Win at the Fair Math investigation using Scratch

I forgot how much I love Scratch, I have been running an after school ASA for grade 4 students using Scratch. Scratch is a drag and drop block coding app that is low entry high ceiling, meaning it is easy to get started but you can program some pretty complex stuff.

I digress

I was working with a grade 7 Math teacher helping her to plan a MYP Criterion C,D probability assessment. The current probability assessment had students creating their own "win at the fair" game to make money. They explored some common fair games and then made a game where the owner would make a profit. While this task is open ended, it took a lot of time and there wasn't very much higher level thinking or Maths involved.

It reminded me of a really cool Math300 assessment from years ago where students were given a win at the fair type game.  The students had to identify who won or lost (the person playing or the fair owner). It turns out the game is set up so the fair owner loses quite a bit of money. Students then have to adjust the game so the fair owner wins. It included an app to run simulations where students could change different variables, explore theoretical probability vs real life results and run the game thousands of times in the blink of an eye. The simulation and the ability for students to change variables to explore real life probability was the greatest strength of the activity.

So with this in mind, we created our own win at the fair game and simulation.

I created a game board in Google Slides

The idea of the game is that each game costs $1, the player places a marker on the start hexagon. The player then rolls two dice and adds the totals together. depending on the sum the marker moves left, up or right.

The player keep rolling until they get to a coloured hexagon, they get the prize on the hexagon they land on.

To demonstrate the game I created this project in Scratch. It can be projected to show how the game is played. It also keeps results and profit / loss.

Once the game had been demonstrated we gave the students a game board and some dice and they played the game and recorded their results. We then collected all the results from the different groups to get a class total.

It was pretty obvious that with these rules the game owner loses and the player wins, meaning the game owner is losing money. There is also a feature in the scratch demonstration that allows you to play 100 game and see the results.

The students were given the scratch project and then answered some questions about the game.

including

• From your results who makes money - remember it costs $1 to play each time? You or the fair owner? Explain.
• Run the (online) simulation 100 times. Describe any pattern or trend. 
• Explain and describe any differences between your data and the 100 simulation. 
• If you ran the simulation again would you get the same results? Explain and justify your answer. 
• Who makes money after 100 plays? You or the fair owner? Explain. What would you expect for 1000 times?
• Would you like to play the game? Think in terms of do you make money? Justify your answer using mathematics.
• Which number comes up the most and the least from rolling the dice and adding the outcomes? 
• Draw a sample space of the outcomes of the sum of rolling 2 dice to illustrate your answer above. Explain how you know. 
• Discuss which direction is the counter most likely to travel and why.
• What is the theoretical probability of getting a $5 prize? Use a tree diagram to demonstrate this outcome, and then explain the probability.
• Mr Derry created this simulation - the fair owner doubts his programming skills. Do you think the simulation is accurate, how can you prove your point using mathematics? (Level 7/8)

That was part 1 of the assessment done, deconstructing and understanding the problem, including experimental results (from the simulation) and comparing the results to theoretical probability.

Once the students have some understanding of how the game works and the probability involved, it is time to move on to the next part of the assessment. 

Redesigning the game.

To redesign the game so that the fair own makes a "fair profit" the students had to think about some of the psychology of carnival or gambling games and the notion of a fair profit. Then consider some variables they could change and test their theories.

To change the game the students can either change the cost (super easy), change the prizes (easy), change the numbers that decide the direction of the counter (harder) or a combination (very complex).

To help with the next part of the assessment, I created another version of the simulation.

Win at the fair simulation

This took a lot more coding, but was lots of fun to make and includes the following features

The ability to

• choose the number of trials
• change the prizes
• change the numbers that decide the direction of the counter

The simulation calculates the total profit and profit per game, so students can get immediate feedback on how their changes effect the long term result of the game.

Once the students have run the simulation multiple times, There is also an extra button to get more data to help with analysis.

The extra data includes the win % for each colour and the expected return for each colour (return x win%).

This is useful because the students can see which prize gives the best return. For the owner to make a profit the sum of all the expected returns must be less than 1.

The actual task given to the students was very open ended with little structure of how to describe their solution, our thinking here was that MYP math criterion C (Communication) asks that students 'organize information using a logical structure.' We wanted the students to choose how they organise and justify their thinking.

This is what was given to the students.

We also gave the students the criterion (C & D) so they could check what they have done against the criteria.

What I liked about this assessment was that it was engaging and was an authentic real life investigation. A student could developed a strategy, then test it by running the simulation, make a change and run it again. This guess and check aspect allowed students to think about real life probability and compare it to theoretical probability. The thinking and creativity behind some of the strategies helped develop higher level thinking skills.

The assessment also allowed students at a variety of ability levels to succeed, a struggling student could make simple changes and a confident student could change multiple variables, they still got to complete all parts of the assessment and communicate their understanding.

Some students also looked at the coding behind the scratch project and had heaps of questions about how I made it

Once the assessment was finished we received lots of positive feedback from parents, teachers and the students.

One parent (who is also a teacher) commented that she had never seen her daughter so much into a math assessment. Her daughter and father sat on the floor and discussed the strategies and thinking behind the assessment over several nights. 

Several students told the teacher that this was the best math assessment they had ever done. In their end of year survey 35% said it was their favourite unit (the most of any units)

Here are some of their comments from their end of year class feedback survey

The teacher was also super excited about the assessment and let me know how great it was to see the students engaged, she commented that one of her less engaged students was on task,seemed to be enjoying the assessment and produced his best mark of the year.

Here is a link to a copy of the assessment (including links to the scratch projects) feel free to copy it and try it with your class.

This Article from the Australian Mathematics teacher outlines some of the benefits and high order thinking from the original maths 300 activity.

Keynote Fraction Animations

A really boring title I know, but this activity was lots of fun and was a great example of learning and understanding concepts rather than just knowing answers.

We are studying fractions in grade 6, in my experience students often know shortcuts and tricks to do equations with fractions

While this approach gives them an answer it doesn't promote understanding, rather it focuses on answers. I am much more interested in students understanding a concept rather than knowing an answer. Often they don't understand what the equations actually mean and written explanations are complicated and confusing.

There are lots of great visual examples online and sites like Myimaths have animations and videos explaining what is actually happening when you add, subtract, divide or multiply a fraction. While these sites promote understanding and make it easy for students to see what it means to solve equation problems, I prefer making my own or even better get the students creating their own fraction animations.

Keynote Fraction Animation

To achieve this we used Keynote and added actions to a variety of shapes and text boxes so that students could create their own fraction animations. About half way through the activity I remembered magic move and that made things so much easier.

Magic move compares one slide to the next, takes note of any changes and then animates the changes. You can easily duplicate a slide, make some changes and turn it into a nifty animation in no time at all.

Here are a series of videos I created on how to make your own fraction animations the first two use regular animations and the second two (multiplication and division use magic move)

Adding Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions

What I really like about this activity is that it is hard work, the students really need to think about what it means to perform operations on fractions. What does it mean to add fractions beyond a set of rules.

They look at fractions and operations in different ways, work backwards and need to problem solve to make their animations reflect what is actually happening when performing operations on fractions.

Make your own Random Google Sheets worksheets

I finally found a use for Macros

A couple of months ago I started playing with Google Sheets IF Formula and RANDBETWEEN to create interactive google sheet Maths sheet, this was essentially a drill and practice activity. I wanted my students know how to do this and create their own drill and practise activities. The idea was that the students could create maths worksheets that have a random selection of the numbers in the equations.

It was easy enough to set up a sheet using predetermined number and the IF statement to check if the students had the correct answer or not. I added some colour and extra formatting using conditional formatting. I then used COUNTIF to count the number of correct answers. It was all starting to look pretty and come together. Then I introduced RANDBETWEEN to make the numbers random to gamify and increase the longevity of the sheet.

The only problem is that when you use RANDBETWEEN anytime a change is made to the worksheet a new random number is generated. that means when an answer is written the numbers that make up the equation change.

I searched online, checked out add ons, tried pasting values, but couldn't find a way to make the random numbers stick, I started playing with Macros and was almost there when I got distracted by some other bright shiny thing. Someone showed me a few websites that do this automagically. Which was OK but not as good as the students creating their own.

I had put this in the back of my mind until yesterday someone in my PLN on twitter asked for some free drill and practice websites that he could give to the teachers in his school, I suggested getting the students to create their own using Google Sheets, the IF formula and RANDBETWEEN. He reminded me of the issues of the constant changing random numbers. I got back to work.

I created a series of ten random numbers in ten cells (H3 to H12),

I then recorded a Macro that copied the ten cells and pasted the values only into the cell next door. A Macro allows you to record a series of steps or activity that you want to do over and over again on a Google Sheet, it then turns those steps into a script, which you can then run and it will do them for you.

Often to run a script you need to use the tools menu.

But you can also add a script to a Google drawing, so I created a button to randomise the numbers when a user clicks the button the script runs. 

Essentially when the button is pressed the script runs, ten random numbers are copied and their values are pasted into the cells next to the random numbers. Because I used paste values only, it doesn't matter how many time the original cells change those numbers in cells I3 to I12 wont change until the button is pressed again.

I then use those values (I3 to I12) to populate my tables test. The Random numbers stick. I hid the columns with all the data so all the user sees is the equations and a button to change the numbers.

I can the use COUNTIF to calculate the number correct and put that as a fraction on the page.

My next step is to work out a way to time how long it takes to complete the equations and add a super cool pop up message when the user gets 10/10.

For your very own copy of the Google sheet to see all the formulas and play with click here

Turning lego into an AR experience

Wind them up and let them go

I have a bit of a reputation around school as the VR and AR guy (I don't know why?) so it was no surprise when a grade 10 student came to me asking for help with his MYP Personal Project. He was in a bit of a panic and sent me this email

He had created several Lego models of buildings in Kuala Lumpur in the Lego Digital Designer program. He has examples of old style buildings and new buildings. The problem was that the Personal Project Exhibition was fast approaching and he didn't have time to order the bricks and build his model. He was hoping he could turn his model into an AR experience.

When I met him I checked out his models (he had put a lot of work into them) then explained that I didn't have a clue how to turn these models into AR. 

We sat together and started searching online for possible solutions (it was a strong example of me being able to model my searching techniques and show me being a learner) after a rather tedious and long search, we came across this post AR augmented reality Lego. There were some sketchy details of how to do it.

We played and finally worked it out

• we had to open the .lxf (lego digital designer) file in the Mecabricks.com website
• download the file from Mecabricks as a .stl file
• on a computer download the edrawingsviewer app and open the .stl file
• save the edrawings version as an .eprt file
• download the edrawings app on an iPhone
• transfer the file to the iPhone (the files can be rather large) open the file in app
• using the downloadable mat from the website bring your model to AR reality

The effect was pretty cool, you could walk around it, zoom in and out, it was AR, while it took a while we did it. The only real issue was that is wasn't a colour version and we needed the mat. The student went away pretty happy. As the AR guy I was feeling pretty chuffed with myself, as per usual when you start getting over confident a dose of humility soon follows.

The best bit

A couple of days later I got this email from the student.

Hi Mr. Derry,

I have been playing around with the different formatting when exporting the files as I had found out that the .stl format takes all the colours out (which was the main problem). After looking through a few ways - I have successfully transferred both my buildings from the Lego Digital Designer, into AR, with colour (it doesn't even need a QR code!). I found another website which supports 3D modelling called Sketchfab, and uploaded the files through a .dae format from Mecabricks, and got Sketchfab on my phone as well, which allows it to be seen in AR and VR. I have attached all the pictures of how they turned out. 

I am very excited to show you everything in school soon (perhaps in innovation tomorrow right after break time), and would like to thank you for all the help you have given me. I wouldn't have managed to pull this out without it! 

Have a great day,

Jordan. 

On his own, he found another way to do it, a better way with colour and no need for a mat or a QR code. You could even go close up and inside the AR model and check out the interior, something you couldn't even do in real life. This is what I love about empowering students with technology, as a teacher I showed him a thing or two and showed him how to search and what is potentially possible. He then took this knowledge and skill and built on it.

I like to call this "wind them up and let them go" get them enthused and excited and watch what they create.

I love doing this with programs like Scratch and GarageBand, just the other day after showing all the grade 5 students live loops,  I had a grade 5 student say to me "Mr D I love live loops in garage band on my iPad. I can't stop playing with it, my parents don't believe I am making such cool music".

We are also doing this in a big way at school through our innovation time, which is 2 blocks per week (the same as every other subject) of passion project time in secondary school, we certainly are winding them up and letting them go. That is a whole other post and we have some great examples to share.

Long may schools and teachers empower students with knowledge, skills and the time to explore their passions.

Everyone can Create - silhouettes

I recently was asked by Apple to run an everyone can create workshop during the latest “Kuala Lumpur Innovation at schools session”.The theme was student agency, but the team were also keen to have some sessions on the everyone can create books.

I had been reading and using the everyone can create photos book and have been doing some of the activities with my own kids at home and thought it would be a great opportunity to share some of the activities in the books.

We looked at techniques and strategies to empower students to take 'good' photos with iPads. We looked at variety, perspective, details, the rule of thirds and Backgrounds. Dave Caleb's book Stories through the Lens was a super resource for this. 

We then explored three of the activities from the everyone can create book - photos including telling photo stories, pictorialize your name and silhouette portraits. It was very hands on, was well received and we had some discussion on how we could use these activities in our classes as soon as we got back to school. Here is a link to the participant created padlet of ideas.

The silhouette portraits is my favourite, I loved using it with my own kids. Seeing as though I was presenting on it, I thought I better try it with some students at school. The next time I had my grade 5 cover we started exploring creating our own silhouette portraits. 

Only using the class iPad's we took profile pictures with a plain bright background, basically we were doing the thing I have been telling my IGBTV students not to do "Don't video with a bright background as you can't see the person being filmed". By doing this we got side on images that we could edit and play with (crop, turn black and white, change the contrast, explore different colours) all using the edit button in photos.

I then took this to the next level, by combing this with another activity from the book. We imported our images into Keynote and then applied Instant Alpha to completely remove all of the background.

Once we did this, we used the add shapes option in Keynote to get the students to add their favourite things to their silhouettes. 

You can search via the magnifying glass and change the colour of the shapes / images, they are also all free from copyright and allow the students to be super creative.

The kids loved personalising their images.

I showed them how to export them as new images and we had a silhouette gallery of all the students in the class and their interests.

The students had lots of fun identifying each other and seeing other peoples interests. We got some insights into the students that we weren't expecting. It was a great way for the teachers to find out about their students and we got a few pleasant surprises. 

As they played with Keynote and shapes the students started exploring different ways to add images they worked out some pretty cool stuff including how to add graded backgrounds and create multicolour and image filled shapes.

The students now have ready made silhouettes that can be used over and over again for a variety of activities. Including

• Exit Tickets
• End of unit reflections
• Brainstorming sessions
• Guessing games
• Poetry (reverse the colours and fill the silhouette with the poem
• Fill the head with a maths problem and solution
• Class displays 
• Add their artwork to the silhouette

The limit is your creativity

We can't wait to explore some of the other activities in the everyone can create books.

Save paper and time with Google Drawings

Creating Google Drawings worksheets

I found this great Factors and multipliers puzzle online here

It's one of those activities where students (or teachers) have to cut out all the bits of paper (right hand side) of the sheet. That means cutting 25 numbers and 10 headings. They then manipulate them on the puzzle sheet until they get the right combination. It is a hands on activity and encourages students to use a variety of problem solving techniques and think about different types of numbers.

When we did it in our 80 minute maths block, many of the students took more than 20 minutes just to cut out the bits of paper, (some took 60 minutes) then bits of paper went missing or were blown around by the fans and air conditioning. A couple of students finished, but then it took for ever for them to glue them in their book. Once the lesson was over, we then had to find a way to store the hundreds of bits of paper.

Rather than being the wonderful learning opportunity it promised, it ended up being an exercise in frustration. 

In hindsight it would have been better to make it a group activity and do the puzzle on A3 paper or spend hours cutting them out and laminating them for the students. Who has time for that? 

Then I got thinking, I could save a lot of time, paper and anguish by turning this activity into a digital Google Drawings worksheet (I hate the term worksheet). It will take me a bit of time to set up, but once it is created I will have a permanent version that can be used over and over again and I would rather spend my time playing with Google drawings than cutting out bits of paper.

The whole process took about 12 minutes, I sped the above video up by a factor or 8 so you get to see it happen in just over a minute

I started by creating a 5x5 table, then added rounded shapes for the headings, if you create one shape and format it exactly as you want it (Shape, colour, font etc) then it is easy enough to copy and replace the text. I then did the same for all the number cards.

Once I made my worksheet I could have grouped all the objects together (so that students couldn't accidentally move the tables and heading etc) but in Google Drawings I find it is easier to take a screen shot, delete the other images and add the screenshot as a single image.

Once the Google Drawing worksheet has been created it is then a matter of sharing it with your students I like to use a force copy link (I like to use Sir Links a lot) so each student has their own copy, the students can then move the shapes around to solve the puzzle. They can rotate the shapes and move them. Do pretty much anything they can do with a paper copy (plus a fair bit more).

No wasting time cutting paper or gluing tiny bits of paper to a sheet, no worries about losing or storing tiny pieces of paper. The puzzle is stored on the students drive. 

You can share different versions for students at different levels. e.g. perhaps one version with the labels in the correct spot or the labels facing the correct direction or half the numbers in the correct position or some blank tiles. It offers lots of scope for quick differentiation, make a copy of the drawing then make the change, make another copy, make the change.

This technique works for lots of different worksheets and once you have created the resource, you have it forever and can share it or use it again and again.

The next maths lesson I used the Google drawings version and the kids completed it much quicker with less stress and we were able to have those valuable discussions about problem solving techniques and how different students solved the puzzle. I am now making many more digital worksheets for my Maths class.

Learning 2 it's true it is all about the learning

In 2010 I had just started teaching overseas and was based in Suzhou (just outside of Shanghai). I had a job as the Middle school Tech integrator. I had only been at the school for two months when the school had the foresight to send me to Shanghai for Learning2.

I had attended large edtech conferences in Australia, but they were the usual keynote speakers and workshop type conferences nothing innovative, new or exciting. Learning2 was different, I was placed in a cohort with people in similar positions to me (great for networking). There was also plenty of time to network and the quality of the workshops was second to none, (I even got to meet some of my edtech heroes) with some really big names and the unconferences were completely new and intriguing. It was conference like no other and upon leaving I thought I am going to the next one no matter what (and hopefully bringing some more teachers with me). It was worth going just for the networking.

I was lucky enough to attend the next 6 learning 2's and presented a variety of 1 hour workshops. I missed Learning 2's return to Shanghai in 2017, (I had already spent my PD budget and had a few other goals that year.

In 2019 applied to be a L2 Leader and was fortunate enough to get the call up. This was something I was keen to do since attending L2 2012 in Beijing where 2 hr extended sessions were first run and the workshop leaders gave pecha kucha talks. At each L2 since then I thought I would love to be up there in front of a large crowd and give a more in depth workshop.

After being a tech coach for 8 years overseas (and a few years in Australia before that) I had presented at a heap of conferences, workshops and school events and had even given a 12 minute TED style talk to over 1800 Heads of schools at the IB world conference in Singapore. I had ticked a few boxes and was a fairly confident presenter. Regardless I was still excited to be a L2 leader and I was going to Japan. I knew the calibre of the sessions and the rigour of the L2 talks.

From my first acceptance email, this was different, I had to sign a contract and commit to a process (including a three week online training course) rather than just showing up and running a one or two hour session. The organisers were constantly in contact and the whole process was super professional.

I had a fairly good idea of what my extended session (AR and VR creation tools) was going to look like. I had done my Google Innovator project on this topic and had already presented at Edtech summits, 21CLHK and the AIMS conference in Malaysia on exactly this topic with good feedback. I also had a couple of ideas for a L2 talk.

Then the pre conference training started and everything changed.

I loved the fact that my preconceptions were challenged and that I had to clearly articulate a set of goals and objectives for my extended session. It made me rethink things and empathise with my learners (that people who would attend my session). The three week online course also allowed me to get to know the other leaders and revisit was L2 and adult learning was all about.

I already felt that I was better prepared for my session than any other workshop I had ever run. Part of the process of being a L2 leader is that you spend a couple of days before the conference starts training and refining your presentation and talk. I was looking forward to working with some super professional coaches and picking the brains of people who know what they are talking about.

The onsite training and planning time was like nothing I had done before, having time to practice my L2 talk and to work with other educators hearing what they were doing and watching them prepare, share and collaborate was one of the best learning experiences of my teaching career. Everyone was focussed on the conference and how to make it great for the participants.

The social aspect was also second to none, a great opportunity to catch up with friends and meet new and dynamic people in a relaxed setting helped build bonds and foster new friendships. I was already getting so much out of this conference before it even started.

Once we did start I felt confident, ready and couldn't wait to get my participants playing with and creating their own AR and VR experiences and I felt like I was giving them a variety of tools and strategies they could take back to their classrooms straight away.

My first two and a half hour extended session went so quickly and it was refreshing to not have to rush through activities and give the participants time to explore, play and create.

Even better though was that an hour after we finished we had in our hands the feedback from participants and the L2 leaders as a team debriefed our sessions and shared successes and failures in a safe environment with the sole purpose of improving ourselves. Like having time before the conference to acclimatise and prepare this immediate feedback and debrief time was new for me and was probably the most valuable part of presenting at the conference. Other times I had presented I might get a spreadsheet back a week later with some scores and ideas on how to improve, not as useful as the immediate L2 feedback and debrief.

Then I got to do my new and improved session again acting on the feedback, although it must have been OK the first time because I had a few people come to me and ask if they could sneak into my second session because they heard from other people how good it was the first time round. Needless to say my feedback scores were even higher the second time.

Finally it was my turn to get up on stage, My L2 talk had been chosen to be done on the last night as part of the closing, talk about pressure. I really couldn't relax and unwind until I was all done. I was nervous as could be, but still had a heap of fun presenting and enjoyed the fact that I had opportunities to workshop my talk and even practice on stage before I did it.

(photo credit to Dave Caleb - a fellow L2 leader)

I got some good feedback, had lots of fun and learnt so much about myself as a learner and presenter.

The entire process (and yes it is a process and not just an event) of being a Learning2 leader was one of the most valuable learning experiences I have had as an educator. Simple things like making a video to advertise my session helped me to clarify my thoughts and ideas. I also had a blast and made a heap of great friends.

It is true that Learning2 is all about the learning