Category Archives: Shape, Space & Measures

154. When will I need to work out the area of a circle?

Answer:
If this is your crop on your farm!

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This is center pivot (or central pivot or circle) irrigation. The area which is watered is pretty obvious. There are plenty of images on the internet and sites full of statistics.

I could imagine this making a good research homework. Apart from simply working out the fertile area, you could look at volume of water used – you could even work out the optimum size and number of circles for maximum coverage!

147. All hexed up

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.

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Top detail:

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Bottom detail:

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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!

134. Revising around in Circles

Ah … beloved GCSE students. Why does revising feel like I’m just reteaching a topic for the Nth time?

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I’ve been trying some new ideas out on my GCSE group. One of the more popular ones ideas, for an unpopular topic, were these Circle Theorems fact cards. Students were given four cards with a diagram and an open question, for example: What is special about angles ABD and ACD? In the gap, they had to answer the question. They soon realised that the answers they had written were the theorems that they’d learnt. Their solutions had popped into their heads, without being bogged down by number stress. They could then try number questions, referring back to these fact cards if they got stuck.

126. Kusudama to meet you

Wow … September again and many people will be meeting new faces for the first time. Learning names, setting out classroom rules, figuring out who’s got all the textbooks you need …

image Made using origami paper.

Back in July I made Kusudama flower balls with a couple of classes. It occurred to me then what a great ice-breaker they could be. They’d also be a nice maths club project.

Definition of Kusudama from Wikipedia

The Japanese kusudama (薬玉; lit. medicine ball) is a paper model that is usually (although not always) created by sewing multiple identical pyramidal units (usually stylized flowers folded from square paper) together through their points to form a spherical shape. Alternately the individual components may be glued together. Occasionally, a tassel is attached to the bottom for decoration.
Resources

You will need:

  • 5 squares of paper for a flower
  • 12 flowers for a ball
  • 60 squares of paper in total (sugar paper is cheap, but doesn’t tape together well)
  • String if you wish to hang it up
  • Card if you wish to mount a half ball on the wall
  • Sticky stuff: glue sticks or glue dots or pva glue or tape or a hot glue gun – whatever works for you!
  • Beads or ribbon for decoration (optional)

Activity

It has an instructional video and very clear step by step photographs. It’s so easy a six year old can (and did) do it!
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  1. The instructions assume 30 pupils in a class. Let each pupil make a petal following the step by step instructions and then independently make another (2 petals each).
  2. Pupils pair up and stick two petals together (1 petal each and 1 pair stuck together).
  3. Pairs team up with another pair and stick their pairs together (1 petal each and 4 petals stuck together).
  4. One person in the four uses their extra petal to complete the flower – that person is in charge of the flower ( three people with 1 petal, one person with a flower).
  5. Flower pupils form a group and start sticking their flowers together.
  6. Petal pupils work with new people in groups of 5 and create another flower.
  7. Eventually 12 flowers are completed and stuck together.

 

Notes:

  • String should be firmly attached before the ball is complete.
  • It is advisable to staple a half ball to card or the wall to prevent it collapsing.

 

Thank you to @c0mplexnumber for the original inspiration for this activity.

Have fun folks!

96. Free (editable) Flashcards

I was looking for some Maths paper when I was on Printablepaper.net, when I came across a ‘sister’ site: Printableflashcards.net. This website has free flashcards covering many different subjects/topics and is worth a browse.
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The biggest selling point to me was you can create flashcards without requiring a double sided printer or cursing the photocopier for misaligning your originals. You don’t have to glue them (unless you want to) as they will stand nicely on the desk once they are folded, with the answer face down on the table. You can use the Flash Card Generator to create your own set of 4/6 (or multiples of 4/6) flashcards.

86. Snapdragon & Resources

I’ve just started sharing resources on the Times Educational Supplement (TES) website.

The first resource is a typed up version of the Trigonometry Snapdragon.
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I’ve omitted the diagrams so you can have a discussion about what the different situations look like.
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Update: I am hosting my own resources now so you can download the snapdragon here: Trigonometry snapdragon v2