Thursday, 31 October 2013

How Big Is Your Classroom - Part 2

So we spent some time collecting data from the P-4 classrooms. This is a bit of a journey thanks to the way our school is set up. P-4 are over one the western boundary of the school - about 250m from Year 5 + 6.

Data Collecting

When we got back we pooled out data. Here is what we found:

Room              Side 1              Side 2               Area

PK                   9.82m            8.51m             8356.82m2
PK                  not measured           
MH                  8.95m             9.25m             82.7875m2
KM                  not measured
1JH                  9.63m             8.2m               78.963m2
1RB                 10.5m             8.0m               84m2
2PM                10.49m           8.5m              
2AH                 9.85                8.0m               78.88m2
3BR                 32FEET          27FEET         
3EB                 8.0m               10.4m             83.20m2
3TM                10.64m           8.1m               86.9288m2
3HB                 8.14m             9.02                73.4228m2
4RB                 8.0m               9.7m               77.6m2
4CS                 10.58              7.75m             81.995m2
4JG                  8.94m             8.9m               79.566m2

Some interesting points:

  • looks like there was trouble with decimal point in one of the PK classrooms - unless their room is actually the size of a football field.
  • One of the Year 4 rooms was missed out. Not sure why.
  • The group measuring 3BR measured in feet and inches. One of them said, "So is there like 30cm in 1 foot so I could try to figure it out that way?" The teacher prompted them to just turn the tape over and use the metric scale that was on the other side.
  • Lots of kids struggled with converting from metres to cms - need to go over that one again.
  • And also the need to take about square centimetres when discussing area.
  • We had a good talk about why the rooms are not all exactly the same. What things were done differently that might account for diversity of responses. And if we all got different results, what statements can we make about this data? Is it fair to say that all the rooms are about 80 square metres? And what room should Mr Black have?

So what?

In a recent chat on #pstchat, a weekly time on Tuesday evenings at 7.30pm EST, I was discussing listening as an assessment tool in maths. An interesting question came up - do the parents think that this kind of assessment is "soft"? Does sitting around listening to kids talk about their actions constitute rigorous assessment? Is it as valid as a pen and paper test?

Here's my response:

  1. If I listen to what the kids are saying as they explain how the went about solving a problem, I will learn more than I would if I just looked at written responses on a page.
  2. By listening, and discretely probing with questions, I can get the students to think deeper than they will if they are just writing answers in a box.
  3. By giving the students the chance to talk about what they have done and to explain the process, I am letting them develop a deeper understanding of the concept that they are engaged with.
  4. There are many students who are disenfranchised by poor literacy skills - their opportunities to progress in Maths are limited because they cannot read or write effectively. These children need to communicate their understanding through talking.
  5. By talking with the whole class, children can gain a broader understanding of the concept by hearing what other students have done.
  6. From this activity that we have engaged in this week, I have been able to modify my teaching (I won't be using tape measures with imperial measurements again), reinforce skills that students were struggling with and clarify concepts that were not fully understood.
  7. I also have a good idea of who can do what - I have notes on individual children and what they said and did. This is qualitative assessment.
So many positives.

And of course we had some fun.

Wednesday, 30 October 2013

How Big is Your Classroom?

This week's inquiry was taking us into the realm of space - we were going to look at how big a classroom is.

The Provocation

I was going to make an i-Movie as a provocation. It was going to be news report featuring my good friend Mr Black (@CpaitanoAmazing). Apparently, Mr Black had decided that he deserved the biggest classroom in the school.

Our challenge was to find the biggest classroom for him.

(Sadly, time ran out and I didn't get the movie made in time.)

So we speculated, which classroom is the biggest?

What do you mean by "biggest"?

There was some discussion about this.

Did we mean greatest volume, largest area, longest perimeter? Did we mean the one with the most desks? The one with the most useable space? Is the art room a classroom? Is the music room?

We decided, by consensus, that we were going to look at the area of all rooms that have a class allocated to it permanently, so not the art or music rooms. And we would measure the area because I didn't want kids to be climbing up on desks with tape measures to measure the height of the walls (yes - I know there are other ways but try to convince a 12 year old boy that he doesn't need to climb on top of furniture.)

Here is a summary of our discussion.

A few interesting ideas:

  • Do we need to measure every room or can we assume that some rooms will be the same size as each other since they are built on top of each other and use the same external walls?
  • Could be seal the room with silicone and then fill it with water??!! What a great idea...
  • Can we get hold of the blueprints for the building and look at them? They probably already have measurements on them.
  • And what about the furniture? Does that need to be subtracted from the room space?

Revision of what we know

Previously we had found that if you multiply the two sides of a rectangle together, you get the area.

Excellent news...but what if the room isn't a perfect rectangle? What if it looks like this....

"Then it's impossible to find the area!" said one student.

Really? That idea needs some more thinking.

Anyway, we started small and broke into groups to measure just the Year 5 and 6 rooms. Each group did one room. There are 8 rooms, each room is the mirror image of the one next to it and the same as the one above (or below) it. Here's a picture:

And when they came back we wrote up the results for the different rooms so that we could talk about our data.

Here are the sizes of each room as measured by each group:

Hmm....there's a bit of a difference between the results. I was expecting some variation but this is a good indicator to me that some groups are not using the same methodology as the rest of us.

A great activity - easy for me to see who understands the concept and who doesn't, gets the kids outside doing some maths and also a productive application of multiplication skills.

Tomorrow we will venture further afield and visit the P-4 rooms.

I wonder where Mr Black will end up?

Monday, 21 October 2013


To celebrate the 50 000th viewing of this blog, I thought I might post a few of the stats...

Date started:  2nd April 2012 

Days since start - 566

Average hits per day - 88.3

Number of posts: 138

Average hits per post: 362.3

Number of countries who have visited: 123

Biggest month: June 2013 (4912 views)

But none of this would have been possible without...

Richard Black - @capitanoamazing who challenged me to get going and keep going

Tina Landos - inspirational colleague and PYP legend

Paul Southwell - @PaulSouthwell my boss who lets me do some crazy things in the name of learning

Dan Meyer - @ddmeyer an man who understands the importance of making it real to engage the kids

Craig Dwyer (@DwyerTeacher), Jason Graham (@jasongraham99) and Steve Box (@wholeboxndice) - some great PYP teachers that I've met through twitter and the amazing #pypchat

Stephanie Adan - @stephyadan a young teacher with a huge future ahead of her

Sandra Ferrington - my incredible wife

and finally...

YOU - for reading these posts and finding something you can use in your classrooms.

Looking forward to another 50 000 visits!

Thursday, 17 October 2013

Order of Oops-erations

We were going back over a few concepts that we thought it would be good to consolidate before the end of the school year and the kids move up to Year 7 and High School.

So we wanted to have a look at the order of operations - it's going to be an important understanding to have as the kids progress into the higher years.

Intro to the Lesson

I wanted to start with some basic skills review so I put up 20 questions on the board. Here they are:

Addition questions:

1 + 1 =

1 + 2 = 

1 + 2 + 1 = 

Subtraction questions

1 - 1 =

1 - 2 =

4 - 3 - 2 - 1 =

Combo of both

1 + 2 - 3 + 4 =

4 + 1 + 2 - 3 =

2 - 3 + 1 + 4 =

4 - 3 + 1 + 2 =

Multiplication questions

1 x 1 =

1 x 2 =

1 x 5 =

5 x 1 =

1 x 5 x 1 x 5 =

Division and multiplication questions

20 ÷ 5 =

20 ÷ 5 x 4 =

20 ÷ 4 x 5 =

20 ÷ 2 ÷ 2 x 5 =

20 ÷ 2 x 5 ÷ 2 = 

I wanted to know, "Why do some of these questions have the same answers?" I was keen to explore the Associative Law and how it can be useful in the order of operations. I also wanted to see if the kids could identify how it was all related. And what problems they might encounter if they didn't follow the correct order of operations.

Hey look! They've got the same answer!

My beautiful scrawl during the excited conversation about the Associative Law


I've seen all these variations of mnemonics to use to remember the order of operations. Lots of our kids had learned BIDMAS.

BIG MISCONCEPTION for our students – they are familiar with the terminology BIDMAS but 90% of the students believed that Division comes before Multiplication and that Addition comes before Subtraction.


I think this is because they have only seen the acronym written horizontally.

So I decided to show it to them vertically:

B – brackets and other forms of parentheses
I - indices
DM – division and multiplication
AS – addition and subtraction

Hopefully this helped them see that division and multiplication are equal, as are addition and subtraction.

How many types of brackets are there?

I wasn't sure how familiar the kids were with brackets and parentheses so I asked the question.

One student replied, "Well on a computer you have the round ones, the square ones and the wiggly ones."

Good thinking.

We ended with a game of BIDMAS Bingo - and then had an argument about how 32  does not equal 6.