The Creative, Collaborative Mathematics Classroom

by Cassandra Portelli

Our school has a lot of big personalities, they like to talk, collaborate, and even argue about their Mathematics.
The Creative, Collaborative Classroom (or C3) is the term used to describe activities in the school that get several classes working together. The school has created a collaborative learning space large enough to fit three classes, Students have access to breakout rooms for targeted learning moments and several forms of technology. Ideally the learning revolves around solving some problem that the students can relate to.
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My World
One project is titled ‘My World’ and requires students to plan the renovation of a space that is important to them. Students calculate areas within the room for painting and floor coverings, create a scale model, and calculate the cost of paint, floor coverings and a few space saving furniture items, justifying the economy of their suggested purchases.

The Task:
Your job is to plan the redecoration of a space you love.
You must:
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● Take measurements
● Create a scale drawing or 3D scale model.
● Calculate the area of the floor and walls
● Calculate the cost of paint and carpet and any other decorative features you wish to incorporate. Explain how you are getting value for money with the choices you have made.

In all cases you should justify your calculations by showing your working out as well as explaining your reasoning as to why you chose the methods you did.

Container Challenge
Students are shown a new, environmentally friendly drink packaging that decomposes in just 7 years. It is a more expensive packaging option, so students are challenged by a local company to find an aesthetically pleasing container shape that will fit nicely in the fridge door, stack well, hold exactly a litre of a new flavoured drink and, importantly, minimises the use of packaging material. There needs to be three options examined by the students, who build the one they think is best, test it holds exactly a litre of liquid, and create the new flavour’s label and jingle.
This project was judged by older students, and the local company provide some prizes for the winning entries. In the process students learn about surface area, volume, costing, and practice their mathematical communication by demonstrating their calculations and justifying their choices.

The Task:
A local company are looking for a new style of drink container. Your team of 2–3 has been asked to design the new container and advertising material to go with it. It should have a minimum surface area and hold exactly 1 litre of liquid. You will also need to consider how the container looks, how easy it is to hold and how well it will stack and fit in the fridge door.
Your task is to produce three ideas for the solid and show the calculations for their surface area and volume. Choose one and create a prototype. A plastic bag inserted in the container prototype will allow it to hold liquid. You must design a label and a jingle for your new product.
Please ask if you have production questions.
Peer marking will occur in week 9 using the marking grid below. The company will be coming on the last C3 day to judge the best 10 containers and hand out prizes.
Good luck!

The Importance of Samples and/or Scaffolding
One of the things we have discovered from running this type of activity is how important it is to have student samples available. Students get a good idea of exactly what is expected from having a look at past student submissions. Alternatively, good scaffolds can help students step through the task.

Valuing the Learning
These projects are built into the formal assessment for Mathematics, so that students understand the learning is considered important and not just a fun add on. Students really seem to enjoy working with peers in other classes and being able to appreciate the classroom learning applied to a context.

​Marking Guidelines
C3 tasks are launched with marking rubrics. This allows students to maximise heir marks by being able to self-assess against the rubric. It also ensures that peer or teacher marking is consistent, and fairly quick, and helps provide obvious feedback to the student where they are not judged at the highest possible level.

Supporting activities
Students also engage regularly in vertical whiteboarding. After a period of exploring individually, or engaging with content and examples, students are invited to solve problems in small groups at the classroom walls, which are covered in whiteboards. It does not suit every student, and might not be used every lesson, but the school experience is that students find it easier to make mistakes to learn and grow when using the whiteboards.
Another example of collaborative learning is the morning study program. Every morning several classrooms are opened at 8am, allowing students to bring homework, assignments, and study into the room, and offering a light refreshment. The classrooms are staffed by Year 10 tutors, volunteer teacher education students from the local university, and a rostered faculty member. The refreshments are donated by the school community.

Reflection
Students have been observed to be highly engaged in these types of tasks and showing ownership of their learning. Collaboration tends to be broader than simply between students, extending to other year levels through peer marking, between students and teachers, between staff in planning, conducting and evaluating the learning, and with families through the homework components.
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Cassandra Portelli is the Head Teacher of Mathematics at Hunter School of Performing Arts, New South Wales — a school that champions creative and collaborative classrooms. Cassandra believes passionately in the value of mentoring new teachers, and promoting financial literacy for young people.