be 20 times larger than the map. It should be 300 centimeters by 300 centimeters (3 meters by 3meters) in width and length. Use the measurements provided on the Model Site Layout Map to place the boulders in their proper locations. Copy one student copy for each team, and the students should understand that the Roamer has to visit all five sites (A – E) and return to its starting point for the mission to be considered successful. If the Roamer misses any site, it should be stopped so the program can be corrected. Prior to the final assessment competition, the Roaming Spirit Program Sheet and the Landing Site Map should be submitted for your approval.

Materials Roamer Model of the Martian surface Paper for the model, or some type of surface material Marker Boulder models (can be 3D models or flat images) Instruction sheets for each team Student copies for each team Metric rulers Protractors

Assessment The team who completes the mission in the least amount of time, without hitting any obstacles, is considered the challenge winner.

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Student and Teacher Guide

Model Site Layout Map 3 units or 3cm on this map = 1 unit on the roamer 90 degrees =a right angle

Landing

Site

Site A

Site B

Site C

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Roaming Spirit Program Sheet

Unit Change

[ ]

Direction

Distance

or Angle

What will

Roamer do?

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

Δ∇

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Additional Exercises Demolition Roamer Build a tower from empty boxes or blocks. Position the Roamer at any starting point. Instruct the Roamer to knock down the tower, using moves and turns. Obstacles may be placed in the path, which the Roamer must avoid during demolition. Collecting Rubbish Place litter around the floor and put the Roamer in the starting position. To collect the rubbish, the Roamer must circle it and return home. If the Roamer does not reach home, there is no score. Decide on a limit for the total distance of each player’s turn. The player collecting the most rubbish programs a tune into the Roamer. Roamer Pacman Build a model of the countryside. Use objects to represent the explorer’s home and obstacles like the mountains, desert and lake. This is a game for two players. The first player plays the part of the Explorer, places the Roamer in the starting position and programs it to take the shortest route home. Write down each instruction, so that you know the total distance home. The second player plays the Roamer Pacman and places the Roamer in the starting position. If the Pacman reaches the Explorer’s home in a shorter distance, it eats the Explorer. The Explorer wins if it travels home by a shorter route than the Pacman.

Roamer Skittles Use cardboard tubes, or washing up liquid bottles, as skittles. Number them and place them on the floor. Place a ball on the floor. Program the Roamer to knock the ball into a skittle. Use as many instructions as you want, but only one press of GO, for each turn. Score the numbers on the skittles you knock over with the ball. The game ends when all of the skittles are knocked over with the ball. If you miss the skittle, or knock it over with the Roamer, the turn finishes and the next player goes. Driving Test Create a street scene with road signs, a one-way system, etc. One person plays the examiner, and another takes the driving test. The examiner decides on a route and tells the applicant where to turn, revere into a side street and do a three-point turn. The applicant programs the Roamer to travel the route, obeying the Highway Code. The applicant becomes a qualified Roamer driver if the route is completed without a mistake. The examiner and the applicant may then exchange roles, and the examiner may take the test. Roamer Hopscotch You will need a long piece of paper with numbers and sections marked out on it. If each section is marked out as a roamer unit it makes things a lot easier. Position the Roamer at the beginning and throw dice to start. The students then have to program the Roamer to move that

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amount. If they are playing in pairs the winner is the first to reach the end. This exercise could be developed in a variety of ways for addition/subtraction practice, with backwards and forwards. Space Journey A Roamer space ship has to make a journey to a distant planet. It interweaves its way around other planets, asteroids, etc. The distance it can travel is limited: Can it reach its destination or does it need to land and refuel? This activity is done with a small group of students and provokes discussion on a range of possible strategies. Wagon Train Roamer hits the Oregon Trail. Which way should it go? As scoutmaster, the students have to decide. As in most Roamer exercises of this type, students realize many problems do not have one answer. A bad solution may simply be a step toward a right answer. They experience the value of communicating and discussing ideas, and that sources of inspiration or information can come from any place or anyone, but they need to be able to listen and learn if they are to seize the opportunity. Paper Route Having some basic arithmetic skills, students are asked to solve the following problem: a newspaper boy/girl has to deliver papers to two houses and then go home. Does it matter in which order he/she delivers them? Students are expected to develop a theory and proof and use Roamer to confirm their ideas. Using the REPEAT function Roamer Racetrack Mark out a racetrack. Place the Roamer on the starting line and move it around the track. Look for a pattern where the moves and turns repeat, and use the Repeat Command to break your record. Try to get round using fewer moves, and beat your ‘lap record’. Roamer Longshoreman A number of ships are docked at the pier. Each contains mixed cargo. These need to be transferred to one of several warehouses. Each warehouse should store one type of goods. Students should program the robot to unload the ships. They are only capable of carrying three items at once. Students should gradually refine their solution to find the most efficient way.

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Using the PROCEDURE function Roamer Car Trials Mark out the Trials course. Write and test a procedure for each section of the course. Write procedures to take the Roamer from one section to the next. Combine all the procedures into one GO Program; so the Roamer will travel round the course with one press of GO. Roamer Play Students should devise a drama using robot characters. Each student programs one of the characters in a way that integrates with the script. Bus Routes Students program Roamer to make a bus journey. Where should the bus stops be located? How long should the bus stop at each stop? And write a bus time schedule. At each stage Roamer is used to model the students solution. Students should not guess. Instead they are expected to study local bus systems, gather data (often from field visits) and find ways to make realistic estimates. Using SOUNDS and Roamer Music Ice Cream Make the Roamer look like an ice cream van. Write a short tune for the Roamer to play when it stops. It will make things easier if you write this in the form of a procedure. Plan a route through the town. Program the Roamer van to travel through the town. It should stop at least three times to play its tune and sell ice cream. It should also obey the rules of the road. Row Your Boat

41 41 41 13 45 45 13 45 16 68

313 113 38 18 35 15 41 48 26 35 23 41

Barney Theme/This Old Man

48 45 88 48 45 88 410 48 46 45 43 45 46

35 36 38 31 21 21 21 21 33 35 36 48 48

43 43 46 45 43 41

Twinkle Twinkle Little Star

41 41 48 48 410 410 48

46 46 45 45 43 43 41

48 48 46 46 45 45 43

41 41 48 48 410 410 48

46 46 45 45 43 43 41

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Happy Birthday

41 41 43 41 46 45

41 41 43 41 48 46

41 41 413 410 46 45 43

411 411 410 46 48 46

Three Blind Mice

35 33 61

35 33 61

38 26 16 55

38 26 16 55

18 213 113 112 110 112 213 18 28 18

113 113 113 112 110 112 213 18 18 18

18 213 113 112 110 112 113 18 18 28

16 35 33 61 Using the Pen Pack

Picasso Make the Roamer into an artist. Attach some pens to the middle and outside of the Roamer. Get the Roamer to draw some pictures. Geometric Shapes Program the Roamer to draw different geometric shapes. Can you program the Roamer to draw a curve? Program one of your shapes as procedure P1. Incorporate it into the program on the next page. R6 [ Repeat 6 times P1 Procedure 1

60 Turn right 60 units ]

Try using different shapes and repeat values. Change the numbers in the instruction.

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Spiral Island Make a spiral shell for the Roamer. Use the scale function and program the Roamer to draw spiral patterns.

Δ[1] Sets scale to 1 cm.

P1 Draw a square

Δ [2] Sets scale to 2 cm.

P1

Δ [3] Sets scale to 3 cm.

P 1 GO Procedure definition: P1 [ R2 [

Δ 1

90 ] ] Experiment with changing the scale of the angle. Roamer Architect Get the Roamer to draw a house. Use procedures for different parts of the house. For example, P3 could be a window, P4 could be the door, etc. Art Gallery Make the Roamer into an artist and draw some pictures. Color and decorate the pictures and put them in an exhibition of Robotic Art.

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Beginner: The Three Billy Goats Gruff, Roamer Style

Objective: To express and create their own version of a favorite story, or to retell a classic with a new twist.

This learning experience is a model for any story within which the Roamer may become a character. The Roamer may be decorated to become an actor in the telling of the story. Will Roamer make it across the bridge or the will the troll eat him? Have students read The Three Billy Goats Gruff. After reading, discuss the story’s elements (characters, genre, story problem, story questions). Students will then create their own version of the story. In groups discuss and generate ideas for constructing a set, bridge and costumes. Three Roamers may be styled as goats and one as the troll. Remember the Roamer must be able to travel across the bridge you build. Over several weeks develop the students’ ideas and build the set, bridge and make costumes. Assign someone as narrator and others to read the parts of the Three Billy Goats Gruff. Once the set and bridge have been built, students will work on programming Roamer. They should estimate distance from one point to another. They should also estimate the waiting time between the Roamers’ appearances as the billy goats and the troll. This will require a lot of teacher facilitation and may be where you find the help of parent volunteers useful. After practicing and making needed adjustments, other classes could be invited in for a dress rehearsal. Invitations can be made and sent home during this time too, so parents can come to watch the final production.

Materials: yarn felt paint construction paper 4 Roamers with batteries google eyes hot glue gun paper towel rolls king size white sheet wooden building blocks Roamer manual The Three Billy Goat’s Gruff Preparation: Read background information on how to use and program Roamer. Batteries should be charged so they are ready to be used. Some tables and chairs may have to be moved to make room for the construction of the bridge. Some of the programming may require a lot of teacher facilitation and you may find it useful to arrange for some parent volunteers on these days. Basic Skills Development: Estimation Measurement Distance

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Beginner: Traveling With The Grouchy Ladybug

Objective: Students will sequence and travel through a story using Roamer.

Can Roamer mimic the Grouchy Ladybug? Have students read The Grouchy Ladybug by Eric Carle. After reading student groups should make figures of the characters in the story and a ladybug costume for Roamer. Determine various locations throughout the room for each character. Mark an “X” on the floor with the masking tape at each spot. Students should choose a character and discuss and verbally sequence the story by traveling from their character to the next character in the story sequence until all characters have been visited. Roamer should be programmed to move around any furniture or obstacles it comes across on its journey. Students can estimate distances or measure with a ruler. Students should be aware of left and right turns.

Materials: Roamer with batteries cardstock masking tape felt (red and black) pipe cleaners google eyes Preparation: Read background information on how to use and program Roamer. Batteries should be charged so they are ready to be used. Basic Skills Development: Estimation Measurement Distance Directionality Sequencing Decision Making

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Beginner: Linear Units of Measurements I Objective: To provide students hands-on concrete methods of learning about linear units of measurement.

How many footsteps or walking strides equal a Roamer unit? Introduce the history of linear measurement such as cubits, digits, and hands to the class. As a learning experience, have the students use a variety of non-standard historic units to measure items/objects around the classroom. Have students record their results. Read the story Twelve Snails to One Lizard: A Tale of Mischief and Measurement. Lead the class to a discussion about the concept of measuring and tools to measure with. Lead the class in measurement of various objects within classroom using non-standard units of measure such as pencils, length of their own foot, length of various books, etc. Measure to an accuracy of ½ the smallest increment. Record and compare the results. A discussion as to why some of the results are different, depending on the tool used for measurement should lead to the understanding that the tools being used to measure were of various lengths. Have the students use standard measuring tools (a metric ruler) to verify the various lengths of the objects used as measurement tools. Then have students measure the same objects using the metric ruler. Students will keep a journal of the items they have measured, using both non-standard and standards measurement tools. In this log they will write down conclusions they have drawn about the questions/ discussions raised in class. Extension: Have the students create a graph comparing their results using non-standard and standard units of measure. This can be accomplished using manual or software graphing programs that are commercially available.

Materials: For the class: Twelve Snails to One Lizard: A Tale of Mischief and Measurement by Susan Hightower, Simon & Schuster Standard/Non-Standard Measurement Tools (Angle Munchers/Protractors) Metric Rulers Objects and Manual or Computer Assisted Graphing Resources For each student: Journal* *provided by teacher Preparation: Students will count in numeric order and compare of numbers. You will need to provide ample time and resources for the class to investigate the attributes of linear measurement using both non-standard and standard tools for measuring. Adaptive devices may be required for children with special needs. Basic Skills Development: Analysis, Inquiry, and Design Mathematics Interdisciplinary Problem Solving Language for Literary Expression Evaluation Strategy: Given various non-standard and standard measurement tools, students will be record accurately and present a measurement for each items / objects available.

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Beginner: Estimations of Linear Measurements II Objective: Students will be provided opportunities to develop and refine their estimation skills.

Read the story, The Fattest, Tallest, Biggest Snowman Ever. Have students participate in a discussion about the items used to measure the snowmen. Have students give estimations on the height of snowmen they have built. Building upon the knowledge base of linear measurements, have the students estimate distances from object to object within the classroom or school building using small non-standard units of measure (e.g. length of their foot). Then have them use that non-standard unit of measure to verify their estimations. Have the students estimate distances from object to object using large non-standard units of measure (e.g. length of their normal walking strides). Allow the students to use their non-standard units of measures to verify their estimations. Using standard units of measure (rulers, meter sticks and yardsticks), estimate the distances between objects. Finally use the standard unit of measuring tool and allow students to verify their predictions. Questioning about the need for accuracy should lead to the understanding that there is a time when estimated distances are acceptable and needed for problem solving and at other times there is a need for accurate measurement of distances and objects. Students will record into their journals running records of estimations of the length of the linear units used within the lesson. They will journal their responses to the question as to when estimation of linear length is acceptable and when there is a need for accurate measurements. Extension: Compare the results from estimations of distances using the various methods of measurement (footsteps, strides, and standard units of measure).

Materials: For the class: The Biggest, Fattest Snowman Ever by Michael Rix Rulers Meter Sticks* Yard Sticks* For each student: Journal* *provided by teacher Basic Skills Development: Language for Information and Understanding Language for Literacy Expression Language for Critical Analysis and Evaluation Analysis, Inquiry, and Design Mathematics Interdisciplinary Problem Solving Preparation: Review with students the attributes of linear measurements. Space within the classroom will be a factor – if space is limited consider moving these lessons to an area in the school where the space is available. Adaptive devices may be required for children with special needs. Evaluation Strategy: Given various non-standard and standard measurement tools, students will accurately record and present a measurement for each items/objects available.

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Intermediate: Scaling Up Objective: To describe and classify the physical attributes of shapes, as well as, measure sides and angles.

How are geometric shapes measured and scaled up? Students will need clean floor space or a table-top area on which to design, measure, and scale up geometric figures/shapes. Discuss and review the terminology you will be using with this activity regarding the concepts of scale and proportion, linear measurement, measurement of angles, terminology of mathematics (right angle, straight angle, obtuse angle, perpendicular lines, and parallel lines) and shapes. Have students select a pattern block (hexagon, trapezoid, parallelogram, triangle and square). Students will measure each side of the selected pattern block. Have students decide how many times they want to scale up the design. Multiply the measurement of each side by that number. Using a protractor, students will determine each angle. Using a ruler, draw the scaled up design on graph paper. Several pieces of graph paper may have to be taped together to accommodate the scaled up design. Have students program Roamer to navigate the perimeter of the design. Next, have students program Roamer to draw the scaled-up shapes on chart paper. The Roamer default setting may need to be adjusted in order to do this. Discussion Questions: How might the scaling up of objects affect the design of structures, playgrounds, buildings, etc.?

Materials: Roamer with batteries Pattern Blocks Measuring Devices (standard and metric) Protractors Crayons Markers Pencils Graph paper Chart paper Preparation: Batteries should be charged so they are ready to be used. In order for students to understand the concept of “scaling up” they will need to understand the concepts of scale and proportion, linear measurement, measurement of angles, terminology of mathematics (right angle, straight angle, obtuse angle, perpendicular lines, parallel lines), and the conversion of standard/metric units are prerequisite skills to understanding the scaling up concept. Basic Skills Development: Spatial Development Following/Giving directions Problem Solving Measurement Vocabulary: Acute angle Obtuse angle Parallel lines Perpendicular lines Right angles Straight angles

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Intermediate: Using Roamer for Linear and Angular Movement

Objective: To recreate a scene from a story, documenting the process used, and produce a program to take Roamer through the journey.

Can Roamer find its way through your story? Read the story Journey Cake, Ho, The Gingerbread Man, or Goofy-On-The-Hill-Side. Lead the class in a discussion about the story. Guide the class through a writing assignment related to the story. Students should retell the story or summarize what happened in a paragraph. Break class into groups. Each group will design a model showing the route the character in the book took during the story. The groups will switch and program the Roamer to be the character in the story and complete the journey. *It is important that the program be written in advance using measuring devices and THEN programmed into the Roamer to check and adjust the program. The music aspects of Roamer can be utilized to make the character speak or sing. The students can refer to the “design loop” in developing the program that gets the Roamer through the journey. Extension: Students could find other stories based on a journey and to compare and contrast writing about the story. Students can write their own stories about a journey. Roamer can be programmed to play songs to represent the songs sung by the characters or to represent dialogue.

Materials: Roamer with batteries Journey Cake, Ho The Gingerbread Man Goofy-On-The-Hill-Side Protractors Linear measuring devices Preparation: Batteries should be charged so they are ready to be used. Space will be needed in the classroom to allow for movement. Basic Skills Development: Listening Measurement Angles Creative writing Evaluation Strategy: Students will write summaries or re-tells of the stories, and provide a sequenced story line. The student will document the process used to create the scene for the Roamer to use for the journey. The student will also produce the Roamer program needed to take the story character through the journey.

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Advanced: Ice Cream Roamer Route

Objective: To provide students the experience of programming the Roamer in a real world setting. The Roamer will travel up and down streets in a simulated neighborhood while playing

music as an ice cream vendor. Street grids can vary from simple 90° corners to more complicated angles. Mathematical terms relating to congruent angles and their measurements will be introduced and utilized in the programs. A Roamer size neighborhood will be generated for program evaluation.

Villages and neighborhoods are as common as they are unique. As adults, we might remember the musical sounds of the “Good Humor” ice cream vendors that enticed children out of their homes clutching loose change. In this learning experience, the Roamer will become an ice cream vendor, play music and make strategic stops along the streets of a neighborhood. You might wish go into some detail about ice cream vendors so that students who are not familiar with this learning experience learn some background information about vendors, marketing, and the business practicalities of speed and strategic stops. Several songs are provided and can be programmed into the Roamer or students may wish to program a unique melody. Decide on the best neighborhood street grid representation for you class and their level of understanding. See examples provided, or construct your own street grids. The focus of this learning experience especially for older children is the mathematical relationships between angles. It is important to use this new information in the creation of the street grids, so that students can see the usefulness of the mathematics and make the connection to the real world. Once an appropriate street grid is determined, students will then need to decide where and when the Roamer vendor will stop and for how long. A possible strategy is to have the class split up into groups of 3-4 students. Each group will decide on their own route, music, and stops. The groups will then begin to write a Roamer program on paper, which should also include a music procedure and the designated stops. After all groups have successfully written a program, the Roamer size street grid can be created to test the efficiency and practicality of each groups vendor simulation. A class critique can then follow to evaluate the best program, song, stops, etc. This learning experience has a lot of flexibility and should

Materials: For the class: Roamer Protractor Angle transparencies and dittos, Rulers Measuring Devices Masking Tape Index Cards For each student: Journal* *provided by teacher Basic Skills Development: Language for Information Understanding Language for Critical Analysis and Evaluation Mathematics Common Themes Connected to MST Preparation: Student will scale and proportion, simple angle measurement with a protractor, mapping routes, and music programming ability. New mathematics terminology include congruency, perpendicular lines, parallel lines, transversals, supplementary angles, acute angles, obtuse angles, right angles, straight angles, corresponding angles, and alternate interior angles. Clean space will be needed on the floor or table top so that an appropriate scaled street grid can be created for use with the Roamer. Adaptive devices may be required for children with special needs.

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Ice Cream Roamer Route continued Page 2

be loads of fun! You might also decide to serve ice cream treats on the day of Roamer program evaluation. Several copies are provided along with transparencies to help students gain information on angles and the relationships of angles in specific settings. The following terms have been selected to help students identify the relationships and measurements of angles in a street grid setting in order to program the Roamer successfully. Congruency is a term used to describe equality. Congruent angles are angles that have the same measurement. The size of an angle can be

measured by a protractor in a unit called degrees (°).

There are 360° in a circle, a straight line is actually a

straight angle whose measure is 180°, an acute angle

has a measure between 0° and 90°, a right angle has

a measure of exactly 90°, and an obtuse angle has a

measure between 90° and 180°. Two lines are perpendicular if they intersect to form a right angle. Parallel lines keep the same distance between them and never intersect. A transversal is the name of the line that travels through two or more lines at different points. Supplementary angles are the pair of angles

whose measurements add up to 180°. Each of these angles is referred to as the supplement of each other. Students will keep a journal of the mathematics terminology and their interpretations of this learning experience from day to day. They may also wish to write a paragraph explaining how the mathematics helped them to correctly program the Roamer. Extension:

Have the students investigate angles and their unique relationships in triangles, parallelograms as well as other shapes. Explore obtuse, acute, and right triangles. What do the measurements of all angles of a triangle add up to be? What are the measurements of the angles in a square, a rectangle, a hexagon, or an octagon?

Evaluation Strategy: The copy on corresponding angles, alternate interior angle, and supplementary angles can be used as a learning tool as well as an evaluation. The creativity of each group as well as a successful program can also be used to evaluate. Different levels of difficulty on street grid patterns will shows different levels of understanding of students knowledge of angles and their relationships.

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Ice Cream Route Programming

I. Traverse The Course Program the following: Interpret the instruction: CM CM ________________________ ∆3 ________________________

90 ________________________ ∆ 3 ________________________

90 ________________________ ∆ 3 ________________________

90 _______________________ ∆ 3 ________________________

90 ________________________ ∆ 3 ________________________

90 ________________________ ∆ 6 ________________________

90 ________________________ ∆ 3 ________________________ II. Traverse The Course To Stop At Designated Spots * Change the Roamer distance unit to 15cm. Program the following: Interpret the instruction: CM CM ________________________ ∆ [15] ________________________ ∆ 3 ________________________ W 10 ________________________ ∆ 3 ________________________

90 ________________________ ∆ 6 ________________________

90 ________________________ ∆ 3 ________________________ W 5 ________________________ ∆ 3 ________________________

90 ________________________

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∆ 6 ________________________

90 ________________________ ∆ 3 ________________________ W 10 ________________________ ∆3 ________________________

90 ________________________ ∆ 12 ________________________

90 ________________________ ∆ 6 ________________________ III. Traverse The Course To Play Music and Stop At Designated Spots Move Roamer to first stop, play music, wait to serve ice cream. Move ahead to next stop, play music, wait to serve ice cream. Move ahead to next stop, play music, wait to serve ice cream. After the three stops, the Roamer returns to beginning of route without stopping. You will need to program a tune for the Roamer to play. Use a procedure P1 to do this.

P1 [ 48 45 88 48 45 88 410 48 46 45 43 45

46 35 36 38 31 21 21 21 21 33 35 36

48 48 43 43 46 45 43 41 ] Program the following: Interpret the instruction: CM CM ____________________ ∆ 3 ____________________ P1 ____________________ W 10 ____________________ ∆ 3 ____________________

90 ____________________ ∆6 ____________________

90 ____________________ ∆3 ____________________ P1 ____________________ W 5 ____________________ ∆ 3 ____________________

90 ____________________ ∆ 6 ____________________

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90 ____________________ ∆ 3 ____________________ P1 ____________________ W 10 ____________________ ∆3 ____________________

90 ____________________ ∆ 12 ____________________

90 ____________________ ∆ 6 ____________________

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Roamer Street Grid

1.A

180cm

90cm

90cm

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Roamer Street Grid 1.B

89

Street Grid #1

represents one house

90

Street Grid #2

represents one house

91

Street Grid #3

represents one house

92

Street Grid #4

represents one house

93

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Roamer Music Row Your Boat

41 41 41 13 45 45 13 45 13 68

313 113 38 18 35 15 41 48 26 35 23 41 Barney Theme/ This Old Man

48 45 88 48 45 88 410 48 46 45 43 45

46 35 36 38 31 21 21 21 21 33 35 36

48 48 43 43 46 45 43 41 Twinkle Twinkle Little Star

41 41 48 48 410 410 48

46 46 45 45 43 43 41

48 48 46 46 45 45 43

48 48 46 46 45 45 43

41 41 48 48 410 410 48

46 46 45 45 43 43 41 Happy Birthday

41 41 43 41 46 45

41 41 43 41 48 46

41 41 413 410 46 45 43

411 411 410 46 48 46 Three Blind Mice

35 33 61

35 33 61

38 26 16 55

38 26 16 55

18 213 113 112 110 112 213 18 28 18

113 113 113 112 110 112 213 18 18 18

18 213 113 112 110 112 113 18 18 28

16 35 33 61

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Advanced: Orthographic Roamer Projections

Objective: To provide students hands-on experiences with the techniques of orthographic sketches of real objects and the ability to visualize three-dimensional spatial relationships.

Three-dimensional objects may be represented on a sheet of paper by sketching one or more orthographic views. Orthographic views are obtained by looking squarely at one or more faces to describe the shape and proportions of the object. We will draw three principal views of the object; the top view, front view and right-side view. Since the views are projections of the same fixed object, the top view must be placed directly above the front view and the right-side view is placed to the right and aligned with the front view. See Figure 1. The correct procedure for sketching the three principal views is to lay out the overall width, height, and depth dimensions of the object to form three rectangles to enclose the three views as shown in Figure 2. The front view will show width and height, the top view width and depth, and the side view height and depth. After “blocking in” the views, the details of the geometric shapes are sketched in light lines. Measurement details are projected back and forth from view to view. Thus all views are completed together, not one at a time.

Materials: For the class: Roamer Objects to Draw Cube Shoe Box Steps (made from shoe boxes) Table Desk Rulers Paper Roamer Measurement Devices Poster Board (Optional) For each student: Journal* *provided by teacher Basic Skills Development: Language for Information Understanding Analysis, Inquiry and Design Mathematics Connecting MST to other Areas of Learning Preparation: Linear measurement, scale and proportion, knowledge of height, width, and depth of an object, Cartesian coordinate system (optional), different views of an object, ability to label top/front/right-side views. It will be extremely helpful if the students have the object to be sketched in a place where they can move around it to “see” and measure the views they wish to draw. For example, a set of small steps made from shoe boxes can be handled by the students very easily. Adaptive devices may be required for children with special needs.

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Orthographic Roamer Projections continued Page 2

To program the Roamer to draw the orthographic projections, you must decide on a scale and a point of reference. Choose a point of reference on your drawing such as the bottom left corner of the front view. Refer to this point when the Roamer is positioned to draw a view so that all views are aligned properly. Record all actual measurements of width, height, and depth on the drawing. Set the Roamer to hold a pen in the center position. Write a program for each view. Place the Roamer in the appropriate starting position for each view with respect to your point of reference. After all views have been drawn by the Roamer, label the front, top, and right side views as well as all dimensions. Remember to include a scale of the Roamer dimensions to the actual object on the finished drawing. Students will keep a journal of the techniques used to create an orthographic projection. They should practice with simple objects, paying attention to details such as proper alignment, measuring, and labels. They may also wish to display their orthographic projections on a poster board display showing their drawings as well as a picture of the actual object. Extension: Have the students record in their journal what prior knowledge they had orthographic projections before this learning experience. Can they locate additional orthographic drawings in magazines or books? Why are orthographic projections mostly used by engineers and architects? Several CAD software programs are available to further explore the curriculum.

Evaluation Strategy: Depending of the age and ability level of your students, you can start with a simple object like a cube or rectangle. Older students can be assessed with orthographic projections of more complicated objects such as stairs and desks. Proper alignment of the three views, neatness, and accuracy of measurements should be the assessment criteria. Student drawings as well as Roamer program drawings can be assessed separately.

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Integrating Roamer into Lessons

Introduction to Linear Units Have students: Estimate distance in small units (foot steps). Program the Roamer to move the estimated distance. Compare with Roamer default movement. Estimate the error. Estimate distance in larger units (large steps). Program the Roamer to move the estimated distance. Compare with Roamer default movement. Estimate the error. Place objects different distances apart and measure with non-standard and Roamer units. Estimate the distances and program the Roamer to move the estimated distance and wait 3 seconds at the second location. Compare your estimate with Roamer movement. Program the Roamer to move forward in a range from 1 to 10 Roamer units. Have the Roamer wait 3 seconds at each odd number. Program the Roamer to move forward in a range from 1 to 10 Roamer units. Have the Roamer wait 3 seconds at each even number. Estimate the distance and send Roamer to a friend. Have friend send Roamer back. The default distance setting for Roamer is 30 cm. To change the Roamer unit distance setting

use Δ [?] where ? is the new unit. Δ[10} would change the Roamer distance movement unit to

10 cm Use Roamer’s distance setting to allow Roamer to move in small units (foot steps). User Roamer’s distance setting to allow Roamer to move in large units (larger steps). Send Roamer to a friend using distance settings that have been changed. Measure the error. Send Roamer back using new distance settings. Find out who had the least error. Find 4 things you can measure with the default Roamer unit. Find 4 things you can measure accurately with smaller units and 4 things you can measure accurately with larger units.

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Introduction to Angular Units

Have students: Use a circular protractor to estimate the degrees they would have to turn, to turn a square corner. Use a circular protractor to estimate the degrees they would have to turn, to turn one half the way around. Use a circular protractor to estimate the degrees they would have to turn to turn all the way around. Program Roamer to turn one half the way around clockwise. Program Roamer to turn one half the way around counter-clockwise. Program Roamer to turn all the way around clockwise. Program Roamer to turn all the way around counter-clockwise. Send Roamer to a friend using the distance setting. Have Roamer turn clockwise one half the way around and return to you. Program Roamer to turn one quarter of the way clockwise. Program Roamer to turn one quarter of the way counter-clockwise. Place Roamer facing north. Program Roamer to point south, then west, and then east. Design a challenge for other students involving turning Roamer to various positions.

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Exploring Perimeter and Area When a Roamer journey starts and finishes at the same point (other than traveling in a line), the distance traveled represents the perimeter of an encompassed area. Children can explore the ideas of perimeter and area through programming Roamer, taking measurements and performing calculations. It is important that children distinguish between the numbers and notations used for distance and for turning. Perimeter of Triangles and Squares Have students: Write programs to draw triangles and squares on your programming sheet. Program Roamer to draw triangles and squares of different sizes. Discuss the concept of perimeter. Draw triangles and squares through use of programs and Roamer pens. Place marks or push pins at each corner of the drawn shape. Using string (without stretching), determine the total distance traveled. Cut the string to the traveled length, lay it out and compare. Analyze relationships between the distance traveled and the programs. Inquire into relationships between triangles of different sizes, squares of different sizes and possible connections between the perimeters of squares and triangles. Area of Squares The space enclosed by a Roamer journey represents the area of the shape. This is the “real”, in scale, area and shape. It is more real, in concrete terms, than paper and pencil tasks. However, the concept of area is difficult for children to grasp. Information about area is not easily inferred from the numbers in the program alone. A strong link can be made between calculations, Roamer programs and their physical representations as drawn by the Roamer. Have students: Program the Roamer to draw a square with the area of 4. Program the Roamer to draw a square twice the size of the first square. Compare the actual results with the expected results. Note: The correct result for the area of 4 is a side of 2. The most common result for area twice the size is a side of 4 for an area of 16, which is four times the original area. Design other challenges related to scale and shapes using the Roamer.

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Fitness Test Every six months, Roamers must take a fitness test. Find out:

1. How fast the Roamer moves forward.

2. How fast the Roamer moves backward.

3. How quickly it turns.

4. What is the steepest slope it can climb.

5. How much the Roamer can push.

6. How much the Roamer can pull.

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Geometric Shapes and Forms

Shape – A flat, two-dimensional figure and/or outline of an object, such as a drawing on paper. Examples could be a circle, a triangle or a square. Generally the flat or two-dimensional (2D) representation of a surface or the surface itself. Form – A three-dimensional figure. Examples could be a sphere (ball, globe), a pyramid or a cube. Generally the 3-dimensional (3D) representation of an object or the object itself. Poly – A prefix meaning many, several, having or consisting of many, such as polygon or polyangular. Polyangular – Having many angles. Examples could be triangles, squares, hexagons and others. Polygon – A flat, closed figure or shape having many faces. A closed figure or shape formed from line segments that meet only at their endpoints. Polyhedron – A three-dimensional figure or form in which all the surfaces are flat. Examples could be a pyramid, cube or rectangular box. Regular polygons – A solid figure or form with all the sides the same length and all angles the same measure. Examples could be a cube, tetrahedron, … Tri – 3 edges Square – 4 edges Penta - 5 edges Hexa – 6 edges Hepta – 7 edges Octa – 8 edges Nona or Ennea – 9 edges Deca – 10 edges Hendeca – 11 edges Dodeca – 12 edges A regular triangle is an equilateral triangle. A regular rectangle is a square.

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Programming Roamer to Make Shapes Have students: Write a program to make a square using only forward commands. Write a program to make a square using only backwards commands. Write a program to make a square using both forward and backwards command. Write a program to make a square using a repeat command. Write a program for a rectangle using the repeat command. Write a program for an equilateral triangle using the exterior angles. Write a program for an equilateral triangle using the interior angles. Write a program for an equilateral triangle using both interior and exterior angles. Write a program for a regular pentagon, regular hexagon, and regular octagon. Can you come up with a general formula that could be used to write a program for any regular polygon? Can you write a program for a star?

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Curriculum for Roamer Technology

Roamer Equations - Myers

1. Roamer has 57 cm available for movement. Roamer cannot go outside of the 57 cm length. Find at

least 10 different ways to get the Roamer to move 57 cm exactly without going outside of this length.

Show the arithmetic in a horizontal number sentence to verify your results. You must be going forward

all the time. Only use numbers between 1 and 10.

Example: Set the Roamer unit of movement to 10 cm and go forward 5, then set the distance to 7 cm and

go forward 1.

Equation: 5 x 10 + 1 x 7

5(10) + 1(7)

Program: F[10] sets Roamer unit to 10 cm

F5 go forward 5 units

F[7] sets Roamer unit to 7 cm

F1 go forward 1 unit

2. Roamer still has only 57 cm of length available. Program Roamer to go 57 cm by use of BOTH

addition (forward) and subtraction (backwards). Be sure that Roamer doesn’t go outside of the 57 cm

length. Write at least 10 different equations to demonstrate this and check by programming the Roamer to

do your equation. Only use number between 2 and 10

Example: Set the Roamer unit of measure to 10 cm and go forward 4, then set the distance to 4 cm and go

backwards 2, then set the distance to 5 cm and go forward 5.

Equation: 4 x 10 - 2 x 4 + 5 x 5

4(10) -2(4) +5(5)

Program: F[10]

F4

F[4]

B2

F[5]

F5

3. Roamer has 4 cm of space that can be used at the beginning and at the end of the 57 cm. Write at least

10 equations that can be used to get Roamer to the 57 cm mark by using both addition and subtraction.

Only use numbers between 3 and 8 in your equations. You must use at least one region of extra space at

the beginning or the end.

Example: Set the Roamer unit to 4 cm and go forward 3, then set the Roamer unit to 5 cm and go

backward 3. Now set the Roamer unit to 8 cm and go forward 8, then set the unit to 5 cm and go

backward 5, then set the unit to 3 cm and go forward 7.

You write the equation and program for the example.

Roamer Ideas

Number sequences:

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How many possible ways could you design to program the Roamer Robot to move 57cm using numbers

between 3 and 9 without subtraction? Present your codes and explain the meaning of each code line you

have written and where the Roamer will move after the execution of each line.

How many possible ways could you design to program the Roamer Robot to move _____ cm using

numbers between ____ and ____without subtraction? Present your codes and explain the meaning of each

code line you have written and where the Roamer will move after the execution of each line.

How many possible ways could you design to program the Roamer Robot to move _____ cm using

numbers between ____ and ____without subtraction? Present your codes and explain the meaning of each

code line you have written and where the Roamer will move after the execution of each line.

Similar problem for degrees of turn…

Symmetry problems…

Repeat patterns or systems

Roamer clock times

Stepping stones

Puzzles

Target Zones with points

Pattern Block Programs

Mazes

Uses of the Roamer Cards

Now try

writing

another

program