Hmming and Hahing round a Spreadsheet Modelling Project for Phase Three.

I have been a largely passive participant, observing the adoption process and use of Google Docs in the classroom.  Several colleagues have written at length about how they are introducing and using Google Docs in sessions with students, and it has been interesting recently to see how the tools presented within the Google for Educators bundle are being adapted by some to support development of school learning platforms.

I have been desperate to have a go myself but did not want to use the tool just because it was there.  Recently I worked with a number of phase three groups to develop tasks around modeling with spreadsheets.  We have introduced the tool's basics and explored the insertion of formula building simple models from the ground up, now we are approaching that point where we need to use and apply the skills we have been working on to begin developing a model of our own.

So her goes with the hmming and hahing... I have been thinking about the idea of collaboratively planning a party.  Quite a common project you might say, but have wondered about taking the tack because of the student's ages of planning an evening out, perhaps beginning at the cinema, going bowling, skating as examples and following this with a visit to for example McDonalds.

In pondering this project I have several assumption

• We will be including everyone in the group,
• We will have to prebook and order because of numbers
• We will need to make sure that the event is affordable.

Surveying and collecting ideas for the pre-meal event seems a little easier to manage with a simple vote being possible, while choosing food from the menu presents more of a challenge with so many potential variables to consider.  In my mind I have images of the chaos that could ensue from students collecting and collating a common data set, so my big question here is how to engage everyone in the process while quickly putting all the information in one place for everyone to access quickly.  Here is where my first real collaborative adventure with Google Docs would come into play, using Google Forms to collect the initial data we would need to begin the project.

Step one suggesting and voting on a pre meal event

Setting the scene with a brief to provide the big picture would be my starting point.

We have been asked to plan and prepare an after school activity to celebrate...............?  The activity will involve us all meeting up to do something for example watching a film, going bowling etc that will be followed by something to eat before we all return to school and go our separate ways.

a However we must agree as a group on the something that I was thinking that we could create a class Google form based simply on suggested venues from the students accepting and adding all suggestions.  Having saved this we might distribute the link to the whole class by email or through the VLE with their votes being added to the associated spreadsheet.  With all votes in the top three venues could be highlighted, and web based research carried out to identify the possible costs of a visit to each venue.

Step Two choosing our menu

Choosing MacDonalds as an after event venue, we could use a second prepared form, again accessed through a link from the VLE, where students could select first and second choices of Sandwich, sides, drink and dessert for their meal orders.  Completion and submission of this form would provide additional  data  we could use as the basis for modelling cost options for our visit/party. This second spreadsheet, once all "orders" were in could be downloaded to the student shared space, or added for download from the VLE.

Step three Collating information

Using data collected the students could begin to use it compile frequency tables tallying and recording first and second choice meals, that they would then be used to populate a prepared template that would form the basis for the final spreadsheet model.

Step four:  Inserting variables to the spreadsheet model

The Excel template provided for this activity would include prepared worksheets
a menu showing current McDonalds' prices
an order form

• a cost calculator for each set of choices
• A comparison book that we could use to compare each meal option cost with the inclusion of the pre meal event included
• A final cost calculator that would help us to decide how we want to divi up the cost of the event and that I hope would allow the students to see the value of using a tool like this when considering and planning events such as this.

The students would be encouraged initialy to enter the variables, the data we had collected together into the relevant worksheets eg

• food items
• cost of one unit
• number of orders

This would be repeated for first and second choice meals

Step Four:  Modeling the creation of rules

The application of formulae to the table for meal choice one would be modelled and then carried out as a class.  Asking the children to describe firstly to each other and then to the class the calculation we would need to use to if we wanted to work out the cost of say 15 cheeseburgers at a cost of £0.99 each

The calculatiuon would look something like this
15 x £0.99 =

To allow the spreadsheet to do this calculation we would expect to...
input =15*0.99

However we want to be able to change our variables and allow the spreadsheet to be able to update automatically, or without us having to input each change individually so.. how have we done this previously?  By using cell references to help

This process was remodeled eg =cref1*cref2 and students asked to complete the task for the remainder of the total cost cells, reminding after three or four cells that we could auto-complete using drag and fill.

Finally a rule would be added to find the total cost of the meal using autosum.

With this aspect of the model complete the students would then repeat the process independently with the second choice meal.

Stage 5: Comparing costs.

Using copy and paste the contents of the two options sheets can be moved to the comparison sheet, and a new set of cells added to calculate the meals combined with the pre meal event.  Suggestions could be sought as to the calculation and formulae we would need to use in order to find the total cost of our meal and the cost of our visit.

the cost of the meal + the cost of the event = total

Using cell references a formula would be added to support rules allow each  table to factor in and compare possibilities that included the new variable, the cost of the pre meal activity.

=cellref1+cellref2

With this complete we could begin identifying not only the cheapest meal option but also begin thinking about the effect that choices of venue for the pre meal event would have.

Stage 6:  Using the Model to Support Making Choices

Just how good a model is this?
How robust, fair and useful is it in helping us to plan and make decisions?
Are there any changes we need to make to the model's design and what might these be if we are to make the cost of the event fair to all of the participants?

In making choices about the event as a whole I have made a number of assumptions that we need to consider as a group that should ultimately lead us back to thinking about the design of the model itself and how it works and how effective it has been in supporting our decision making process.

The most contentious I hope is that everyone should pay the same amount on the night regardless of choices they made in the vote in order that the collection of monies be made easier.  It will be interesting to see what the students have to say about this in terms of fairness, however as a starting point it opens a number of interesting discussion points around the validity of the model in relation to an outcome and purpose not shared at the beginning and how this might impact on our starting point.  The concept of fairness, also gives a personalised in for students to to begin thinking about and suggesting how the essentially sound principles of the model itself might be adapted inorder to make cost distribution fairer. Eg should we have surveyed at the beginning the most popular meal choices, and then limited the order around these to balance the costs.This has been an interesting thought experiment...  Any thoughts?

Google Forms, Calc, Bar Charts and Excel: Data Handling Gets Creative

In the process of doing housekeeping on the PC and at my blog, I have come across a number of partially completed posts waiting for an audience.  So to work, this post outlines a series of activities I used with students in Phase 2 while introducing Spreadsheets for data handling last April. 

Communal Data Collection Using Google Docs

The unit began in class using our Asus netbooks and a Google form I had prepared entitled " A Few of Our Favourite Things."  The form was set up as an online questionaire, with free entry text boxes.  The students accessed the web and followed a prepared link from the VLE to the data entry form.  In pairs the students were encouraged to talk about and then respond individually to a collection of questions around the subject of our favourite things, such as what is your favourite colour/song/football team/subject at school?  Completing the form and pressing submit, automatically updated a Google spreadsheet, that was displayed on screen.  The live data collection was a real draw, as they watched each other's data arrive and the spreadsheet update in real time. Pace in this part of the session was generated by the sense of urgency to submit their information and see it appear before others.  We knew how many students were in class, and so the size of the sample we expected to see.  We could check quickly that everyone had submitted their data by counting the number of rows completed, before closing the "poll" and exporting the data sheets for use table top based activities. When all the data was in the spreadsheet was exported and saved as a pdf file, this was then printed and distributed to groups of students to use as the basis for tallying and data entry.

As a primary teacher, I am familiar with the amount of time that can be taken up with student data collection, as individual students navigate the room, collecting responses by tally.  I like the idea that using this method a range of data was collected relatively quickly, and as a communal act was then available to all following submission.  One of our key questions before engaging with our data sets, must be has everyone responded.  Placing the google spreadsheet centrally to the IWB, the students could see the sheet being updated as data came in,  since the form had been set up so all fields were compulsory, no one could submit until they had completed each field, and then simply counting or tallying the number of respondants visible we could identify who we were waiting for.  Having a range of data available allowed us to use real information in our initial skills teaching activities, and then for students themselves to select from data sets they were interested in to develop their own individual data sets for further exploration.

Rerepresenting our Samples as Frequency Tables

With  the downloaded "spreadsheets" distributed to pairs of students, we worked together on our Netbooks as I modelled, using a projected image of the screen how to create a frequence table using Open Office's Calc spreadsheet. We did this using the same data set.... Our Favourite colours.  The students were shown how to enter text labels in one column, elimnating duplicates as they went, before in the parallel column counting/tallying and recording the frequency of voters for each colour.  These tables were then given a group constructed title, and the cells into which data had been entered were adjsuted for fit, and then formatted with borders. Each student pair then saved their file.

Next the students were asked to choose two data sets from those on the spreadsheet printout and to create frequency tables for these independently, saving their work periodically so the data would not be lost. 

From Frequency Tables to Pictorial Representation

With our data enterd to the Spreadsheet and the tables formatted, we moved on together using the data set we had set up together as our starting point.  Using the chart wizard students were guided through the creation of a bar chart.  As we worked students discussed and were encouraged to add appropriate chart titles, and also axis labels.  We identified which axis was the x and which the y, we discussed what was special about the data represented on these, and appropriate titles and labels for them.  The students were also, shown how to change formatting and how to recolour the columns and bars in the chart.

Students were then left to practice this process creating a set of bar charts for each of the three other data sets they had created.

• Applying really clear and thorough titles for their charts that would help their readers.
• Producing Axis Labels that would inform their readers of exactly what was shown there
• Recolouring the data plots and bars, choosing appropriate colour fills and effects to match the data.

The charts we had created were used to raise questions and respond to them, extending these to look at more than and less than, by comparing frequencies represented using difference models of subtraction to seek out answers.  Drawing on the dynamic functions of the spreadsheet, we also asked, what would happen if... we used the spreadsheet to order data sets, highest to lowest and vice versa, predicting and then comparing our thoughts to the visual representations created as a result on screen.

This process took approximately 3 sessions of an hour each.   Once completed files and charts were upoaded to the VLE, from where they could be accessed for printing out and display.

Moving On: Presenting Pictograms in a Garden

In class the students had been introduced to Calc and Google Spreadsheets, and they had experienced using these tools as part of a collaborative task, to input and collect data remotely and to tally, enter, present and rerepresent data locally. In the final stage of this project however I wanted the students to get creative, considering other elements in chart creation with a spreadsheet environment, that might make our maths more appealing interesting and accessible to a reader.  To do this I used another prepared data set, but this time based on a set of survey data I had available to me around songbird populations in the UK.  For this series of activities the students were given access to Excel, rather than calc which they had been using on the netbook.  We began the session by discussing Excel and comparing it to the other tools they had used. What did they notice about the environment?  What was the same about it and what was different?  For all intents and purposes the tools were largely the same, they were visually a grid, made up of cells arranged in rows and columns.  We formatted the cells, rows and columns in a very similar way.  With these identified, the students were then provided with data sets to enter, and format as before.  We identified the chart wizard tool, and then set to work creating charts based on the data, adding appropriate axis labels and a clear title, with the students recolouring and reformatting the chart.

The students were then asked about the data itself.  How many of these birds had they ever seen?  Where would they expect to see them?  Did the students think it would be possible to create a bar chart that would really draw in their audience, or even wow passers by as they were working?  Could we create a chart that included images of the birds, and set the birds in their natural habitats.  Viewing charts as part of the Multimodal world this would add an additional layer of meaning making to the outcomes.

The students were now engaged in a collect and store task, using an image search to locate individual images of each of the birds in question and one final image of a garden.... A bar chart in a garden...

The students were then encouraged to further explore the formatting tools for their charts, and to apply the skills tha already had from work with Calc.  We made a second version and this time instead of colour formatting bars, used the fill effects button and picture tab to insert individual bird images to our chart columns.  These were then scaled by 1, to create a pictogram type effect. Highlighting the chart area the garden image they had found was then applied as a background to the chart plot area itself.  Very pretty.  However with the images inserted the axis labels and values as well as the chart title were less readable, requiring some further formatting effects to be applied, changing font colours and backrounds became a necessity to make them readable.

The outcomes are very attractive, as well as introducing for me a key aspect to the purpose of data handling the idea that we produce charts and graphs to be read and interpretted.  Like other visual text sources, they are created to help an audience access and interpret them, the more relavant our content to context the more likely we are to portray the meaning we set out to share.  Persuading students to use formatting devices for other reasons than because we can, is a key aspect to helping them understand the roll of such devices, and ICTs offer incredibly powerful and creative ways to do this. In this unit I wanted students to engage with Spreadsheets as a mathematical tool, not only for its pace and dynamic nature in presenting and representing information, but also as a way of managing the process and engaging with charts and graphs as a form of visual literacy.

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.

Making and Playing Computer Games With Scratch Episode 1

A while back I found myself downloading and playing with scratch, considering it as a possible tool to complement work I was already doing with Phase 2 students around Shape and Space and LOGO.  With a move to work with Phase 3 students I have been "encouraged" into the slightly steeper learning curve of using Scratch as a programming platform in its wider sense, resulting this term in a series of sessions exploring arcade games and working with students to use the tool as a basis for designing, making and evaluating one or two of our own.  I have decided however, as an offshoot of this and to support my personal professional learning to use some of the materials from Phase 3 sessions with my phase 2 ICT club as well, and to see how they got on.  Our first session worked really well, and I was impressed at how creative some of the younger students were with the basic scripts in hand.

The first Session involved students familiarising themselves with the layout of the tool's interface.  Following given instructions and scripts to bring about increasingly complex animation effects. Within the session students used the default "sprite" initially and blocks from the control, motion and looks scripts areas only to bring about 3 different types of animation.

• Activity one bringing about movement as a flip in position using an on mouse click event.
• Activity two bringing about continuous movement of the sprite from one side of the stage to another, with an image swap to add interest to the sprite's actions and a change of direction when it reached the edge of the screen.
• Activity 3 using four separate scripts, that on click or use of a keystroke would allow user control of the sprite to move it around the stage using the up, down, left and right keys on the keyboard.

 Within the session the following scripts were were provided for students to use.

Activity 1

As the students worked with the above script they discovered that the sprite didn't simply flip, but rather rotated as it changed direction.  The students were encouraged therefore to explore what would happen if... they changed the settings of the motion buttons highlighted in the image above.  Could they

• make the sprite mirror as it turned
• stand on its head 
• step forward and back?

Activity 2

Running this script, the sprite walks back and forward across the stage when the green flag is clicked, its moevement repeated because of the forever loop until the red stop button is pressed.  Again in running this script students were asked to explore the effects of changing the position of the motion buttons, but in addition to explore what would happen if we altered some of the variables in the motion blocks.

• Could we slow down the sprite?  
• Could we speed it up?  
• Could we make the sprite's speed vary so during some parts of the routine the sprite seemed to be moving faster than at others?  
• How did our changes effect the way he/she looked as they moved?  

What would happen if...

we changed the green flag header block for the

"when [something] key pressed,"

or "when sprite clicked"

header blocks.



Activity 3

Here students were encouraged to recreate a script that would enable them to control the sprite using the arrow keys, so that for example when the right arrow key is pressed and held down the sprite walks towards the right side of the stage. This example with the addition of a cap block will bring about movement towards the bottom of the stage by the sprite when the down arrow key is pressed.

Having completed one of the scripts the students were shown how to duplicate it and then how to edit the values according to given models values in the images below.  The addition of green flag caps to the procedures, meant that on clicking the green flag the program would run, allowing the students to control the sprite's movement across the stage in the up. down, left and right directions.  In effect they could take the sprite for a walk.

These were then tested to ensure that they worked, and then further edited if need be to correct them.


To engage the students in evaluating this Focussed Practical Task, they were asked...  If we were making a computer game of our own...
How might this set of procedures be useful
Where might we use them, and what might be happening in our game?
Following discussion several familiar gaming type scenarios arose

• Perhaps we might want to move our character around a room, perhaps colecting things.
• Perhaps we might want to move our character around a maze.

What seemed to excite the students most however was that they now had a working model that they could explore and play with, and this lead to our extension activity... 


Extension


Having copied the scripts and set a scene where the sprite could be moved with the keyboard the students now wanted to play with what they had done..

• Could they change the sprite or character they were animating?
• Could they set a scene for the character or sprites actions to happen in?

With the model in place the students 

• explored importing new sprites to replace the cat. 
• investigating how they could get their new sprite to follow the instructions they created for the cat.
• Adding an extra sprite and having it move using one of our earlier scripts at the same time as the original sprite.
• Editing, recolouring and changing the sprites they had imported.
• Importing image backgrounds from collection or from the web as well as creating background images  providing context to the action.

The session created a great deal of excitement and raised towards the end an important question we need to address if we are to make a game of our own such as.. 

• How do we get the characters to do things when they meet or bump into each other?  
• How do we get sprites to interact with each other?..

This seems right now a good place to stop.. As it was with the students... Leaving them with a cliff hanger and waning more next time, when I have promised them with this as the prerequisite scene setter, that during our next set of activities involving the use of "sensing blocks,"  we wil be creating a very simple game a "keepy uppy type" game.  This will involve creating a "paddle" and "bouncing ball" the first steps in creating our own versions of "breakout."  Hope you drop by for our next installment.

Additional Stick Figures for Pivot

This week I visited students in a secondary phase ICT extended learning session.  The students were using Pivot Stick Animator, to develop short stories following on from previous sessions where they had planned and developed their own background scenery to help them tell these.  As I was talking to one of the students about their work from nowhere there appeared a beautifully crafted jet fighter that flew across the scene, needless to say I came away from the session with a new online space to share and explore. 

Droidz a webspace recommended by this group of students hosts collections of ready made stick figures and effects for use with Pivot, these include creatures, vehicles and weapons, as well as a forum and share space.  Though they may not all be everyone's cup of tea, and the existence of a forum and share space will have esafety considerations for direct use with students, the characters and figures available do provide interesting extension possibilities and variety for the existing set downloaded as part of this freeware tool.

I would recommend however a visit to the site in order that colleagues can review and check out for themselves figures available, and that primary colleagues might like to create collections using those they feel are appropriate to the activities they they want to develop with students, rather than giving free reign. Hopefully this space will make an interesting visit and add an additional tool set to your bookmarks.  Thanks go to the student group who pointed this out to me this week.  Can't wait to read your outcomes.

Revisiting Viewpoints: Working in the Style of Monet

In a previous post, Viewpoints: Working in the style of Monet I presented a learning story, showing how I and a group of Y4 students had used

• images as discussion points around the work and style of the artist
• drawn on these over a number of weeks to sequentially develop graphics using ICTs based on this work

The unit, involved the use of a common graphics package (MS Paint) to construct and manipulate student self created images while also consolidating functional ICT skills.  These include

• limited tool choices to create image elements in the given style. eg spray can and colour pallette
• Select and copy tools
• Introducing and consolidating the "cascade save" process, using save as and "sensible file" names to build a portfolio of progression through each activity, and return points to which we can go if errors are made, and navigation of network drive spaces.
• Understanding how we can use a graphics package to compose images by drawing together elements we create seperately
  
• Using a collection of predeveloped (drafted image) elements and toggling between software instances, through the use of select copy and paste tools to arrange image compositions.
• Explore cause and effect using rotation and flip tools (in Paint) or by extension to use more complex graphic tools, to investigate and explore filters and effects, before choosing images for our final outcome.

Previous units have resulted in students creating "IKEA" style Prints.  Using MS Publisher to import their final image before adding text and printing out their work on the colour laser.  This time around though I am intending to develop an entirely digital outcome by exploring Monet scenes that reflect seasonal change.  Working with KS2 Students the outcome and brief is to use graphics tools and the collect, store, share and prepare process to produce a short animated sequence based on a single viewpoint or landscape that shows how a scene might appear at different times of the year.

How will this be achieved?

Using Microsoft Paint the students will create a landscape, showing skyline, mid and forground and develop a simple tree skeleton motif using the spray can tool to include trunk and branches.  The tree skeleton will be saved as treespring, treesummer and so on.

Drawing on discussions about how trees appear in images representing the seasons, colour choices made by the artist for mood and effect, the students will  develop their own representations of the tree motif during each season considering  colour choices and exploring the effects they can create by layering spray effects. We will maintain a copy of our original tree skeleton motif as a return point, and for later use in the project.

Using the original tree skeleton, students will be encouraged to create a single landscape starting point, by copying and pasting instances of it to the landscape they have created, composing their own particular viewpoint before saving four copies of this, named landscapespring, landscapesummer and so on. 

To each of these landscapes the students will apply the effects  they developed during their exploration of their tree images to show how they think they might appear during each of the seasons.  They might also explore further detailing, eg sky colour effects perhaps through the use of additional painting tools and the undo tool,  while using save as to keep copies.

Digital Outcome

Using Photostory and the images the students have developed I would like them to create a simple morphing sequence of change for their landscape.  They will be encouraged to select 4 of their images 1 representing each season and to import these to Photostory.  These will then be chronologically ordered on the timeline, before applying transition effects and times.  They will be encouraged also to choose one additional image from those created and to add text to this forming a title overlay.  To complete the project they will add a music track before exporting their completed video for addition to either their class or personal blog space within the VLE for review by colleagues and other students.

If readers have any thoughts about how this project outcome might be further developed I would love to hear from you.  In my new role this year I am also working with a number of Key Stage 3 classes and would be interested to hear from colleagues any ideas they may have about how this type of work might be adapted, extended or used as an element within projects for students in this phase of learning.    

Lego Digital Designer: Another LEGO based CAD environment.

"

LEGO Digital Designer : Virtual Building Software

This tool and free download has been all the rage in school recently. Discovered by a couple of our Y 6 students, who having used it at home managed to download, install and get it to run from one of the shared drive spaces on the network, it initially gained attention as the focus of some firm but I hope fair discussions about our acceptable use policy and argeement.... The ingenuity of it all!

I hope you'll agree with the resolution, too good to miss as a tool, but also because I want our AUP to work within the realms of trust, I agreed to download and look into an installation of the tool for them to use, on the proviso that in future, they should share tools like this that they would like access to in school with me first. This situation was an ideal opportunity to discuss the reasons why we do this and esafety issues such as licensing and copyright.

The Demo provided by the students and the brief play I have had with LEGO Digital Designer only scratches the surface of the potential uses I think it could have. It includes an extensive library of components that include Mindstorms and Creator kits. On a basic level the tool could be used in ways outlined in this previous post about the Freeware tool BlockCAD. Digital Designer is quite a different beast however, and with the inclusion of Technic and Mindstorms components could be used to support design work or recording from control activities using nxt. In addition the interface allows the user to switch betwen a number of different onscreen viewing modes.

• Build mode where models can be developed from existing prototypes or from scratch,
  
• Viewing mode where the model can be placed on different backgrounds, rotated, exploded and in some cases animated,
  
• Building guide mode, where completed models can be put together step by step, using a walk/step through video presentation, or building guides exported in HTML format.
  

My brief engagements with the tool don't as of yet I feel do full justice to this potentially powerful freeware platform. To get your imagination whirring and creative juices flowing I'd recommend you download it and check it out for yourself. Certainly the students who recommended it to me, J and T love it and this has got to be the best starting point for thinking about how the tool might be exploited further engage them. I would love to hear your thoughts, and ideas about where and how you might use the platform.

BlockCAD: Modelling Onscreen with "Lego" Style Blocks

I have had lots of fun playing with BlockCAD in between my other dabblings this week. This freeware tool has been pointed to for a while now by colleagues, with referals through feeds from del.icio.us and my colleagues on Twitter. Having seen it used in school on a Teachers TV programme this week I thought it was time to have a play for myself.

BlockCAD, is a computer aided design (CAD) environment allowing its user to build onscreen, 3d models using LEGO type bricks.

Screenshot From Anders' Corner of the Web home of BlockCAD

On opening BlockCAD the user is presented with an empty base board in the main design window onto which bricks can be laid. The dimensions of this board are not fixed and can be changed by typing the desired dimensions into text boxes to the bottom right of the window labelled base. To the right of the design window is a component gallery. To begin your creation, select your block clicking and dragging it to the baseboard. Clicking the left mouse button locks it in place. Rotating a block is achieved by right clicking the mouse before placing it. Within the gallery are a wide selection of blocks, that include many familiar components including wheels, windows, doors and so on. The colours of these components can also be changed by clicking the colour pallete above the component window.

I found that it was easiest to place bricks accurately if the baseboard was rotated to a plan view. Rotation tools on the tool bar allow the models you build to be turned through 360 degrees in both vertical and horizontal planes at any time during the construction process. There is no undo button. Deleting a brick requires the use of a mouse and del key combination. Pressing the del key before clicking on the brick in question, highlights the brick with a frame and hitting the del key again removes the brick from the model.

Throughout the making process the 3d model as a whole structure can be viewed from diffferent perspectives using the rotation tools. Using the capture tool, images of these various perspectives can also be captured and saved. Clicking the capture tool opens a dragable window that can be dragged around like a camera viewfinder to frame the image and view of the structure you want. These in turn can can be saved in a number of different image formats for use in other software environments.

I really like this tool, and as freeware students can access it and download it away from school too, opening opportunities for them to extend their creative uses and learning away from school. It uses as a model a construction kit type that we have readily available for students to use in school, and that they themselves may have at home.

The tool has obvious cross curricular applications within DT, where it could be used in the IDEAS and FPT phases to model outcomes and facilitate evaluation onscreen before students begin construction. If included as part of an onging design and make process by groups of students it could also be used through a cascade save process to track, monitor and present changes they make as a result of difficulties or considerations within their making processes. The images could be used in DTP outcomes for display or included alongside photographs in learning stories presented in Powerpoint or even photostory.

I also like the idea of the environment being used as a scaffold for onscreen instructional writing, mediated by talk. Images exported from the environment could be used to help students create and design new models, and frame instruction leaflets for others to use as reading tasks. Context, purpose and audience for their work. I'd like to add this to our modeling and simulation tool box and see what the crew make of it.

Greenfoot: A Summer Project

Came across Greenfoot, while I was floating around the web the other day, thinking about a control environment or microworld creation tool that we could perhaps make available on our Asus Toolkit for students. I was really looking for a version of LOGO or pondering Scratch, but what interested me about this environment was its use of Java as a development framework, with its ability to compile executable programmes to control elements introduced into the space. Even if we can't use the environment with the Asus platforms, the possibility of involving students in building interactive object oriented games, seems really appealing right now, though whether it will later or not I'm unsure. As an absolute novice programmer this tool looks really interesting as a personal in, so have downloaded to play over the holiday, and explore the possibilities. The video tutorials look really useful. If all works out perhaps this could be another tool to add to our simulation and control tool box for older students, its certainly a recommend and look see for secondary colleagues.

Softease Branch, Y3 and the Properties of Shape

As we aproach the end of term and the end of another school year, I am in the process of what might be called mopping up, looking at areas from the Mathematics framework that we have either not yet engaged with, or which the students have found tricky. Alongside this are some ICT curricular elements that I have not fully developed with the students. We have used data handling environments to for example present data from Science Experiments and as teaching aids with the IWB, but the children themselves have had limited independent access to the tools, other than in small groups at classroom based PCs.

This week we have been involved as a class in a Using and Aplying Mathematics unit, to consolidate our use of vocabulary relating to the properties of 2d shape. At the same time I wanted to embed and develop key skills from the ICT curriculum through the use of a Branching data base. The tool I chose to use for this series of tasks comes from Softease Studio, and is called Branch.

The sessions began however, not with Branch, but with a drag and drop sorting tool I had made using Smart Notebook. Other whiteboard users could make something similar, and an image of the tool is presented to the left for reference. The key to making and using Branching Data bases, binary trees or "dichotomous keys" is an ability to generate, ask and use "null" questions to divide a set of objects into two sets initially, gradually refining questions to distill the set until the branches at the end of the tree have only one object. This involves asking questions that have "yes or no" answers. This is process I have found easiest to develop using the observable features and properties of sets or collections of familiar objects. We often use Carrol Diagrams and Venn diagrams to do this, and the whiteboard tool I used as an introductory frame to support student and teacher discussion around this process before engaging with Branch itself, was designed to act as a link between these tools.

Since our task had a mathematical focus, we began with the shapes to the left of the book engaging the children in paired discussions around questions such as

• What can you see?
• What is Special about this shape?
• How is this shape different to or the same as this shape?
  

These were used to focus the students attention around the visible properties of the shapes, and to begin drawing on their prior experiences to describe them, for example

"It has four sides and four corners, all of the corners are right angles."

A great set of reponses describing the properties of a rectangle, however in our set we had two rectangles, a square and an oblong. Developing this we began to use the sorting tree model above dragging the two rectangles to the top of the simple tree, and asking the students to propose questions that focussed how they were different. Is it a rectangle ? Or does it have right angles? don't work since both shapes have right angles and by defintition are both rectangles. Are all the sides the same length? Provides a yes or no answer and allows the two shape to be separated.

We used the notebook to practice this idea together, comparing a number of shapes from our collection and then, testing our questions to see if they worked. The children were then introduced to branch and starting with only two shapes each time initially were were encouraged to make a series of trees practicing and rehearsing their questions together.

During follow up sessions the idea of working with 4 shapes was introduced and the children challenged to devise questions that would begin by dividing their shapes into two equal sets. This sounds easier than it is. Eg I have a square, an oblong a triangle and a pentagon. A good starting question might be does the shape have right angles? Does the shape have 4 sides? And because of our previous activity the children suggested these? From here the next question was also fairly straightforward for them based on the practice sessions of small trees the day before. However what happens if we drag a circle, a triangle, a square and a pentagon into the tree? Is it curved? Does it have three sides? Although having yes or no answers don't work in relation to the challenge question set at the beginning of the session. What is needed is to ask a question such as does the shape have "more" or "less" than x numbber of sides/corners/angles? The students were then encouraged to use Branch to explore these ideas, Before during our final session requiring the children to begin with 8 given shapes to design a game for their friends to play and test out.

The children really enjoyed this series of tasks, which challenged their thinking and enabled them through paired discussion to use and apply vocabulary developed in previous classroom based sessions to a decision making process. The UK Primary Mathematics Framework says students in the course of their work should

• Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information
• Describe and explain methods, choices and solutions to puzzles and problems, orally and in writing, using pictures and diagrams
• Use Venn diagrams or Carroll diagrams to sort data and objects using more than one criterion
• Relate 2-D shapes and 3-D solids to drawings of them; describe, visualise, classify, draw and make the shapes.

As a guided and collaboratively based series of activities, using Branch in this way really helped support and scaffold this particular group of students engagement and discussion around these processes. It also enabled me to give context to the use of a tool that I have found frequently to be used because it is expected within the ICT scheme of work structure. As with many ICT tools I feel Branching data bases are incredibly useful and powerful tools, if they are used in designed and considered cross curricular learning situations where they can act as a "person plus," or a frame and scaffold to support use, application and transfer of skills and experience from one subject domain to another.

Eureka! Using Line Graphs to tell stories

I wanted to share this web based resource with everyone since I've been writing about data handling this week. Its been sitting, soaking and reclining in my bookmarks and at the bottom of the Maths recources page in our school web site for ages, but is a really nice resource to use as a starting point around time and change using line graphs.

Bathtime with Archimedes now on ColemanWeb, is an interactivity, that uses a combination of animation and pictorial representation to model the principles and effects of displacement. While users run the model a number of variables can be altered, you can turn on or off the tap, put in or remove the plug, and have Archimedes sit in or get out of the bath. As these "physical variables" are altered and the model is run, the level of water in the tub obviously changes, and this can be observed by watching the position of the rubber duck in the tub, my personal favourite touch, but also a line graph that is created to coincide with the events as they are carried out along the bottom of the page. Time and depth values are also recorded as the model runs in a table to the right of the screen.

As a "shared text" during maths or science sessions, this tool affords lovely opportunities to draw on the visual elements as the modelling process unfolds to support oral work, through engagement with the chart to recount the story and events that lead to its creation. Screen capturing the model, or a previously created model to an onscreen notebook, opens possibilities to engage students with the resultant image multimodally, and the use of hide and reveal techniques to mask areas of the image, promoting and focusing discussion, to draw on their previous experiences.

Following this up students could be provided with a one I prepared earlier version of a bath tub model presented as a line graph created in a spreadsheet, and asked to prepare a recount or story around the chart.

I put in the plug and ran my self a bath. I was just settling down when the phone rang, I got out of the tub, it was freezing as I dashed through the house but before I could get there the caller rang off. I clambered back into the tub. running some more hot water before laying back to relax.

Alternatively students could tell stories for others to sketch, using discussion to generate the charts they think would result from it. What do you think?

Measurement and the Probot

In a recent post I was excited to report that the humble Probot moved 1cm for every unit input, and was keen to take advantage of this as soon as possible with my students during numeracy. Last week we were exploring scales and investigating the relationships between standard units of measure, and this seemed like too good an opportunity to miss.

Over the course of the week our key objective was to be able to read scales to the nearest half division, and since we are Y3 as the week progressed I wanted the students to engage practically with a range of scales. The context chosen was linear measure, where we began practicing our use and appropriate choice of tools and units, Using rulers and tape measures, to estimate and measure to the nearest whole and half division, while also considering the relationships between the units.

• How many cm in a metre?
• How many mm in a cm? And so on...

All of which would help us to create and solve the problems we would be working on with the Probot later in the week.

To work with the relationship between metres and cm, we carried out a group challenge to construct a skeleton of one member of each group. The students cut strips of sugar paper to represent two circumferences of the head, the length of the spine, each arm and each leg, the distance around the waist and three different measures around the chest, and across the shoulders. They estimated the length of each before using rulers to measure these in cm. Once the measuring tasks were completed the skeletons were assembled using a stapler. I mention this here because it was a task that really engaged the students, and which they really enjoyed.

On Friday we were ready to use the Probot. The session began with the students sitting around a large piece of card, a metre rule placed along its length, and the Probot bumper lined up with the start of the scale. The class were reminded of previous work they had done with BeeBots, and asked to identify the differences they could see between this tool and that.

• It was a car not a bee
• It had different buttons
• It had forward and turn buttons, but it had a pad like a phone

The students were asked how they thought I would get it to move and a little time was spent as we discussed and established how we needed to press the direction buttons and then use numbers, rather than previous experiences of repeatedly pressing direction buttons to move the turtle.

The students were then asked to close their eyes, as I input fd 10, and then asked them on pressing go what they thought I had asked the Probot to do? We tested some of their suggestions, before confirming that I had pressed fd 10. What would happen then if I input fd 20, fd 30, could we predict where the Probot would stop. The students were asked to close their eyes again as I input fd 35 and pressed go. What had I input now? How did they know? Gradually we established that 1 Probot step was 1 cm.

Next a pen was put added to the Probot, and the class talked through the inputting of fd 10 rt 90 fd 20. Before the go button was pressed the students were asked to discuss and predict what they thought would happen. We then observed the trail left by the vehicle, and they were quick to recognise the right angle turn, enabling us to establish that this was the 90 (degree) input given with the right command, the 1/4 turn they were familiar with and had used with the BeeBot.

For the main activity the students were organised into groups. Each group was given a Probot, a collection precut paper strips of different lengths and some measuring tools to choose from. They were challenged to make mazes for each other, that included only right angle turns. Their friends were then to be challenged to use the things we had learned from our carpet time to input accurate instructions to navigate their Probot through the mazes. Throughout the task the students used measuring tools accurately and with purpose, discussed and planned routes applying mathematical vocabulary beginning to predict and using reasoning about the choices they were making. Above all however they really enjoyed themselves.

Goldilocks and the Three Turtles: Sadness Dawns!

Even though I have been playing with the Probot all week, it never dawned on me to check or measure the size of a Probot Step until this morning. And so needless to say this post probably seems a bit trivial and sad, but do I care... Not a Jot...

This is a bit of a Goldilocks moment, so bear with me.
"A Roamer step was always to large to use when thinking about about standard measuring units (as it needed to be scaled), A LOGO step was too small. But guess what it appears that a Probot Step is just right."

Because...

1 Probot Step = 1 cm

This little nugget/discovery has really excited me because it promises another route into practical and investigational work around shape, space and measure with my ocassionally challenging Numeracy Group.

Goldilocks Image Courtesy of the British Council

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.

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?