Working with 3D Shapes

I love Twitter.

I love the way you can go to your PLN and ask for help and ideas.

And I love being able to help when someone else puts out the call.

So when I got a message the other day from a Twitter follower asking for ideas for promoting inquiry into 3D shapes with a Year 2 class, I was happy to help.

Here's the ideas I came up with. You can probably think of others that you might suggest in the comments section below...

 
1. I like to refer to 3D shapes as "real"shapes - they exist in reality. Unlike 2D shapes which only exist in the imaginations of geometrists. 2D shapes are not real - they cannot exist in the 3D world. We can see representations of them but everything "real" has depth.

2. Get out some paper shapes - circles, squares, triangles etc to see what shapes the kids can make using flat shapes as faces. And what about if they curve the flat shape, like to make a cylinder? What shapes can't they make? (Have a chat with Mr Mercator about the sphere..) Continue the discussion about nets and how to assemble a 3D shape from a net.

3. Get some solids and paint the faces then print onto white paper. Reassemble a copy of the original solid from the net formed. Try with a sphere haha!

4. Use playdough to make 3D shapes - very tactile and great for kinesthetic kids. Make sure sides and angles are straight with a ruler or flat edge.

5. Do cross sections of prisms etc by cutting playdough with plastic knife of pulling apart the stack made in 4 (above).

6. Use plastic shapes, squares, triangles, circles etc, to make a stack of similar shapes to create a prism - a shape projected through itself. What happens when you lift up half of the stack? What shape do you see in the cross-section?

7. Get kids to group a set 3D shapes - what properties do they have in common? What characteristics can be used to classify them - prisms, pyramids, curved faces etc.

There are lots of ways to explore and investigate 3D shapes. The most important thing is to actually make physical contact with a few of them, not just look at pictures in a textbook.

Have some fun.

And post a comment if you have some other ideas on how to explore 3D shapes.


Here's some suggestions that have come through so far:

Suggestion 1: Imagine you live inside a 3D shape. Design the interior. Next, perform a mime for the class about living in that shape. Class guesses what shape you are living in.

Suggestion 2: I love the feely box activity! Hide a 3D shape inside a box with holes in the side so a student can insert their hands and feel the shape. The class ask the student questions to try and guess the shape. The child with the box needs to feel the shape in order to answer the questions. Its great to do a number of times to develop the children's questions and also the terminology they use. ie Does the shape have more than one right angle? What makes a good question? discussions are good too.

The Super Savers Supermarket!

Financial literacy (or numeracy) began in earnest today. The kids in Year 4 had been bringing in empty boxes, bottles and jars for a few days and we had a great collection of items for our own shop - the Super Savers Supermarket!

To make it even more fun, I have an old cash register that I acquired from my wife's pharmacy when they upgraded to a bar-code scanner system. We loaded up the register with play money and gave the kids instructions on how to work it correctly.

Then we went shopping!

 I organised a few introductory activities to get the kids into the swing of things. Each activity had a set of brief instructions and space for calculations and a copy of the docket.

Activity #1 required buying things for breakfast. The students were given $15 each and needed to record what they were buying, what it would cost and how much change they expected to get back. This needed to be done before they went to the checkout because:

1. they needed to know that they had not exceeded their budget

2. they needed to know that the shop keeper was giving them the correct change

 And this is how it looked when the activity was completed.

Additional activities include shopping for a picnic, buying snacks for school and getting something for afternoon tea.

So far the kids have shown they can use the cash register efficiently and they are becoming pretty good at counting out change.

It's going to be a fun time in Year 4 for the next few weeks.

The Price is Right

Do you remember this game show from back in the 80s and 90s? It was something my grandmother used to watch. Apparently it's making a come back on Australian TV.

This is great news for all young mathematicians - as this is a show with a heavy maths focus and some great activities for you to try at home or at school.

We did.

The Shopping Game

@CapitanoAmazing brought his class in from next door and we played the Shopping Game.

This is a great game from The Price is Right where the contestants have to try to arrange a set items in order from cheapest to most expensive.

We had a collection of common shopping items and laid them out on a table. All students had a sheet with pictures of the items printed on it so that they could make their predictions about what the order should be.

Next we picked volunteers from the audience to "Come on Down!" and pick the next item in correct order.

Finally, we revealed the correct prices of the items and showed the children the order they were meant to be in.

Lots of great fun, some interesting predictions and a great introduction to our current inquiry into money and financial literacy.

 

You can see in the background the whiteboard where we  brainstormed some ideas, sayings and songs about money as part of the introductory conversation. Then we began to group these ideas into common themes. This was a really valuable exercise for the kids to get thinking focused and tuned in.

Ellie Cole - Paralympic Hero

We recently had a visit to our school from Ellie Cole, Australian paralympic legend. She trains and studies in Canberra so was out visiting local schools after her huge efforts at the London 2012 Paralympic Games where she won 4 gold and 2 bronze medals in swimming.

Here is a link to our school website with a picture of Ellie with some of our students, including two lucky kids from 4BF!

http://www.radford.com.au/

Visit the Kick Sarcoma organisation

Anyway, while Ellie was talking to the kids about her life, her battle with sarcoma and the "Kick Sarcoma" organisation she represents, she said a really interesting thing.

While she was having breakfast at the paralympics she met some people who she considered to be really inspiring. They were athletes with severe physical disablilities who were doing great things in representing their countries at the paralympics.

One such athlete Ellie mentioned had no arms yet he was able to eat his breakfast by holding his cutlery with his feet. Ellie, who is pretty amazing herself, said she was enormously humbled and challenged by what she saw around her.

She said,

If they couldn't do something the way everyone else did it, they found another way.

This is exactly what I want the kids in my class to hear.

And this is exactly what I want them to do.

Inquiry is all about finding new ways to do things, to solve problems using your own strengths and overcoming your own limitations. To be a life-long learner is to be constantly seeking to find another way...

An Interesting Thing About Square Numbers

I was driving along this morning thinking about square numbers and how they look. And then I thought of an interesting "thing" about square numbers. You've probably seen this before but I found it quite nifty.

Anyway. pick any 2 numbers that are 2 digits apart, say 4 and 6. Set them out as an array:

4 x 6 = 24

Now if you take the number in between the 2 numbers you used in the array and square it, you need an extra counter/egg/chess piece to make the array:

5 x 5 = 25

Doesn't matter what you use - could be chess pieces or coloured squares or anything.

Or if you want to get symbolic:

X² = (x-1)(x+1) + 1

That's because...

(x-1)(x+1) = X² - 1

So I start thinking, what if I throw in a few decimals?

Like 4.9 x 5.1? They're both 0.1 from 5 which we are squaring.

Hmmm, it equals 24.99

Or how about 3.9 x 6.1? They are both 0.1 from those original numbers we multiplied, 4 and 6.

Well, that equals 23.79

And what about 4.999999999 x 5.000000001?

And that one equals 24.99999999 - is that a calculator error because I only have a 10 digit display? Or is that the "real" answer? And what does it mean?

And what if I use numbers that are 2 integers higher and lower than the square number?

Like 3 x 7 = 21.

But 3 x 8 = 24

Why is that? And will it work for every square number?

Too many questions, too little time.

Just wait till I get back into the classroom next week. Look out kids....





The Moral Imperative to Teach

This morning I heard Tim Costello, boss of World Vision, address the #ACEL2012 conference.

The one big idea I got from his talk:

There is a moral imperative to educate all children.

That's it. Quite simple really.

We need to get out there and teach.

To the best of our ability.

Do it.

Let me know how it goes.

What Should a 21st Century Classroom Look Like?

I had the pleasure of listening to Lee Crockett (www.fluency21.com) address the ACEL 2012 Inquiry Mindset conference this morning. He was very easy to listen to and made a few points that stuck in my mind.

His topic was "What should a 21st Century classroom look like?"

He was not really interested in the architecture or soft furnishings. The main issue was what was happening, the educational process, and how it was being played out.

So, some interesting comments:

1. He quoted a comment from Woodrow Wilson: "It is easier to move a cemetery than it is to change a school, though they are very similar actions." I may have misquoted this quote, but I am in good company.  I googled the quote to clarify what it actually was and found several variations on this theme, all attributed to WW. The point was the change does not come readily to schools.

2. Creativity enhances the value of the function through the form. The idea here was that if any item in the world can be mass produced at minimal cost in a factory in China, then we need to use our creativity to make our product look good or no-one will bother buying it.

3. Relevance + Creativity + Real World = 21st Century Learning
This, I hope, is something I endeavor to promote in my classroom and record in this blog.

4. "Teaching as Talking" vs "Learning as Doing" - learning is active, not passive.

5. Final point that impressed me was that all the left-brain, serial, sequential, process jobs that our Industrial Age education system prepared us so well for have all but disappeared or been taken off-shore. The growth area in employment focuses on creativity and problem solving - divergent dentists, creative chiropractors, artistic engineers....

Oh brave, new world that has such people in it.

The Best Thing I Heard Today

Cate Elshaug from Elwood Primary School in Melbourne gets my vote the best presentation  on Day 1 at ACEL 2012 Inquiry Mindset conference.

Here's a few of the things she said that stuck with me:

1. Using the Inquiry Process in Mathematics

This was her topic And really focused in on using the PYP framework as a planner for the organization of Maths across her school. She made the great point than it is rare, almost unheard of, to find a school that can articulate it's plan for Maths and has consistent documentation that supports the plan from K to 6. So many schools have teachers doing their own thing regardless of the official school policies. And no - a textbook series is NOT a curriculum plan. Hmm, think there's work to do here when I get home.

2. Use immersion activities at the start of the Tuning In phase is critical to engaged student attention and developing inquiry questions. Cate quoted Lane Clarke saying, "Children don't know what they don't know." The importance of tuning in is that it gives children focused experience in the area to be explored.

3. Some inquiry questions are "through line" - that is, they will be explored and revisited as the inquiry progresses. Other inquiry questions are taught explicitly, or at least the required skills are taught so give the children what they need to answer the question.

4. Cate also recommended using "Wonder" or "Discovery"  books as part of the tuning in, where children record what they know and what they want to find out.

So much to think about.

Thanks Cate - it was provocative and gave me lots to think about.