Monday, 24 June 2013

Rainy Day Maths

It was raining at school this morning so I let the kids into the room to stay warm and dry - what a nice teacher!

Some kids sat in front of the heater and chatted.

Some kids got out a game of monopoly.

And some kids got onto the white board....and started doing maths!




One decided to calculate the value of 10! - that's 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10.

Here's his working:







And another chose to calculate 310. 


Here's the working for that one:







Think we got a bit carried away with that one but the thought was there


What a great way to spend 10 minutes on a rainy morning!








Sunday, 23 June 2013

Sugar in Your Cereal

I have a pracky working with me and the class for 8 weeks. She's 3rd year and has some really good ideas that we have been trying out.

One of the things that she has provoked us to think about is sugar. We were all amazed at some of the foods that contain added sugar and the vast quantities involved.

She also found a youtube clip for us to look at about the sugar content found in a certain fast food brand. (Click here to find out more...)



Maths for Breakfast


Which got us to thinking about other foods. Breakfast cereals are also very high in sugar, a fact that we confirmed when we researched inside our pantry cupboards for home learning.

To make it visual, we decided to spoon out the sugar content of some popular cereal brands and measure them on the balance scales.

I didn't really want to go and buy sugar for this purpose, so we used sand from the sandpit - it probably has a different molecular weight and density so it was never going to be a perfect substitute for sugar, and yes it tastes different too.

But it served as a satisfactory sugar substitute for our purposes.









































Data summarised from http://www.sweetpoison.com.au/atp.pdf 


Using data from David Gillespie's website "Sweet Poison", the students completed measurements by converting teaspoons of sugar (or sand) to grams.







Starting with a cup of sand and a spoon





Carefully measure the sand out.
Lots of interesting discussion about spoonfuls.
Should it be level or heaped?
Do all people have the same sized spoon?
Is a spoon a good measure of mass?





Balance out the sugar with the weights.


So what?

It was:

- really visual

- really hands-on

-really fun

And we got a bit of an idea as to what a gram is like, and 5 grams, and 10 grams....











Saturday, 22 June 2013

The Convertameter


I had a good idea the other day. 

It's quite simple. 

I call it "The Convertameter".

It looks like this.






That's it. A simple piece of paper with a few words on each side and a dot.

But what can this little baby do?

Let me show you.




You start with a line of zeros and some digits 1-9.

Place the digits to indicate what the value is you want to convert - in this case 1250 grams.



Simply flip The Convertameter over and hey presto!

We have the answer in kilograms.

I gave this little treasure to the kids a few days ago.

They didn't believe I'd thought of it.

"You must have got it off Google!" they said.

Well, no I didn't.

Anyway, we used it for 10 minutes to convert a few grams to kilograms and back again. Here's a few other things that the kids had to say:

This is becoming too easy.

You just move the decimal point three spots over.

When you want to convert grams to kilograms you move the decimal point three spaces left.

If you want to convert kilograms to grams you need to times the kilograms by 1000.

There’s three zeros in a thousand which is how many 1kg is.

1.654 – on this one you just take off the dot.

And with a bit of prompting, they soon realised 
the beauty of The Convertameter.

Well, you could use this for meters and millimeters

Or litres and millilitres

Or kilograms and tonnes

Or.....







I retain all rights to this idea, the name "Convertameter" and the design BUT if you want to use it in your classroom, you can as long as it is not for any financial gain, profit or benefit. Just for educational purposes in your own class okay?








Thursday, 20 June 2013

Report Wordle

I've just finished writing the half yearly reports for my class.

It's always interesting to reflect back on what I have written. Here is a Wordle I created of the comments that I wrote:



Interesting to see what words I use a lot - "good" seems to feature pretty frequently, as do "knowledge", "work" and "understanding".

I'm pretty happy to see words like "learning", "enjoys", "discussions" and "inquiry" up there as well.

A feature of our reports is the student comment. Each student gets to write their own reflection on the front cover, giving their own perspective on their learning over the semester.

I did a Wordle of their responses as well:






I'm really glad that "enjoyed" is the most used word in their comments. "Maths" is in there - along with "fractions", "dance", "art" and "inquiry". All positive signs.

Give it a go. See what your kids come up with.





Mass - Tuning In

We have started a new inquiry - this time we are looking at "mass".

I am keen to avoid the confusion between "weight" and "mass" and as a result have deliberately steered all conversation away from this point.


In our initial discussions, I asked the kids what they thought mass was.


They had lots of good ideas, all worth exploring:



It's a measurement of objects.

All things have it.

It is to do with the space a shape takes up.

Bigger things have bigger mass.

You can measure it and then compare things.

You measure it with scales and things.



All these were good but a bit general. We needed to get more specific and to get our hands dirty. Time for some inquiry...


The Task


We got a range of different balls out of the PE store room as well as a few from home. The job was to arrange them in order according to their mass. Sadly, the teachers had taken away all the weights so the kids had to use the balance scales to compare the balls against each other.

We chose to use a tennis ball, a golf ball, a marble, a ping pong ball, a volleyball, an AFL ball, a bocce ball, a softball and a cricket ball. I was keen to get some examples where the order of size did equate with the order of mass.



Finding Out/Sorting Out


So, we got the gear out and broke up into small groups.

Lots of talk. Lots of conversation. Lots of, "Try this one next, I think it's heavier than that one."




The yellow ball is an AFL ball, for those out there who were puzzled. 
AFL is a sport from Australia, which over the last 100 years has been 
dominated by the mighty St Kilda Football Club.


And pretty quickly we got to the realisation that it was unnecessary to compare each ball against all the others. Once you had organised 4 or 5 of them, you could start near the middle of the line each time you selected a new ball. If it was lighter, you could compare it to the ones at the lighter end. If it was heavier, you went the other way. 


What would be the least number of comparisons needed to add a new ball to the completed line?






The final result - an interesting arrangement



Having got consensus on the line, the kids were then asked to  make an estimate of the mass of each ball. To assist this process, they were told that the golf ball weighed 35g and the bocce ball weighed 4kg - this provided a frame of reference for the estimates.



Going Further


Finally, many of the students started to play with other ideas. One student came up with a suggestion: 


"I want to see how many marbles equal one ping pong ball."


A few minutes later this was modified.


"I want to see how many ping pong balls equal one marble."


Here's the result:








And so began the inquiry into mass.




Taking Action


The next morning. one student came into class and said, "Last night I was talking to my big sister about mass. She told me that mass is different from weight. If you were on the moon..."


Ah! Home Learning at its very best!


(see http://4thgradebigquestions.blogspot.com.au by Capitano Amazing for more information about our school's journey along the road to Home Learning)

















Monday, 17 June 2013

Fractions Assessment - Part 2

So, we talked yesterday about how I had done some assessment of our learning about fractions. I posted some student comments on a few diagrams that had inaccuracies and problems. The responses were very illuminating.

Anyway, the assessment continued with a few pretty standard questions sorting out some knowledge about adding and subtracting fractions - nothing ground breaking. 

The last question is what I want to share. It asked students to complete some sentence starters. 

Here are a few things they said.



Complete these sentences...


a) Fractions are....

a way of representing something that is not quite a whole

pieces of things that are divided up

a way of showing non-integers

a part/portion/piece of a whole

dividing between the denominator and the numerator



b) When you add two fractions, you have to....

add the numerators together if they have the same denominator

GUESS

add the numerators together unless the denominator is different then you have to x it by something else to make it the same

I don't know exactly what to do but I suggest you draw a pizza

If they have a common denominator then you  merely add up the top numbers but if they don't you can draw a picture or find a common denominator


c) You use fractions when you....

divide up things evenly or to represent something that is not whole

are cooking. e.g. pour 2/3 cup of cocoa powder in the cake mixture

cut up fruit

are trying to divide things into different parts

can't make a whole

cut a pizza, build a building, pour some milk

have a pizza and your friend says I want 3/4 you have to work out that you don't get much


There were lots of other responses - too numerous to mention here - but by being able to hear what they all said gave me a real insight into their thinking.

I am in a  position now to identify who needs a bit more support, who has really got it and who is ready for the next challenge.

In so many ways, a successful assessment.












Sunday, 16 June 2013

Fractions Assessment

Well, we got to the point where we were ready to assess our work on Fractions, to see what we had learnt.

We use a variety of assessment tools, including pencil and paper.

I was interested to see if the kids could explain why some understandings of fractions might be inconsistent, fallacious or even straight-out wrong. So I gave them a few non-examples and asked them to explain what they thought was wrong with the diagram.

Here's some of the responses.


Task - Can you explain what is wrong with each of these examples?


Example 1




The quarters are not equal.

?

The fractions aren't shaded fully.

Not equal = no fractions

All of the fractions are different sizes so they're not fractions.

The four sections are not divided equal. It is important for each section to be equal to make the fractions true.

The bottom and the top of the circle are different areas from the middle.

Bad colouring.

This is wrong because the are of each shape is different. If it is going to be even then it should be cut like a pizza.

Perfect

The quarters are not coloured in properly.








Example 2






 One is bigger than the rest.

Just like the first example this fraction is uneven. Each of the thirds is its own size and they are not equal.

The middle part is bigger than both the other parts making it unequal.

All the squares aren't measured to the correct measurement so they're everywhere.

The lines are slightly off so it's not equal.

The area is not the same as the other parts.

Using grids to shade fractions makes it look like there are more than 3 sections. The thirds are not equal!


Example 3



The blacks are scattered.

It's wrong because 1/4 isn't shaded. 6 squares are supposed to be shaded.

The quarters are not accurate.

The fractions are split up all over the place.

Not enough fractions are shaded to get the right fraction. The fraction would be 1/6.

It's not showing 1/4 of the rectangle.

A quarter is not shaded in and it would make more sense to put the shaded parts in line.

It is not a quarter of 24.

Not enough squares are coloured in and it is not very easy to understand.

Well, unlike the other example, this one is even as in shape and the dividing up of the box. But it is false. It says it is 1/4 of this box but it is wrong. It would be 1/6 of this box.



Reflection


I have not included every response here - only a select few of those that were interesting for one reason or another. There were many children who got the idea for each picture but it was not important to include all the similar answers.

So, it is interesting to see the things that act as distractors for the kids and get them off topic.

Colouring and shading seem to be pretty significant for some kids. It is the thing they focus on first of all. 

Also, many seemed to want the shaded sections to be grouped together - but instead maybe they should have been exposed to more examples where they were not.

The diagrams themselves need to be unambiguous. The picture is meant to help the kids see the idea - not confuse them even further.

Lots for this teacher to think about. Some good responses but also some areas that still need clarification.

We will revisit this topic again later in the year...