Wednesday, 6 May 2015

The Typical Student in Year 2

We are currently inquiring into "Who We Are". It is a opportunity to learn a little bit more about life and our central idea is:

Birth, growth and death are part of 
the natural cycle of living things.

To find out about ourselves, we decided to collect some data. We wanted to know what things we had in common and what our differences were. Some of our questions were about physical features, some about our personal preferences.

Here are our 5 questions:

1. Are you a boy or a girl?
2. How old are you?
3. What sport House are you in?
4. What is your favourite colour?
5. What is your favourite school subject?

All students in Year 2 were surveyed. Here are our results:

Now that we had some data, it was time to start playing with it. 

Our "Typical" Year 2 Student

We found that we had one student who was in the highest scoring category for each question.

She was a girl, currently aged 7, in Acacia, liked blue and her favourite subject was PE!

We had found a typical student - she was very excited!

Our "Atypical" Student

We also found we had a student who was in none of the highest scoring categories.

He was a boy, aged 8, in Kurrajong, liked red and loved doing maths!

An atypical student - he was equally excited.

We showed our data about ourselves…

…compared to the typical student…

…and then recorded this in a table and made a statement based on our data.


Much discussion followed once we started playing with the data. Lots of questions started to come from the kids.

Boys could never be the "typical" student in our data set because they were eliminated by the first question. Similarly, girls could never be the "atypical" student, since they would always have their sex in common with our typical student even if they disagreed on everything else.

Interestingly, our "atypical" student has a twin brother but they could be differentiated by their favourite colour - the other twin liked the colour blue - but all their other answers were the same.

We ended up producing a large graph showing how many of the responses each student had in common with our "typical" student.

An interesting distribution and one that brought on more questions. Prior to representing the data in this way, we asked the students to predict which group they thought would be the largest. Most opted for 2 or 3 things in common, agreeing that it might be expected for people have a few things similar but that there was plenty of option for differences.

The kids were engaged, focused and ready to take it further.

I wonder what they will come back with tomorrow once they go home and reflect on what they have done?

Tuesday, 5 May 2015

Friends of 10 - Is there another way?

One of the key things we need to nail early in Year 2 is "Friends of 10". 

0 + 10 = 10
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
      4 + 6 = 10 etc

Hopefully most of the kids have this concept by the time they get to us - but there will always be a group of recalcitrants. 

For those who have mastered this idea, they will get frustrated if they feel they are spinning their wheels while they wait for the rest to go through the process each day of trying to recall these number combinations.

And this is indeed what happened.

As we were going through the Friends of 10 number pairs, a couple of my students had them written down and were back to me in less than a minute. Several other students were still rolling around on the floor looking for pencils.

So, using one of my favourite questions, I asked them:

"Is there another way?"

This puzzled them.

"What do you mean?"

"Well, I can see you've done the obvious ones: 1+9, 2+8 etc. Is there another way?"

They hadn't actually expected to have to think about Friends of 10. They thought they knew them all. This was unfamiliar territory.

Then a moment of inspiration!

"Oh! Do you mean with negative numbers!!??"

"You show me," I replied, annoyingly.

And here's what they came back with:

There's a nice pattern kids!

"That's great!" I said. "Can you show me another way?"

"Another way?" they asked.

More thinking required.

"Oh! Do you mean with Roman numerals??!!"

"You show me," I replied, annoyingly again.

And here's what they came back with:

Nice work! Just check the spelling...

It was getting to the point where we needed to move on. I suggested that it would be good to see how many other ways they could show Friends of 10, perhaps as a Home Learning activity.

The next day, I was presented with these ideas:

1. Building on the Roman numeral idea, here are a few Friends of 10 using number systems from other cultures.

2. Looking at fractions and decimals

 3. Using more than pairs, thinking outside the box.

 4. Graphic representation - the Friends of 10 Rainbow.

 5. Going further - some students decided to explore Friends of 20 to see what happens.

Some examples of Friends of 20, nicely typed but a bit random 
which makes it hard to see any patterns.

Friends of 20 done as "buddy pairs": 12 + 8 and 8 + 12

Friends of 20 - an incomplete list but could see where it was going. Do I really need to write them all out if I can see that it will repeat itself once I get past 10???

 Friends of 20 - the complete list

So - I was a bit surprised. I thought, as did several of the students, that this Friends of 10 business might be pretty simple. Who would have thought there could be so many options to explore?

Hand it over to the kids - they will think of things that will never occur to you.

And have some fun.