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September 25, 2010

shapes

This post was for the Teach/Learn carnival but I didn’t finish it in time.  If you are looking for other ideas for learning maths go and visit the participants in the carnival at Science at Home.
Maths is a huge subject with applications in most areas of life.  There are many different ways of looking at mathematical topics.  However, people often view maths as a subject in which there is one right way to approach a problem and one right answer. 
I recently read this ‘Disposable Checklists for Unschoolers’ which considers the many ways to explore a topic in depth.  I think that this is very applicable to maths topics.  Approaching problems in maths from different angles improves your understanding of the topic and there is often a way which will make the principles ‘click’ for you.  A deep understanding is what gives maths meaning, rather than being able to apply the right rule at the right time.
So, the demonstrate the variety of ways you can approach learning maths I picked a topic – shapes – of interest to most children and one of my favourite areas of maths and I want share with you a brainstorm based around the 5 senses of play that would increase your child’s understanding of shapes.

An understanding of shapes and geometry underly most fields of design, from architecture to fashion design.  So, what do we need to know about shapes to be able to use and manipulate them properly.  Some of the basic knowledge that occurs to me is …
  • How do we know it is a circle, square, pyramid, octahedron …?
  • Measuring and finding the properties of a shape – size, area, volume etc
  • knowing what is the best shape to use for your purpose
As you play and talk about shapes, keep in mind that these are the questions that you and your child are trying to understand

Ways to play with shapes
SMELL
Well, this is the tricky one, but
  • how does the shape of a container affect the smell of a substance?  Is it easier to smell something in a round or square container? What is the difference if the opening is wide or narrow?

TASTE
  • create meals where all the food is one shape – eg. a circle meal (perhaps served on a circular plate).  Talk about how you know something is a circle.
  • why do foods have a particular shape?  Why are apples round but pears are not?  Would the food taste differently if it was a different shape?  Try and grow food in a different shape.  Here is a way to grow a square tomato.

TOUCH
  • building with blocks – wooden blocks, base 10 blocks, Lego, whatever you have
  • when building with blocks explore how many different shapes can you make with 5 blocks, or 8 blocks and so on.
  • build a shape out of Lego, what is the area/volume of the shape in Lego units?
  • does the shape of the building blocks affect the shapes that you can create?  Can you make a sphere out of cube-shaped blocks?
  • make shapes out of playdough or plasticine
  • draw a picture using just one shape in different sizes
  • build shapes out of toothpicks and marshmallows.  How much weight can different shapes support?  Which shapes are strongest? 
  • make shapes on a geoboard.  Can you find the area of each shape you make?
  • draw shapes on different types of dot or graph paper
  • create string figures in different shapes

SOUND
  • explore shapes in music.  Explore the shapes of musical instruments - how does the shape of the instrument affect the sound?  for example, what would happen if guitars had corners not curves?  How does the size of the shape affect the sound eg. violin vs. cello,
  • invent riddles to describe each shape and see if people can guess which shape you are describing
  • think of a shape and play 20 questions

SIGHT
  • choose a shape and create a collage of things of that shape shape or make a sculpture with just one shape
  • hunt for shapes in nature, artworks or architecture.  What shapes are most common?
  • play with pattern blocks, tangrams, pentominoes
  • What shape are bubbles?  Why?  Have you ever seen a square bubble?  Could you make one?
  • fold paper to make window patterns in different shapes

If you want even more activities for exploring shapes, I like this site – IMAGES, Improving Measurement and Geometry in Elementary Schools

5 comments:

amandab said...

So many of those things have got me curious, and of course, I've never really thought too much about how the shape of something has an effect on it's taste (really? Maybe. See, never occured to me!) or sound (well, perhaps I have thought about this, but not too much). So many wonderful things to do and consider! Thanks for sharing, even if you did miss the carnival :)

Hope you are doing much better now :)

Juliet Robertson said...

OK - forget teaching older children! I think you need to return as a pre-school or infant teacher once you have raised your children.

It's really nice to see this article focus on the wider aspects of shape. 10 out of 10!

Melissa Taylor said...

I like your shape through the senses perspective - you have tons of fun ideas! Thanks,

Melissa

Briana said...

My kids like to play with shapes all the time. And I am so happy with that because it is really helping a lot in her mental development. But I am impressed of your ideas about shapes. Nice article.

kevin said...

Shapes are fascinating things, the way they can become something else, represent something else. Thoughtful article you have. As as visual designer, the maths of shapes is a lot of work for me, but playing with shapes is at the core of visual thinking, proportions, relationships between one shape and another, shapes conveying meaning. My site has a tutorial about playing with shapes to make simple designs of birds. Be good for children. Cut out make birds for instance. Then stick them on the wall. Great rainy day activity