Here is a quick photo prompt starter for you:
What does this picture make you think of?
If you said favourite colour bar-chart or line graph, you’d be wrong.
The shorter the bar, the more popular the colour.
However turn it upside down and here is your line graph:
The heights of the blue bars are the amount of each colour used – hence more popular.
I spotted this ‘Expert Tip’ whilst flicking through a supermarket magazine:
Image credit: tesco.com/foodandliving
Question
If this cake has a diameter of 18cm (7in), is this a fair way to split it between guests? Can you prove your result in general terms?
Of course, this assumes that the icing on the side doesn’t count in the diameter or guest preference.
It’s amazing what maths you see when you go for a walk along a canal on a beautiful afternoon. After helping a canal boat through a lock, the following problem occurred to me: how many times must you turn the handle to raise the sluice gate?
Fact: The sluice is controlled by a series of cogs. The handle turns a ratcheted cog with eight teeth.
Fact: The handle turns a small cog with thirteen teeth.
Question: The next cog has ten teeth on a quarter of it’s circumference. How many is this in total?
Fact: This large cog is attached to a small cog with ten teeth, which lifts the vertical post.
Question: From the picture can you estimate how many teeth are on the vertical post?
Question: Given all this information how many turns does the handle need?
Extension: Look at this picture. What is the angle between the foot supports?
You know you are a Maths teacher when you go around a British city seeing shapes and maths everywhere AND you take pictures of it! Here are some discussion starters based around the area of Liverpool ONE:
Curved building
What would the plans and elevations look like? Why do you think the side windows are parallelograms not rectangles? Are the end windows similar shapes? What mathematical word describes distorting a shape? (Skew)
Stacked shapes
What would a plan and elevation of this building look like? What shape is the base of the projected level? (Trapezium)
Sine wave
Is this an approximation of a sine wave? Is it representing a convergent sequence?
Triangular roof
Why are triangles so popular in architecture?
Interesting shopfront projection
What would an aerial view look like? Would you see the zigzag projections?
Security door
What shapes can you see? Is it like isometric or squared dotty paper?
Curved stairwell
What mathematical things can you see? Are the handrails parallel?
Circular skylight
What features of a circle can you see?
Do you know that feeling when you are starting a topic which is building on existing knowledge and you are not sure how much to recap? Too much recap and they start the topic bored, too little recap and the new work is too difficult. What to do?
To quote an old UK TV ad: “I want to be a tree!” (Prudential, 1989).
I have a bright class of 13/14 year olds and needed to start some algebra work. We ended up making a tree.
Equipment
Activity 1
In small groups, pupils draw mindmaps for the word ‘Algebra’. Encourage them to group or link topics.
Activity 2
Collect the answers on the main board. Any concepts which are not specifically algebra can be categorised as foundation skills eg understand calculating with negative numbers.
Activity 3
Split the diagram into parts:
Stones: foundation skills which are essential for algebraic success
Branches: subdivisions of algebra
Leaves: specific topics or objectives
Fruit: examples
Activity 4
Assign the different stones, branches, leaves and fruit to pupils to complete.
Activity 5
Assemble your tree. I added an owl and a disembodied voice asking ‘which careers need algebra?’. My branch labels were quickly covered by leaves, so I substituted extra leaves with these labels instead.
Variation
This could work for any topic in any subject. Imagine how good a tree lined corridor would look – a new tree for every area of study.
Review
I moved around the room chatting to pupils as they worked and got a good idea for where I need to start the next lesson. The pupils now have a visual representation of how algebraic concepts link and overlap. In hindsight, I’d probably make the leaves and fruit smaller so that links are clearer.
Show me your learning trees on twitter and I’ll share them on here. @Ms_KMP
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!
The summer is a memory as we dig out the wellies and jump in puddles.
This photo made me feel summery and geeky all at once. Click here to find out more.
