Patterning With LOGO

Adding the National Geographic Photo of the Day widget to my Google Desktop and blog has been a real winner in terms of personal inspiration and as a creative spark over the last couple of years. Usually the images lead me to Language and Literacy ideas, but  this image from the 6/5/10 set me thinking about a possible context and and alternative in to working using LOGO with our older Phase 2 students next term. 

In previous posts I have explored the use of MSWLOGO a freeware tool and MS Paint within the context of the Mathematics classroom, developing ideas around the properties of shape, rotational symmetry and patterning, but using this image as a starting point and available design for the journey, what would happen if... this was extended to explore tessellation and repeated patterning, using copy and paste processes?



Image Credit: Hazrat Ali Mosque, Afghanistan  National Geographic Photo of the Day 06/05/10

Riddle Me Ree! What a Difference a Name Makes.

Floor Turtles and Procedures..  Or Riddle me Rees?

I 've been working on an iterative unit of learning with some of our Lower Phase 2 students this term, that seeks to build on their previous work using Beebots.   The unit has focussed on

• routes
• giving and following instructions
• developing procedures
• and prediction and reasoning about shape, space and measure

while drawing on creative and imaginative work evolving through ongoing activities in class.

There is enormous potential for cross curricular activity using control based activity within the primary curriculum to engage with the concept of routes and navigation.  Younger students have enjoyed creating games based on programming the Beebot to navigate mazes, collect and sequence objects, moving the floor turtle from point a to point b with as few breaks in the programming structure as possible.  Moving to the Probot should not be that different it seems to me.  The process of inputting procedures may be new with the addition of a numerical keypad, but the type of game or activity can remain quite similar.

The students are currently engaged with a theme about Pirates... They are excited and stimulated by treasure maps (several making, designing and then aging these at home with their parents), huge wooden sailing ships, and the writing and using of riddles and clues, but one key tool was missing two weeks ago that would truly aid a successful pirate in navigating his/her ship, and unravelling and following the clues left for them.

In my first session with the students I decided to create floor compasses with them. What self respecting pirate would head out on treacherous seas and high adventure without one. This was an entirely give and go session

• modelling how to use the Probot
• inputting instructions with the keypad
• how to clear memory when we had finished
• use of the pen holder as a means to record outputs from the probot
• observing input and output in action.  

This took a little longer than expected, creating the skeleton for the compass rose with the probot and pen was fairly straightforward, but the additional measuring and drawing tasks needed to create the rose from the skeleton were quite a challenge for the group.  Persevering and extending the session to allow for additional support, taking students out in small groups to complete the task however really paid off in terms of the student satisfaction and pleasure at their completed outcomes, and the discussion that evolved.  The students were asked to choose  3 colours with which to decorate their compass, and as they worked to identify the shapes and patterns they were creating within the rose.

• What shapes could they see?
• How many of each shape (triangles and quadrilaterals) could they find?
• What was special about the shapes that touched?
• Could they see any lines of symmetry within the shape?
• Could they label the cardinal points of the compass?
• What might be the names of the points in between? 

The completed compass roses have been trimmed, mounted and displayed as part of ongoing classroom work.  

During Literacy sessions the students have been working on writing riddles and solving clues.  To consolidate and link to this I decided to create some riddles that the Probot could be used to solve.  This would allow the students

• to practice input independently, 
• and to observe output.   

Each group was given a support sheet containing a series of "riddles," procedures, that when the Probot was programmed would result in the pen tracing particular shapes on large sheets of paper.  I hoped that the students would enjoy the task, but was not expecting the excitement that followed.  Changing the name of the task to "Riddle Me Ree, What can I be?" and adding the idea that this was "Pirate Challenge" that we needed to work on as a "Crew" really motivated the group. They wanted to be first to finish, but when pointed to the idea that finishing first was less important than accuracy in following clues they worked hard to organise themselves

• Taking Turns to enter inputs
• Checking that inputs were accurate, 
• Correct where mistakes had been made, sometimes this involved deleting the whole procedure and beginning again, and for some groups who had spotted you could navigate the menu, only removing parts that were incorrect and correcting them.

The students were initially surprised by the idea that these instructions could produce recognisable shapes, but this further motivated them to see what the next procedure would produce.  Working with each group I encouraged them to look at what they were entering into the key pad, and the outcomes they had developed.  Could they predict what shape their next riddles might produce.

eg You had four sets of  fd 10 rt 90 this had produced a square.
     You had three sets of fd 10 rt 120 this produced a ?
     What might 6 sets of fd 10 rt 60 make?

The final riddles included repeat procedures, and the students had not had these explained to them, either what they were, or how to input these to the keypad.  This challenge was theirs, could they figure this out for themselves.  Several of the groups had few problems, but I have to admit to not actually explaining the how to any of the groups I worked with, yet they all managed to find out how for themselves, seeking help from others when they got stuck, another winner in this session.

To complete the challenge the students had to label the shapes with their names and add the riddle that had lead to the creation of the shape.  These too are ready for display, perhaps in the ICT space.  I realy like this activity and intend to adapt it when I begin using LOGO next term with Years 4 and 5.

This week the students began creating treasure island maps on large sheets of paper.  On these the students have again been encouraged to draw on their classroom work, to add mysterious and hazardous places with strange and spooky names.  I really want the students to add 10cm x 10 cm grids to these maps, though they may need some help with this reflecting on experiences with the floor compass, before using their floor compasses, their developing knowledge of input and output with the probot, their experiences of writing riddles and using my clues to create written directions to the mystery location of the treasure.  These will then be tested and evaluated by other students who will be challenged to use these clues to find where an imaginary X marks the spot.  Hopefully the students will be as excited and motivated by this challenge as they have been by the others.

From Probot to LOGO: Some previous posts in action

I have put together this photo montage for the time being to share some of the activities my students have engaged in while using Probots and MSWLOGO this term. Even though presented here in an ICT context, references placed towards the end of this post highlight a number of areas from the Primary Framework for Mathematics with which the children engaged, through the using and applying strand, and which draw into focus the cross curricular potential of work such as this to help children make links between areas of learning.



The file is progressive and begins with the children using the probot to create skeletons around which they made and then decorated their own floor compasses. From here working in groups the students used their floor compasses to learn about compass direction, predicting outcomes from given inputs, eg if I am facing east, and make a 1/4 turn east what direction will I be facing? This required them to know and use the numerical values for rotation sizes, or to calculate these using halving and doubling strategies. Within the problems set we also replaced fractions of a turn with the number of degrees, and the directions of a rotation with clockwise/anticlockwise, and right/left. The children went on from this to make up challenge questions for their friends in other groups.

In the next series of activities the children made mazes using strips of paper. Working initially with right angles, some children chose to extend the activity to include 45 degree turns. The children used their knowledge that a Probot step was 1 cm to help them measure the distances the probot would need to move, and estimation to predict and test the size of turn they would need to make at each point in order to navigate the maze. After step by step planning the children were asked to input procedures, that would take the turtle from one end of the maze to the other without stopping.

The final photographs in the series represent a session in the ICT suite where children used MSW LOGO for the first time. The students were given a prepared treasure map which they loaded into the LOGO workspace, before we discussed as a class and decided the route around the island we would take, or the order in which we would visit particular landmarks. Transferring the floor based experiences of the students to the screen was not difficult, and after only a brief introduction to the commands and how these should be input, they worked very successfully and independently, to resolve many of the issues they encountered. In the plenary to this session the children were asked what they would like to do in the next session, and suggested that they would like to have a blank treasure map, that they could add landmarks to themselves, they could then ask their friends to journey around their island following a route they had prepared.

This series of activities, as well as the obvious ICT and Geographical links, offered opportunities for the students to engage practically with the following strands and related objectives from the Primary Framework for Mathematics

Measuring

• Know the relationships between.., metres and centimetres..., choose and use appropriate units to estimate, measure and record measurements
• Read, to the nearest division and half-division, scales that are numbered or partially numbered; use the information to measure and draw to a suitable degree of accuracy

Understanding Shape

• Read and record the vocabulary of position, direction and movement, using the four compass directions to describe movement about a grid
• Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles

Counting and Understanding Number

• Read and write proper fractions, interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes;

While using and applying their knowledge and understanding of these areas in the context of problems and puzzles.

Many of the activities here are drawn from or build on previous posts that can be found within the control category to the left of the page.

Scratch and

I was desparate to call this post "Scratch and Sniff," as really that is all it is, a tip of the iceberg set of statements and a momentary expression of appreciation about a tool I have been pointed to a number of times through blog posts, feeds and del.icio.us. Until a recent post and a thumb's up on mrstucke's Masterplan I didn't realise just what I had missed out on by not actually installing the download I had made or looking further than the handful of videos on the tool I had watched. Installing the application, taking a spot of time to aclimatise and familiarise myself with the environment and its visual tool box, it has been really cool to watch kitty boogy his way through a set of routines I had previously scripted for my turtle in LOGO.


Can feel a few posts of my own coming in the future. Thanks Daniel. Interested in having a play for yourself, you can download a copy of Scratch from here.

Making a Floor Compass With A Probot

Last year when I was working with Y3 we made small hand held cardboard compass models that we could use to help us with our LOGO based map work. This week I am thinking about introducing angle and turn by using the Probot to make floor compasses that students can use with their turtle. This will help introduce and practice using the keypad.

To Make a Compass

Drawing the cardinal points (N,E,S,W)

Place a pen in the pen holder, and the Probot in the centre of a large piece of card, or paper.

input

rpt 4[
fd 20
bk20
rt 90 ]

and press go.

After the Probot finishes, leave it in its end position

Adding The Intercardinal Points (NE, SE, SW, NW)

clear the menu

input rt 45 and press go

clear the menu again then

Input the previous procedure again, but this time substitute 16 for the fd and bk parameters.

ie

repeat 4[
fd 16
bk 16
rt 90 ]

and press go

Turning A Skeleton into a Rose

• Use a ruler to mark a point 1 cm along each line drawn from the Probot's home position.
• Join each of the cm marks on the Intercardinal directions to the tips of the Cardinal Compass points.
• Join each of the cm marks on the cardinal directions to the tips of the Intercardinal points.

As a discussion point about the value of the angles between each rotation around the compass I am hoping this will prove invaluable. Eg there are 90 degree turns between each of the cardinal points, 45 degree turns betwen the cardinal and Intercardinal points, while a 90 degree turn or right angle can be made between each Intercardinal Point too. We have explored right angles in numeracy hour, and hopefully the children will recognise these as sketched by the turtle. Using this model the students can mark the turn sizes as well as recording the compass directions. In practical terms I hope the tool will support ongoing work.

I want ultimately the students to design maps and tours using their Probots, and using compass directions to challenge other groups to use their probot in following directions they give. This will later be transferred to onscreen activities using MSW LOGO and imported bitmap treasure maps.

Playing With Probots

We have been using TTS BeeBots with younger students in school for a while now, but have not until recently had an affordable floor turtle option that we could use with older children to support extension of floorwork and transition to the onscreen LOGO work we want to develop with them. Last Summer I invested in a class set of Probots also from TTS to help us bridge this gap, adding a new layer in the progression of learning in control and modelling with students at school.

The BeeBot has proven a popular and fantastic device to use with young students. I have posted a number of times about how we have used these in the classroom, to play sequencing games, develop prediction and conslidate spatial language. Staff who have used the BeeBot, have begun to find some very creative ways of including the "creatures" in their classroom activities to support learning and sequential thinking particularly across the curriculum, through self developed play mats, based around experiences using TTS's Focus on BeeBot software . The simplicity of the beebot as a device has helped open up and engage my colleagues with the teaching of Control and modelling in the early years and Key Stage 1. This has been supported by work on how with a little creativity and use of other tools this device can enable us to support learning and meet the current early control experiences our students need.

The Beebot's simple keypad enables forward, backward, right and left turns to be input as strings of commands, before using the go button to start the turtle out on the process of carrying out its programmed actions as a procedure. Turns to the left and right are input in multiples of 1/4 turn or 90 degrees. Developing learning within the control and modelling curriculum however is not just about the toole we use, but the pedagogy and thought process behind and which we bring to the activities, and how we use the resources available to contextualise and set problems.

Enter the Probot, here spotted at what I am told is the most picturesque view in the UK, Wastwater. Shaped like a car this device has a numerical key pad, enabling more complex sequences of commands, to be entered. Its programming language based on LOGO, enables commands to be input as strings as with the BeeBot, but in addition, through use of the onboard menu, procedures can be written and saved, for inclusion in more complex procedures. Rotations are input numerically as well as distances , so the vehicle is able to make turns other than right angles, and does not require repeated input of commands.

Here is a short video clip to show you what I mean.

In the Video I revisited a pattern sequence I created earlier using LOGO.

First of all the Probot was programmed to travel around/trace the perimeter of an imaginary hexagon by inputting

rpt 6[
fd 5
rt 60]

then pressing go

Then a pen was placed in the central pen holder, the placed Probot on a large piece of card and the go button pressed. This lead to the Probot tracing its route on the card and drawing the hexagon I had previously input.

Selecting from the menu to make a new procedure (proc 1), the sequence of commands to draw a hexagon were added, and the procedure saved

now entering
rpt 6[
proc 1
rt 60]

and pressing go
resulted in the probot drawing the hexagon 6 times, with a rotation of 6o degrees in between each hexagon.



The ability to store and run procedures, rather than inputting strings of commands, means that this turtle can be used to mimic on screen activities, and through the use of a usb cable onscreen activity and procedures can be downloaded from the software package Probotix , to the device, enabling onscreen activities to be transferred to the "floor turtle." I have to say that at the moment I am not having as much fun with this software as I thought I might, though this may be just due to my lack of familiarity with its quirks. I will get back to this later I hope, but currently it tends to lock up, when it doesn't recognise code, or when I make mistakes. Perhaps this will be different if I treat it more like the probot, and less like the LOGO environments I am familiar with. This however is a worrying aspect, especially if I want to use this software to support the floor to screen links I want to make.

MSWLOGO: Creating and Decorating Patterns

Enjoying half term and the chance to just play. A game of Mountain Hockey this morning, a spot of domestication this afternoon, before playing with MSWLOGO and Microsoft Paint this evening.

Having got my substitution procedure for making a polygon working yesterday, at Andy's suggestion I added another attribute to alter polygon side length so the polygon procedure now looks like this...

to polygon :SIDES :LENGTH
REPEAT :SIDES [FD :LENGTH RT 360/:SIDES]
END

I can now change the type of regular polygon I draw and its side lengths too.

What this means is I no longer need to tell LOGO to draw a particular polygon, However I do need to know its properties, in terms of the number of sides and angles I want it to have, and to decide how large I would like it to be, before I can input these for the turtle to do the hard work of drawing it.

I decided to just play with what I had for the time being and to make a pattern using my polygon procedure and a simple repeat routine, inputting several pentagons that gradually increase in side length before turning through 36 degrees.

Experiences, working with y4 students making "flowers" tell me that this is what they tend to do and get excited by when we explore the environment, having compiled and saved their static polygon procedures, and why not its fun and exciting to see what the turtle draws when he has been programmed.

In this instance the procedure I asked the turtle to carry out looked like this

repeat 10 [polygon 5 50 polygon 5 100 polygon 5 150 polygon 5 200 polygon 5 250 rt 36]

And this was the resultant pattern.

When the turtle had finished and put his feet up, I saved the workspace as a "bitmap image," and then opened it in Microsoft Paint. Again in work I have carried out with students this is a task they love to do. Using the "fill tools" with the Bitmap created in MSWLOGO, students are able to colour the repeating patterns made, and the design you can see at the top of this post was created in this way.

When I set out to create the pattern, I originally set myself the pattern rule, to use only 2 colours, and fill the design so that no 2 shapes in the pattern that touched or were adjacent to each other would be the same colour. However as I moved outward from the centre of the pattern, I reached a point where it was not possible to follow the rule, so I needed to introduce a third colour.

I am really enjoying this free piece of software and looking forward not only to exploring it further, but looking at how the processes I have missed out on by not engaging more deeply with it, can be applied to my play with the Probot I have brought home with me this week. I am also beginning to reflect on how the use of prewritten procedures might facilitate and support investigational work and consolidation activities in Mathematics sessions around the properties of shape and measure, as well as extension and challenge for more able students in ICT sessions as suggested by previous comments by Andy. Thanks

Investigating a Rectangle with LOGO

This week I will mostly be playing with Probots and the Educational freeware environment MSWLOGO I had installed in school a while back. LOGO is an environment I haven't explored in as much depth as I should have, or so I am beginning to discover, particularly with the increased focus within the New Primary Framework for Mathematics on the using and applying strands.

As I have begun to play with these tools this week, exploring beyond the simple repeat and build procedures I initially work through with students, I am beginning to discover just how superficial my personal understanding and capability with the tool is, and just how big a mistake it was on my part not to persist with the environment in my early teaching career. These short sharp sessions are beginning to challenge me to think more deeply about how I could use tools like LOGO more regularly to challenge and support reasoning and thinking with students during the numeracy hour, a place where I have long believed this aspect of Control and modelling within the primary ICT curriculum should be embedded.

Experience tells me there is a tendency for LOGO to be used and taught in the Primary School these days when the QCA Units for ICT that utilise it make that requirement. This leads generally to control sessions being developed through the delivery of standalone units such as this in Y4. What concerns me about this is not children learning to build procedures that make pretty flower designs, but that from a pedagogical perspective there is much more to LOGO as a learning tool than this. By linking the tool to help develop units of work involving application of knowledge and understanding of shape, space and measure. As a "constructivist" learning tool, LOGO affords opportunities to design learning contexts through which to apply, link and develop strategies for problem solving and investigational work while using the environment to model and explore generalisations and hypotheses.

Thinking about Rectangles

While playing today I have been thinking about rectangles and how, when shown an oblong many of my students are able to identify and describe its basic properties, eg. it is a rectangle, it has four sides, four angles or corners, and each angle is a right angle. When we compare the shape with a square that shares these properties, and the students are asked how they differ? discussions usually begin with how one shape is longer than the other. Further questioning and discussion will lead to us identifying how opposite sides of an oblong are the same length, and how the square is a special (regular) rectangle, but making specific reference to the nature of the opposing sides of an oblong is something which is quickly forgotten.

Coding LOGO to draw an oblong requires us to use and apply this property. Even though the shape has 4 sides, a repeat 4 procedure, would not be an efficient way to input the parameters. Writing even a simple repeat procedure, requires us to think slightly differently about the way we should input our commands in order to draw the oblong. So how might I use LOGO to explore and consolidate understanding about the properties of rectangles as members of the quadrilateral family.

Thinking Through an Investigation

In previous sessions, adapting the QCA Unit linked to above while working with students I have tended to stick to developing regular polygons of a standard side length, returning to making Irregular Rectangles or oblongs later, perhaps if or when students have asked how to do this. This leads to a naturalish discussion about the properties of rectangles.

As said above squares can be classified as Regular Rectangles, as such they have 4 equal sides, 4 equal and identical angles, and the same number of lines of symmetry as they do sides and angles. Each angle is a right angle measuring 90 degrees.

A square can be made with a repeat procedure

repeat 4 [fd X rt 90]

Or using the polygon procedure I published previously, by inputting polygon :side :length.

This would not work for an oblong since adjacent sides are different lengths, while opposite sides are equal.

Building a Procedure to Draw Rectangles

Lets say we wanted the turtle to travel around the perimeter of an oblong 300 units long, we could do this by inputting commands that would draw 2 sides of 100 units and 2 sides of 50 units, using a set of commands that look something like this

fd 100 rt 90 fd 50 rt 90 fd 100 rt 90 fd 50 rt 90

To turn this into a repeat procedure, we could rewrite it something like this:

repeat 2 [fd 100 rt 90 fd 50 rt 90]

So a build command would look something like this...

To rectangle
repeat 2 [fd 100 rt 90 fd 50 rt 90]
end

Saving this procedure, typing in rectangle and hitting the enter key would draw a rectangle where 2 sides were 100 units long and 2 sides were 50 units long.

Building a Procedure to Create Variable Rectangles

The last procedure would be fine if we always wanted to make our rectangle the same shape and size, or we were happy to edit our procedure every time we wanted to change the size of our rectangle. But if we wanted to use our program to help us investigate for example the perimeters of rectangular fields that a farmer could fence with 300 metres of wire? Or the different rectangles we could draw with a particular perimeter it would be useful to have a program where we were able to substitute parameters. (Thanks Andy am having lots of fun with this!) In this case we might use a procedure something like this:

to rectangle :sidea :sideb
repeat 2 [fd :sidea rt 90 fd :sideb rt 90]
end

Investigating Rectangles Maybe!

Now I could begin either inputting side lengths to the procedure to randomly draw different rectangles, or I could begin applying my knowledge and experience about the properties of rectangles, using other areas of mathematical experience such as calcualation, addition and subtraction, halving and doubling etc to help me explore/investigate the substitution values that total a given perimeter, using my procedure to model and test my work by inputting my values and testing on screen. Eg with my length of 300 metres or Turtle units

rectangle 40 110 and hitting the enter key would draw on oblong with this perimeter

40+40+110+110= 300

The procedure models the familiar formula for calculating the perimeter of a rectangle

2l+2w=p

(2x40) + (2x110) = 300

What about rectangle 45 105?

45+45+105+105=300

A suitable problem might be for children to investigate some of the different ways of fencing a rectangular field with 300 metres of wire (using 300 turtle units to represent this).

I don't think I would show the children the procedure and how it works. Instead it might be fun to begin with trial and error processes through the introduction and investigation of a systematic pattern, similar to the example below

40+40+110+110= 300 (rectangle 40 110)
45+45+105+105=300 (rectangle 45 105)
50+50+100+100=300 (rectangle 50 100)

What might the next sequence or input be? What can we see happening in the pattern? What would happen to the pattern if we changed 40 to 41 or 42 and so on? The students could use whiteboards to record their patterns, inputs and informal jottings if necessary, with the focus of the task being around paired discussion, mediated by the onscreen feedback and success of their input in relation to the expected output of a rectangle.

Moving on perhaps we could ask the children to use their experiences to visualise, map out and draw what they think the turtle has to do in creating each of the rectangles they have drawn, focusing their attention to the visible properties of each shape and how these relate to the numerical values they have inputted. Notice the line (perimeter) made by the turtle travels around the shape, so each step carried out must have been in sequence. Even though still focussed on the properties of oblongs and the relative location of their sides, we also have the contingency within this activity to begin to introduce the idea that 2 of the values in each of the patterns are the same, and that as the turtle draws them they output to become opposite sides of the oblong and that adjacent sides are of different lengths. So perhaps at this point we could look at or introduce a simple repeat procedure for drawing a rectangle and explore how each value might be substituted into the program, talking through the effect, drawing and visualising it before returning trying it on screen, perhaps with trace enabled, and finally reviewing our square and oblong, discussing how or if what we have learned during our investigation has changed our view of the two shapes. This might also support introduction of the formula for calculating perimeter of squares and other rectangles, by comparing and deriving the standards from the LOGO procedures.

eg repeat 4 [fd x rt 90]

could be reduced to the perimeter of a square is equal to 4 times the length of 1 side

so p=4xl

repeat 2 [fd x rt 90 fd y rt 90]

could be reduced to the perimeter of a rectangle is equal to 2 times the length add 2 times its width.

so p=2l+2w

Using the rectangle procedure again the task could be extended to enable students to test and investigate the shapes of fields that can be fenced using different lengths of wire by the farmer. What length would each side be if the farmer wanted to make a square field using the length of wire he has?

In class and at table tops, this activity could be further extended to explore the relationship between area and perimeter in each shape, using squared paper to explore the different shaped fields the farmer can make, and the area of each one.

This may seem an ambitious proposal, but I would be fascinated to see just what a KS2 class would make of the activity. I think most of us would be surprised to see just what a Y4 class can learn about the properties of polygons and rotation when using the idea that 360 degrees is the same as a full turn, and substituting factors of 360 within repeat procedures to make "flowers" from fixed shape procedures. The potential mathematical outcome of the Y4 unit linked to above, is way more complex than on first viewing the unit expects, yet if students are to appreciate and understand the outcomes of the tasks, beyond the making of flowers and context is to be given to what is being learned we need to engage the children with the mathematical ideas inherent within it. Perhaps this unit can be taken to pieces, and bits and pieces used or built into wider mathematical work. How might changing our view of this unit enable exploration and application of visual models to support reasoning and understanding about shape?

Expanding my Horizons With LOGO

Thanks to Andy Roberts for his comment a couple of weeks ago on my post Logo Routines: Building Polygons, where he said,

"To differentiate for the top stream it should be possible to teach the concept of parameter substitution so the challenge would be to write a procedure called Polygon which draws one of any number of sides depending on the number passed across. Most class teachers will stop before getting to this stage, which is a shame because for those who 'get it' a whole new world of constructionism opens up.

I have to admit to being one of those class teachers who never got to this stage, so having had a browse around and a bit of a play, here is my first LOGO procedure using parameter substitution routine, is that the right term Andy?!* It is for drawing a polygon of x number of sides as suggested:

To polygon :SIDES
REPEAT :SIDES [FD 100 RT 360/:SIDES]
END

So if I now if I want to draw a hexagon, I can input

polygon 6

The procedure, substitutes sides with the number six, and calculates the turn size, by dividing 360, by the number of sides I want the shape to have.

If I now input

repeat 6 [polygon 6 rt 60]

I can create a pattern like this..I guess my next adventure will be to create a "pattern" procedure or write a program that will allow me to substitute not only the :side parameter in the polygon procedure, but also to include a series of turns to output my pattern drawing on the polygon procedure. Mmmm! Looks like I am all set for a bit of a personal engagement to expand my LOGO programming. Will have a crack at this while preparing my unit of work with the Probot for my students. Maybe you can teach an old dog new tricks!!!

LOGO Routines: Building Polygons

In my search log on Feedburner today I had an interesting search request, "probot hexagon instructions." I am assuming that this was from someone seeking help in writing or inputting a routine for the floor turtle that will generate a hexagon.

Creating a regular polygon with the Probot is similar to doing so with LOGO, though the tool has its own programming quirks. This post is intended to be a generic response to help with a variety of tools and I hope it pays off. To draw shapes, commands can be input to such devices either by repeatedly inputting a turn size followed by a distance (this represents a side length), or by creating a repeat [procedure].

Turns are measured in degrees, and the size of the turn inputted depends on the number of sides and turns you want the turtle to make in drawing the shape. On completion of the shape, the turtle will make one full turn of 360 degrees, so the size of the turn each time will be 360 degrees divided by the number of turns.

Lets reason for a minute and say I wanted to draw a square. What do I know about the properties of a square. Well it is a regular shape, it has 4 equal sides and 4 equal angles. To draw the shape my turtle will need to travel along the shape's perimeter, turning 4 times, after traveling the same distance between each turn. Since a square is regular every turn, angle or corner will need to be the same size.

By the time the turtle has finished its journey around the square it will have made one complete turn or rotation. A full turn is 360 degrees. each turn must be 360 divided by 4, every turn inputted will need to be 90 degrees, if each turn is to be equal.

Since my square is a regular quadrilateral all forward distances will also need to be the same, as all sides are the same length.

To make my square then I might input each step individually

fd 50 rt 90, fd 50 rt 90, fd 50 rt 90, fd 50 rt 90

pressing go or enter in between each step

or since I want to go fd 50 rt 90 four times, I could use a rpt command and enter a procedure like this

Using the Probot

Rpt 4 [
Fd 50
Rt 90
]
End

In LOGO

To Square
Rpt 4 [ Fd 50 Rt 90]
End

before pressing enter or go. End tells my turtle, that once it has done everything in the brackets 4 times I want it to stop.

Usually I need to name a procedure like this, so I might call this one square.

Changing Shape

Within a procedure if I want to change the shape I make, I need to change the size of the turn.

In order to calculate the turn size, I need to know how many turns the turtle will eventually make to complete the shape, and then to divide this by the size of a full turn ie 360.

LOGO and use of the floor turtle is a fantastic context in which to set investigations and multistep problem solving involving the properties of shape.

Equilateral Triangles need 3 turns of 120 or 360/3
Regular Pentagons 5 turns of 72 or 360/5
A Regular Hexagon 6 turns of ? or 360/?

Challenge:

Can you calculate the turn sizes necessary to create all of the regular polygons with angles totaling 4 to 10. (ie squares to decagons)

Insert a pen to the probot or floor turtle, or in LOGO ensure you have typed pd, or pendown before you begin

Test your predictions by substituting your turn and repeat values in your procedures?

Make and then save procedures for each shape by name, and test these do they still make the shapes you predicted?

What happens if.. I repeat 6 [hexagon rt 60] end
What happens if.. I repeat 10 [hexagon rt 36] end

Can you find other pairs of numbers, that when multiplied together make 360, try substituting these in the routine, for the repeat and turn numbers, what happens?

These activities should work equally well with floor turtles and a variety of on screen LOGO based environments, though be warned each tool and environment will have its quirks so be prepared to play with the kit first, to ensure you are familiar with these. I hope this is helpful.

Want to play with onscreen control at home, why not try MSW LOGO, a personal favourite freeware download for educational use from softronix. The processes and procedures can be practiced here and then adapted to work with other tools. There are also some really helpful guides hidden behind the scenes on the website so check these out too.

NPS Teaching Tools for Mathematics and Some Other Goodies

One of my colleagues on the Y3 Primary Maths Day today mentioned how she had found it difficult to find the ITPs, that on the Numeracy Strategy Pages were all in one place. Resource files available on the new site are also grouped together and listed for download from the following pages.

• ITPs
• Interactive Whiteboard Files
• Excel Resources

Long before the NPS discovered and began publishing Excel based resources this site, numeracysoftware.com , was a regular haunt of mine, the free download pages provide access to a number of really interesting and powerful Excel based interactive tools and resources, including support sheets and materials, as well as some cool PowerPoints. I have downloaded and used a number of these in the past, and particularly liked the Excel symmetry tools, which my previous year 4 classes loved using, Some of the worksheet generators were also quite useful time savers in creating Notebook pages for consolidation and practice activities, input the number ranges, generate the calculations and select and print to notebook. It was through visiting this site, that I first encountered MSW LOGO, the programing environment, free for educational use, that I now have installed and available for use by students. The children like its no frills look so much, many have downloaded it at home to use on their own computers. Onsite they have some nice resources and ideas available to use with with this tool too.

I'm not usually one for ready mades, but if you are looking for hands on tools, editable and printable templates or support materials for class use then why not pay a visit to The Leicester Maths Web, flip flaps, follow mes, Tables Fold Ups, place value grids, target boards, and much more.

From Floor To Screen: Imaginary Journeys and LOGO

In a previous post I talked about using BeeBots with year 3s to develop floor compasses and promote discussion around the cardinal compass points. Since then we have used Roamers, borrowed from the Local CLC to explore and develop these compasses, introducing numerical values for the measurement of turn, and helping to establish and consolidate the language associated with rotation. We have introduced the idea of right angles, quarter, half, three quarter and full turns as multiples of these right angles, applied 90 degrees as a value of turn in a right angle, and introduced the idea that we can turn easterly and westerly, clockwise and anticlockwise as well as good old right and left. We have also introduced and consolidated the eight points of the compass and derived through our knowledge of halving and doubling, that the turns in between must be 45 degrees more or less than the compass directions we, or our turtle are currently facing. The hardware used for these floor based activities may be quite expensive to buy, but there is no doubt that the concrete and physical experiences they have provided, have made acces to the on screen turtle in LOGO smoother and less painful. They have also informed my intention to buy a class set of floor turtles. Currently my first choice for this is likely to be the Probot, from TTS.

Extending these experiences from floor to screen, the LOGO environment I have chosen to use in school is an open source tool called MSW LOGO . It has none of the bells and whistles of some of the commercially available packages, but with an uncluttered interface, it does exactly what it says on the tin, for this reason I think it is easy to use, with fewer distractions, and is more accesible than many of its counterparts. The turtle is a simple triangle, the apex it's head and the base it's tail. Transferring experiences from the BeeBot (as I didn't use or have access to Probots this time), forward is always towards the head end, back towards the tail. East and clockwise equate with right, and west and anticlockwise the left. A common problem children seem to find with the onscreen turtle is wanting to input up and down for forward and back, encouraging the children to visualise the BeeBot in it's place, helped them to understand what inputs needed to be given, and that head directional movements would be forward, while tail inputs would be back.

Why develop this unit? Well I felt we needed a unit of work for Year 3 which would bridge concrete floor work in key stage one, with the onscreen environment, and that this should incorporate an element of play and familiarisation. The suggested use of LOGO in Year four is quite heavy going, and a steep learning curve for the uninitiated. A nice feature, of MSW LOGO is the ability to import and use background images. Building on previous floor work where we had made treasure trails for the Roamer to follow, and written mystery tours, I decided to extend this on screen. I could have used Roamer World or a host of other similar tools, but was interested in the skills progression and familiarity students could build on later. Besides, with this software, making backgrounds for the turtle to move in is quite straightforward, and good fun too.

Opening MSW LOGO, you can export the workspace as a bitmap, or graphics file. I began by inputting a procedure to draw a very small square at the home position of the turtle, eg repeat 4 [fd 5 rt 90], then saved this as a background. This was then opened in Microsoft Paint, and the background created. The image at the top of the post is what I eventually produced. The icons and compass rose, were made from clipart, which was copied, pasted and resized before placing around the map. This was all done before the land and sea were floodfilled.

Using MSW Logo, the students used the bitmap menu to find and Load the map, and following the main teaching session were left to explore the island, inputting commands to travel to different locations. It was a fascinating to watch the interchanges as children made decisions about whether to turn right and left, by how much, and as they estimated and refined decisions about the distances the turtle would need to travel, adjusting inputs in response to on screen feedback. The physical gesturing and body movement of the students also reflected their thought processes, turning hands, and whole body movements seemed help with their predictive processes. For the remainder of these sessions we will be continuing to build on the outcomes of this session, by writing mystery tours for our friends, consolidating the ideas of the eight points of the compass, before in the the final session using storyboards to record the views on the island, we would see at various stopping off points planned for us by our friends.