Primary Maths Challenge
Educator: Debbie Taylor
Location:Littlehampton Primary School
Student age group:Year 6/7 class
This task “evolved.” My aims were to raise student awareness, to support an initiative of our student forum leaders and to collect and analyse relevant and realistic data. Our written presentation was as a means of sharing this information with families on our schools open morning for Literacy and Numeracy week. Today, when I offered the posters to our school co-ordinator, she suggested the work should, instead, be submitted for the Primary Maths Challenge.
When I instigated this investigation, it was simply designed to meet classroom objectives.
Debbie Taylor 29/8/12
Background
Student forum leaders in our school initiated the WOW Less to Landfill challenge to reduce the amount of material going to landfill. I noticed that by the end of recess, our bin was regularly overflowing with wrappers from convenience foods. A large part of this challenge is the students actually sorting the classroom waste after lunch each day for 5 weeks. Our school has also received a grant to purchase plastic containers for each student and we need to demonstrate that this initiative does reduce waste being sent to landfill. I wanted to raise student awareness and get them to become involved in a very personalised and relevant use of data as a tool to change personal practice.
All of this came about at the same time as a short inquiry topic on the human body which saw us investigating body systems and healthy diets.
Planning and Programming
With the Challenge beginning, I saw this as a great opportunity to involve the students in a realistic and relevant learning experience which included data collectionwith a particular emphasis on working mathematically and the proficiency strand of problem solving. I also wanted to convince families that saving landfill was both important and affordable, so chose to link in some financial mathematics.
My perception of my students understanding of volume was that they could apply formula to solve questions but that the concept wasn’t fully established and they didn’t perceive a need for understanding volume beyond food packaging and cooking in our kitchen. I wanted to reinforce that collecting data is important in making informed decisions and that there are often multiple factors to be considered.
Starting Points andQuestioning
Without any prior warning, I had every student bring their recess into the room one morning and take their own photo of it. I then commented upon the overflowing bin, the unhealthy range of foods and posed a question
I wonder how much landfill we create in a year…
I explained to the class that we were going to calculate both the environmental and monetary cost of our recess. My preferred questioning style has been influenced by Dylan Wiliam (overall) and Tierney Kennedy (mathematically). I expect all students to contribute and I ask for their input, as opposed to seeking volunteers.
What will I do with this container / package / peel after I’ve eaten the food?
Where does this fit in the healthy eating pyramid?
What does it cost me to pack my lunch box? How could I calculate it?
What does this lunchbox cost the environment? How could we calculate this?
We decided to use our data collection from the rubbish survey to sort categories (reuse, recycle, compost, landfill) and classified lunchbox items accordingly.
Modelling and Process
My lunchbox was opened and the differences and similarities between the contents of theirs and mine were discussed. I opened an online shopping website and found the cost of apples. I used the measure up website ( to investigate serving sizes to establish that 150g is a serving of fruit; a medium sized apple.
I chose to model two process for finding the price of an individual apple, one using regular lineal maths and the other using logical reasoning (Ann Baker – save brainspace).
If 1kg of apples costs $5.98, there would be 6.6 apples in this kg. I rounded off the cost to $6kg and could divide the 600 cents between the 6.6 apples to find each would be 90 cents. I suggested there may be an easier method – that of finding the cost of 10 apples. Through guided questions we established that 10 apples would weigh 1500g and that this was equivalent to 1 ½ kg. If one kilogram is $6, 1 ½ kg is $9 – divide that by 10 to get….. Not surprisingly, most students preferred method two.
I then asked questions about how we could calculate the cost of a muesli bar asking the students to suggest what we would need to know.
Questioning was also used to establish that my apple core would end up in compost but that a muesli bar wrapper would end up in landfill. I asked the students how many wrappers they would create if they ate this same recess every day of the week for the 40 weeks of the school year.
Having the students effectively envision this was difficult.
Every day we fill our classroom bin, so that’s 200 bags of rubbish. Rubbish which goes to landfill is compacted to reduce the amount of space it takes up. How can we find out how much space our landfill will take up?
We decided to collect both bar wrappers and mini chip / biscuit wrappers. Our challenge was to see how many of each type could be packed tightly into a small box (our pen box measured 15cm x 6.5cm x 2.5cm). We calculated the volume of this box and worked out how many boxes each student would personally fill in a school year based upon their recess on this day.
What if everyone in this class ate the way you did on this day? What if everyone in the school ate this way? Would it fill our classroom? If there are 8 bars in the box, how many boxes do I send to recycling each year?
Assessment
From their calculations –
- Ability to work mathematically, both independently and with peers (using internet and calculator)
- Ability to work from individual to week to year to class to school (not all could move beyond year)
- Ability to visualise volume as different shapes
- Ability to compare the two buying and packaging styles to decide upon a “best” option
From their posters
- Ability to communicate findings
- Ability to use findings from data to make informed decisions, and toinfluence the choices of others
Suggested improvements
I missed a great opportunity to incorporate some percentage and fraction work. What fraction of your lunchbox is eaten at recess? How much of this is considered healthy?
Reactions and Reflections
We have discovered that the average student would create “about a shoe box” of landfill each school year from their recess habits alone. Many students were quite confronted and surprised by this when the space was measured out in front of them. We have also found that the cost can increase by over $300 dollars in a year if pre-packaged foods are used. Already about ¼ of the class have made changes to their recess habits such as using containers, buying in bulk and reusing snap lock bags. Others have shared their findings with their families and are making different choices about the foods they bring.
It is wonderful that these changes have come about due to the student’s investigations.
With thanks to Debbie Taylor, Littlehampton Primary School,Year 6/7 class 2012, who received a commendation for this great work!