The Dangers of Learning Your Times Tables

...or How I Broke My Arm Last Night

This brief post is dedicated to an enthusiastic and energetic young man who took up the idea to do something kinesthetic while learning times tables facts. This is a great strategy to combine left- and right-brain and get things really embedded in the memory.

The choice of action was trampolining.

Sadly, our young mathematician misjudged the jump and ended up with a broken arm.

So be careful out there. Those times tables can be dangerous.

Calculating the Area of a Rectangle

...and how it relates to multiplication facts

Alright - we all know this remarkable feature of multiplication.

And we already know the formula because someone taught us back in high school: 

area = base x height

But what about my team of Year 4 kids? 

What links could they find between area and multiplication facts?

So we started with some coloured rectangles, carefully cut to be pretty close to whole centimetres.

Then, using our multilink cubes we worked out how many we would need to cover the shape.

Much discussion ensued using words such as "area", "length", "height", "centimetre", "compare", "larger", "smaller" etc

"Ah, yes! 3 rows of 6 cubes. So the area is 18 square centimetres!"

And then the moment of epiphany!

Like a crack in the dam wall, the realisation came that we don't need to cover the whole shape.

We can in fact use our knowledge of multiplication facts to simplify this task.

So instead of putting out 150 centicubes, I only need to know the length of the base and the height.

Viola! 10 x 15 = 150

The final step was to compare the areas of larger shapes.

Who had the biggest rectangle? How do we know? How can you prove it?

So what?

This may not seem too spectacular for a lesson idea, but the lights really came on for a few individuals in the class. Sometimes what seems obvious to us adults really is remarkable to kids.

My Name is 6 x 7

Here's a great idea for multiplication facts

...and like any great idea it was stolen from another teacher (Mrs P-W, two rooms down) who found it on a web-site somewhere.

For the day, all kids in Year 4 were given a sticky label with a multiplication fact written on it - this became their new name for the day.

Here's 48 and 64....

...and 108 having a chat with 56....

...and 63 with 144!

We all had to use our new "names" for the whole day. It was a great way to get the kids to think multiplication and to remember a few of those harder facts.

Teachers also participated - I became Mr 42 (or 6 x 7). (Douglas Adams fans may see the significance)

Churchill Fellow 2012

Earlier in the year I applied for Winston Churchill Memorial Trust Fellowship to study the inquiry process in mathematics education.

To my surprise, my application was successful and in 2013 I will have the opportunity to get out there and see what is happening.

Receiving my Churchill Fellowship from the Governor General, the Honorable Quentin Bryce

The Learning Journey

During April and part of May 2013 I will be visiting schools in New York, San Francisco, Tokyo and Singapore. I will also be attending the NCTM conference in Denver, Colorado.

I'm excited already - it should be lots of fun and a great experience. While I have made preliminary arrangements with several schools, if you happen to be in any of these cities and would like to arrange a visit, let me know and I'll see what we can organise.

Special Thanks

I'd like to thank several people who helped me in the application process - Peter Sullivan of Monash University, Melbourne; Philip Heath, Principal of Radford College; my staff team on Year 4 whose enthusiasm and support really encouraged me; and my wife and family - thanks everyone!

Want to apply for a Fellowship?

Interested? Are you an Australian citizen? (UK and NZ - you have your own associations)

Then look at the Winston Churchill Memorial Trust website - http://www.churchilltrust.com.au/

Maths is...

Listening to the voice of the child

Something I want to do more in my class is to listen to how the kids are feeling about what they are doing. I make too many assumptions about what they think and feel and I make important judgments based on my own skewed views.

So what would the kids say when I asked them to complete the sentence....

Maths is...

I got my class, and the one next door belonging to CapitanoAmazing (find him on Twitter or at http://4thgradebigquestions.blogspot.com.au/), to finish the sentence. I sorted through their responses and found lots of interesting and thoughtful comments.

Here is a selection that I have grouped into sets.

Awesomely Positive Responses!

There was always going to be a few of these. Some kids are so positive about everything they do. Being so effusive doesn't make these comments any less important - they need to be acknowledged and celebrated along with the rest of the team.

This is hard but I think I can do it

An interesting group of responses from kids who found that Maths is easy but who were prepared to take the challenge and have a go.

I really encourage kids to try a variety of strategies to reach a solution. This really helps them, and me, to reflect on the problem solving strategies being used and which might be most effective.

Maths is meant to be a challenge. We need to take kids from what they know to what they don't know - this is the essence of learning. I'm really glad that these guys identified the challenging nature of learning. 

 

Help! I think I'm drowning!

There is almost a sense of desperation in some of these comments, where the child can see that things aren't going in the right direction but they don't know how to turn it around.

How many kids are sitting in my room thinking that they are failing? Not just in Maths but in writing? spelling? reading?

Well, now I know about a few of them and guess what? Now you're on the radar I can do something about it.

This is formative assessment, isn't it?

Something to think about

And some of these responses made me sit back and think.

Maths is a sum that has one answer? Really? 

Or Maths is the basic number operations? Isn't there anything else - just figuring out?

I do encourage the "fun" idea and the problem solving side of maths so I'm glad a few kids identified that as part of the process.

And "Power and Knowledge"! A very interesting concept to explore.

Maths is Life!

And then there were those who saw the real-life meaning and application of Maths.

Maths is everyday life.

And if that message is all that my kids hear this year, I won't be disappointed.

(Well, maybe a bit - but it's a really important lesson to learn.)

Year 4 Run The Marathon

What an awesome marathon!

...and what a great run from Uganda's Stephen Kiprotich! Inspirational!

And in Year 4 we were inspired to have a go and see how we would go. 

How far could we run (as a team) in 2 hours, 8 minutes and 1 second?

The Challenge

We have 98 kids in Year 4. If they all ran around the quad for about 1.30 minute we would do the equivalent of the marathon time run by Kiprotich.

So, we got organised and started the run, which went from 8.40am to 10.48am. 

The Results

• the kids ran for 2 hours, 8 minutes and 1 second 
• ran a total of 326 laps

And how did that compare to the Olympic runners?

• we measured our lap of the quad to be 76m
• so our total distance was 326 x 76 = 24 776m - a bit over half a marathon!
• and our speed was 24.776km divided by 128 minutes multiplied by 60 minutes = 11.61375km/h

And then we calculated how fast Steve Kiprotich ran:

• 42.195km divided by 128 minutes multiplied by 60 minutes = 19.76953125km/h

So our Year 4 team had done a great job, run over half a marathon and done it in a speed that made us really appreciate how fast those guys in London were running!

Seriously, how much of this did the kids do?

Seriously? Well, they did all the running.

And we led them through the calculations. A few would have got there with minimal help but it was interesting to explain how to do the calculations.

And I think one or two got the idea of the relationship between time, distance and speed.

And we all had some fun!

Sally Pearson and the 100m Hurdles Gold Medal

What are those numbers?

To celebrate Sally Pearson’s great win in the 100m hurdles today, the teachers planned a special welcome. When the kids came in to the building this morning we had the following numbers written on the white board:

100

 85

105

1235

868

13

10

 Sally - an Australian hero!

“All these numbers relate to the 100m hurdles,” we told the kids

No other information was provided. Time for the kids to start thinking.

Ah! Now some lights start flicking on.

“100 is the 100m for the race!”

“And 1235 is the time Sally ran – 12.35 seconds!”

"And there's 10 hurdles in the race."

After some prompting we got to the last numbers:

13m from the start line to the first hurdle.

Each hurdle is 8.5m apart.

It's 10.5m from the last hurdle to the finish line.

And the hurdles are 83.8cm high. (Why the crazy height? Well, it used to be 2' 9" in the imperial system)

...and in this discussion we covered such mathematical concepts as:

- decimal points

- need to use correct units of measurement

- fractions

- addition of decimals

- length, time and speed

A great conversation to start the day!

So we got out some till paper (long rolls of paper from an old cash register) and held it at 83.8cm so the kids could have a go at a hurdle.

Learning an Old Game - Fly!

As a bit of fun, we learnt a an old game that I used to play at school called "Fly".

Here's the rules:

• You have seven sticks and you place them about a foot apart. 
• Then all the kids stand in a line and run through putting one foot in between each stick. 
• The last person in the line is the 'Fly", they run through and then at the last stick they jump as far as they like, then they pick a stick to be moved to the spot where they landed. 
• Eventually the spacings get bigger and bigger and harder and harder. A person gets out when they put more than one foot in between two sticks (ie they don't make the jump) or miss one. 
• When 'Fly' gets out, the second last jumper becomes the new 'Fly'

Maths and the Year 6 Exhibition

Year 6 Exhibition - what's that?!

Our school operates under the International Baccalaureate Primary Years Programme (PYP). A key part of this programme is the Year 6 Exhibition, a culminating activity designed to demonstrate the awareness and understanding of the students of what they have learnt over their time in the PYP.

It involves group work.

It elicits deeper learning.

It is a transdisciplinary inquiry.

So I'm keen to see how our Year 6 students are going to use their maths skills and knowledge to explore this year's concept of "Conflict".

The Good News - I am a Mentor!

Each collaborative group finds or is assigned a mentor - someone who can help the group find their direction, clarify their questions and distill their message.

Fortunately for the group that I will be mentoring, I will have a special interest in how they explore the concept of "Conflict".

And, of course, how they use their maths skills as part of this inquiry.

The Bad News - I am a Mentor!

So look out team - you have been warned! I'm looking for something more than a column graph and a table of numbers. I'm hoping to see some creative and insightful uses of maths skills to underpin this significant inquiry into a big, big concept.

I'll let you know how the team and I get along as the journey unfolds...

Maths and the 100m Sprint

Year 4 Was pumped Up About the 100m

- Usain Bolt, Asafa Powell, Yohan Blake, Justin Gatlin. What a race!

....so we thought we'd do some inquiry about the race and see what mathematical concepts we could uncover.

We Headed for the Oval

On the 100m track, we spaced students out at 10m intervals holding signs saying 10m, 20m, 30m, etc.

At the first whistle, children started running to see how far they could get in 9.63 seconds.  When the clock got to 9.63 seconds, I blew the whistle again and the runners stopped, checking how far they had got and looking to see how far Usain Bolt had got in the same time.

Our Responses

So what did the kids have to say? And what mathematical concepts could they uncover?

"I ran 55m. That's 45m less than Usain Bolt."

"I almost got halfway."

"I got 64m before 9.63 seconds was up. I ran 6.6 m/sec. Usain Bolt ran 10.38 m/sec."

"I got between 60m and 65m."

"Usain Bolt would be twice as fast as me. In the Olympics I wouldn't even be second last!"

"I ran approximately 55m whuile Usain Bolt would have run 100m. 100m divided by 9.63 seconds is about 10.38.  So Usain Bolt ran 10.38 metres every second. If I divide the metres by 1000 you get 0.01038 km. Then you multiply by 3600 seconds to get km per hour - that is about 37 km per hour. That was his average speed."

....and my favourite:

"I look down the track and murmur to myself - Usain Bolt is really fast!"