I’ve been at a meeting in the Manchester Chamber of Commerce today and I was fascinated by how sympathetically the building has been renovated and preserved. The plasterwork, tiling, glasswork and carving demonstrated exquisite use of shapes, symmetry and tessellation. Here are a few images that you could use as discussion starter:
Just think of all the shape related problems you could set from each image!
I love tessellation! You get the chance to be a bit more artistic and creative. I’m a fan of this particular website too: http://www.tessellations.org/ The website has examples of fine art and student work, how to make different types of tessellations and even 3D tessellations.
Now I’m sure we all often use tessellation as a homework – the ‘Finish off your amazing classwork at home’ kind of thing. When collection time comes you get many different standards of work:
All, apart from the last case, can be enhanced and developed with the use of a laminator and a guillotine.
Why a guillotine?
To trim off rough edges and forgiveable errors where the student got muddled at the edge of the paper.
Why a laminator?
Laminating the work flattens out any crushed/folded bits. It also preserves decorative edgings when the work is on the wall.
Students who spend ages with coloured pencil produce lovely work which just doesn’t stand out:
However, laminating it makes the colours more vibrant:
It’s hard to show the difference in a photograph, but take my word for it – it works!
You mentioned feedback?
It’s tricky to feedback on visual work without writing an essay or scrawling over the work. A simple solution is to use a marker pen to write on the laminate. Hand out the laminated work and board pens. Students can critique each other’s work by drawing around the individual tiles and annotating them, any errors can be highlighted and other comments made. The wipe-off pens make it less threatening and avoid permanent marks. The great thing is that the original work is not damaged and all comments can be removed with a damp cloth. Of course if you are using this for a wall display teachers may want a more permanent pen for feedback.
Final display
These works of art will be more hardwearing than your average display. You could hole-punch the corners and tie them together to make a wall hanging. You could laminate work back to back and hang them from the ceiling. You could even use the wall hanging as a temporary curtain if you have a rail in your room.
I take no responsibility for this blog post. It is all down to the amazing teachers I work with. We have recently had our Year 6 open day and one of the activities was this amazing tessellation:
As you can see each rhombus has a pattern or picture which links to the next rhombus. You can stand in front of the full wall display and spend ages tracing the different routes across the wall. The clever use of colour means that from a distance the wall pops out as 3D cubes. Older students at school have commented that the display is ‘Awesome!’ and ‘Amazing!.
It was inspired by Vi Hart’s videos on snakes and doodling: YouTube
I’m sure you’ve done or heard of people using their classroom as a basis for problem solving. How much would it cost to paint/wallpaper/carpet the room?
What about the literal cost of flooring a room?
Image credit: Pinterest
Many people have calculated that it is cheaper to use 1 cent coins rather than buy tiles. There are many examples collected together here: Keytoflow
I think this idea could be adapted to look at different sizes of coin, areas and tessellation. Even simple circular coins can tessellate in different ways – how much does this affect the cost? This is also an open task which could lead to some great strategies and discussions.
Update
@LearningMaths suggests students could investigate the percentage area covered by different types of coin. A great extension idea!
Look what my class did today:
We used a hexagonal Tarsia puzzle on expanding single brackets to create large hexagons.
The puzzles were stuck on paper, cut out and the edges reinforced with tape. Twelve hexagons make a splendid snowflake. Once it was stuck together, the wall display was as tall as a Y7 pupil.
Just think what you could do with Tarsia puzzle shapes: snowflakes from hexagons, christmas trees from triangles and bunting from dominoes.
If you want more puzzles, visit Mr Barton Maths for a plethora of resources.
So, we all know that regular hexagons tessellate beautifully, but name an example in life that isn’t a honeycomb … takes a bit of thought before you start listing examples.
Here’s a picture to add to your list: the gates at a local playing field.
Top detail:
Bottom detail:
What is more interesting is each hexagon is made from and connected by overlapping S shaped strips of metal. Recreating the structure out of strips of card could be an interesting challenge!