By Samantha Millar 

Picture this; 20 excited, nervous Year 5 students, a lake and a bridge constructed from pallets and random planks of wood. I use the word ‘bridge’ loosely. In actual fact, the pallets and planks are not fixed and are simply lying on top of one another. More alarmingly, in some cases, floating away or alternatively sinking into the lake. My students are excited and nervous because I have just announced to them that we will be attempting to cross the ‘bridge’.


I love the concept of unexpected, authentic learning and am always on the lookout for experiences that offer just this. This bridge crossing was a fun challenge that, on the surface, encouraged risky play however, it turned out to be probably the most memorable maths class this year.


I am a Year 5 teacher at Cornish College, an ELC – Year 12 independent co-educational school which is located in Bangholme, Victoria, Australia. At Cornish we are educating for a sustainable future and one of the ways we do this is by incorporating Outdoor Learning into our curriculum wherever possible. We are lucky that our school is on 100 acres and we are encouraged and supported to utilise the land as much as possible. Our weekly Outdoor Learning program is called Dhumba-dha biik (pronounced Dum-bar-dar-bick). Cornish College is located on Boon wurrung country and Dhumba-dha biik in Boon wurrung language means Talk Country (used with permission).


During this particular Dhumba-dha biik, the two year 5 classes were told that the Secret Second Island was now “out of bounds” as it was being planted out, to become Land for Wildlife. The Secret Second Island was a wild space that we had been visiting throughout the year as, due to the drought, the lake bed had dried up and we were able to access this otherwise inaccessible island. The students were disappointed to lose the space but recognised the importance of creating a safe space for wildlife. My teaching partner suggested that each class could have the opportunity to say good-bye to this much loved area. To do this, the classes needed to cross a ‘bridge’ which had been constructed by the Year 9 & 10 Sustainable Land Management students, to enable them to gain access to the island for their wildlife plantings. As I recognise the importance of risky play, this was an opportunity that I simply could not pass up.


In the preceding weeks there had been quite a bit of rain and the lake was now at around 60% capacity which translated to waist deep water. It had been raining since my teaching partner’s class had completed the challenge earlier in the day so we knew that the lake would be a little bit deeper and the bridge a little bit slipperier. We also knew that a number of his students had ended up falling in and that there was a real risk of the same happening to us. As I gathered my class around me I said to them “Let’s think about the maths.”


Where possible I like to link maths into Dhumba-dha biik but without making it a huge deal. It is generally more of a discussion. I asked them “Knowing what we know about 5T, what are the chances that we are going to all make it across the bridge?” Likely, unlikely, impossible, maybe, possible, certain were all terms that were tossed about as they excitedly assessed and discussed the physicality of our class. “What chances do you give yourself to make it across?” These responses were varied with some individuals sidling alongside me to quietly tell me that they fully expected to fall in because they did not believe that they would be any good at this activity. I made it clear that attempting the crossing was optional – no one would be forced to do it. “What percentage of the class will make it across?” After some quick mental calculations, the general consensus was between 75-80%. At this point I started to get the distinct feeling that some of the more physically capable boys were going to deliberately fling themselves into the lake. So I told the students that I thought, as a class, we were physically capable and significantly more able than 5T, who had a least 3 people end up in waist deep water. I felt confident that we could smash 5T’s record. As there is a healthy rivalry between 5M and 5T the challenge was accepted and everyone decided to stay dry.


As we walked to the bridge I listened in on discussions about how deep the water potentially was now compared to when 5T attempted the crossing. A few students picked up sticks and talked to their classmates about the possible depth of the lake and how they would determine what it was with their stick. There was lots of chatter about individual success and the various possible strategies they would employ to cross. There was also talk about being a risk-taker and giving it a go.


Once we arrived at the bridge, it was clear that 5T’s attempts at crossing it had caused sections to float apart. I believe that it’s best to lead by example and so I confidently stepped out on to the structure to discover that it was anything but stable. It immediately started to sink, much to my class’s delight, and there was a real risk that I was about to be the first causality. Suddenly, students began stripping off items of clothing on the bank and I could see and hear them plan their route and helpfully yell out alternate ways for me to take.


As I moved across the perilous structure I reassured them (and myself!) that the bridge was sinking because of my weight. I tried to set their minds at ease by declaring that I probably weighed at least double what they weighed and that I felt sure that the bridge would not move in such an alarming fashion when they began their journey. A few demanded to know how much I weighed and once I supplied them with the answer there was a range of swift calculations to determine if they weighed half as much as me or not. They also began reassessing their chances of crossing, based on their mass.


Slowly and carefully the class commenced their trek. I stood in the middle praying that I didn’t end up completely submerged. I held their hands, encouraged and directed as they tackled the unpredictable bridge. They excitedly watched one another, nervously chattering and cheering. The first few students made it successfully across and they then guided the others using their knowledge of position, depth, direction, mass and angles.


Some of the students who were waiting amused themselves by filling their gumboots up with water. They experimented with the tipping point of water overflowing into their boots and then observed and noted the volume of water in their boot, displacement when their foot went in and out of their boot and the potential capacity that their gumboot held. Whilst not every student experienced this (as not all deliberately stood in the lake with the intent of filling their gumboot) and whilst I drew no attention to their experimentation, the maths was there and it was real and meaningful.


We successfully traversed the bridge and the whole class made it across to the Secret Second Island without incident. We celebrated our 100% success rate and our bravery (the entire class ended up participating in the challenge) and we then said good-bye to the space that we loved. The return trip began and the students were far more confident in their bridge crossing abilities, however this confidence led to speed and lack of attention. Unfortunately, they soon discovered that the faster you went, the more likely you were to slip, and the bridge began to claim its victims.


Once everyone was safely back on dry land, we discussed and reflected on our initial predictions. We had been correct in our prediction that it was unlikely that our entire class would make it across. Individuals expressed amazement and pride that they had not expected to make it and yet they had, twice! Our original percentage prediction was that 75%-80% of us would be successful and we were pretty close with a 72% success rate.


In addition, the unexpected maths that we covered was weight, depth, angles, mass, speed, volume, capacity, displacement along with mental computation. In fact, the entire experience was one of unexpected maths as the lesson intention had originally been about risky play. I could not have covered all of these mathematical concepts within the walls of my classroom in the same time in such an authentic, engaging and fun way, nor would the maths class have been anywhere near as memorable!


I believe that the outdoor environment is the perfect platform for rich and authentic mathematics and, if you can add a touch of risk-taking to it, you have the perfect combination for an unforgettable and powerful learning experience.


Author Bio

Samantha Millar is a Year 5 classroom
teacher and Outdoor Learning Co Ordinator
at Cornish College in Bangholme, Victoria, Australia.
She is passionate about getting children outside
and connecting them to their land and country.
You can follow her on Twitter 


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