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.

Discussion

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?

Maths in the Year 6 Exhibition 2013 - Part 1

What a week - I am exhausted! I imagine the kids are too after an amazing PYP Exhibition. This is a culminating activity  for students who reach the end of the Primary Years Programme where they get to develop their own inquiry into an area of interest. 

Being transdisciplinary in nature, I am always keen to see how the kids will use maths in their Exhibition presentations. How will they display data? How will they analyse data? What creative ways will they find to use maths to make sense of what they are doing?

It will probably take a few posts to get all the information up about the different inquiries the students engaged in.

Here's an example of how one group inquired into the use of transport by people coming into our school each morning...

Displaying Data

The "Transport" group decided to collect some data about the makes of cars that come into our school each morning and also how many people were in each car. So they got to school  about 45 minutes early and set themselves up near the front entrance.

When they collated their data they decided to display it as a picture graph because the audience for exhibition was going to include a wide age range, from pre-school to pensioners. 

They made a second graph based on the fuel consumption of the most popular cars to come into the school each morning. At this point they realised that their initial data collection only included the make of car, not the model as well. Consequently, they decided they would calculate what the fuel consumption for an "average" Toyota etc would be by getting the fuel consumption of all models of each make of car and finding the mean. 

They also distributed a survey via Survey Monkey to all the staff at the school to see how they commute. The first graph shows that the vast majority drive cars while only a few walk, ride bikes or catch buses. 

The second graph asked how many people came in the car with you. This question was a bit ambiguous as there was no option for zero - did it include the driver or not? Anyway, the most overwhelming response was "1" - which might mean none or one.

The final graph asked for the age of the car that was driven. They asked this question to explore the idea that older cars produce more pollution. It also showed that not many teachers have new cars, in fact many have cars that are 10 years old or older.

Data Analysis

The data for this group was well displayed and easy to read. The really exciting part was reading their analysis of what they had learnt.

Here are a few of their comment:

Well, I'm not buying a Lexus then - I think I'll get a Land Rover.

Or...if you can afford a Lexus, do you worry about the cost of petrol?

Australia is very big on 4x4 cars. Interesting to see some data.

Can you get this from the data or would you need to ask a few more questions?

This one makes me ask a few questions - where are they driving? City? Country? How fast are they going? Does it matter? What type of Toyota do they have? How big is the bucket?

Like all good learning, it made me want to ask more questions. Hopefully, the "Transport" group feel the same.

The Human Graph

As our culminating activity for a Week of Maths and to celebrate National Maths Day, the whole school got together to create a human graph and to answer the age-old question...

What Fruit Did You Have For Breakfast?

Very sneakily, this combined maths (data collection and representation) with a healthy diet.

Here are a few pics of what it all looked like:

Getting ourselves organised - yes, it took a bit of time. 560 kids to organise.

That's the "apple" line disappearing into the distance - very popular with the kids. "Bananas" is the next longest and the one you can see further across coming in third place is "strawberries" - they're very cheap at the moment.

Yep, that's the "strawberries" group with "apples" and "bananas" on the far left of the picture.

I got some Year 6 kids to design the data categories. They chose:

1. Apple
2. Avocado
3. Banana
4. Fruit Salad 
5. Grapes
6. Kiwi fruit
7. Mandarin
8. Orange
9. Peach
10. Pear
11. Rockmelon
12. Strawberry
13. Tomato
14. Watermelon 
15. Other
16. None

Results

 1. Apple was the most popular fruit for breakfast, followed by banana and then strawberry.

2. Only 25 children had no fruit for breakfast.

3. Only 1 person had tomato for breakfast and 1 had avocado. These were the two smallest categories.

4. There was a protest that bananas are a herb. 

5. There was an interesting selection of fruits in the "Other" category  - star fruit, cherries, pineapple, etc

6. Everyone had some fun.

So what?

Over the week, have we achieved anything?

I think so.

• We have focused the kids' attention on data collection. 
• We have got them to think about some of the issues behind working with data.
• We have constructed graphs.
• We have made statements based on information represented in graphs.
• We have made some sound generalisations about how to handle data.
• We have participated in an activity across the whole school P-6.
• We have had some fun.

Can't wait till next year...

More Data Handling

Day 3 of our Week of Maths and we got to look a bit more closely at some data that compared the average intake of various food groups in four countries - Australia, Italy, China and Ecuador.

The data was presented on the AAMT website in graphs produced on an Excel spreadsheet. It looked a bit like this:

You could enter a value from 1-4 and the data for each country would appear.







The students were asked to get the data from one category and compare it across the four countries.

Comparison of grain consumption as a percentage of total

Comparison of drink consumption as a percentage of total.

Do they really not drink anything in Ecuador?

Comparison of average meat consumption in $US per week.

Naturally, once we started playing with the data, the questions started flowing and we were able to make some important generalisations:


1. Garbage in, garbage out


You can only work with the data that you have. If you collect poor quality data, you can't improve it by manipulating it. So, if the data provided says Ecuador has no expenditure for drinks, does that mean:
a) they don't drink anything?
b) they don't pay for anything they drink?
c) the data hasn't been collected properly?



2. Your scale needs needs to have all the numbers up to your biggest quantity


The scale need to be cover the range from your smallest value to (at least) your largest value. It also needs the have graduations that are useful, that make the data accessible and that inform the reader.


3. Say the exact amount for each category

When dealing with data, it is important to be as accurate as possible. It was difficult for students to read exact money values off the graph provided. They resorted to estimating which meant that they ended up with different numbers. This made it difficult for them to compare their information.


4. Spreadsheets can give an exact number - roll overs

At this point, one of the bright young things discovered that if you hold the cursor over the individual data column, the exact dollar amount was shown. Now, that's something you can't do with a piece of paper.


5. Zero is data and we need to show all data

And so the conversation came around to the question of "zero". Ecuador had 0 for several categories of data. Students began to realise that if we leave out zero it will change the meaning of the graph. Zero values need to be included in data sets to show that the question was asked, the measure was taken, the observation was made but the result was zero.

A Week of Maths at Radford

This week is National Science Week in Australia. The AAMT (Australian Association of Maths Teachers) has prepared a range of activities on their website for school to look at on National Mathematics Day (Friday this week). As this is also the International Year of Statistics, the activities are based on data and statistics.

Here at Radford, we have decided to make this a focus for our week. I have drawn on the AAMT resources and developed a set of Home Learning activities for all classes (P-2, 3-4, 5,6) to get some conversation going. 

Each day there is a "take home" activity looking at food resources around the world - it's transdisciplinary and international, two elements of PYP learning. 

Here's a sample of the Year 5-6 activities:

On Friday we are planning a "human graph" on the oval - based on the answer to the question "What fruit did you have for breakfast today?"

And while there is very little in the way of explicit number skills being drilled for "home learning" this week, there is lots and lots of thinking and talking about how we handle data.

Inquiry into Graphs and Data

Well, first week back from "The World Tour of Maths" and Tina the Awesome from next door had our classes sorted for the week. We were going to launch into an inquiry into graphs and data. Here's how it looked - you may see some references to Australian Curriculum here:

Inquiry - How I am going to organise this data?

An inquiry into - how we can collect, organise, represent and draw conclusions from data.

Skills - Addition; Subtraction; Collection of Data; Graphs

Learning Intention - Collect and organise data and draw conclusions. To understand data can be represented in different ways and some ways are more appropriate than others.

Success Criteria - 

• Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)
• Interpret and compare a range of data displays, insulting side-by-side graphs for two categorical variables (ACMSP147)

Teacher Questions - 

• What is the percentage of people in Australia are aged 0-14 years?
• What is the percentage of people aged 0-14 years in 9 other countries?
• How do these countries compare with Australia?

Student Questions - 

Children generated 3 questions of their own.

My plan - 

Children devised a plan. How were they going to get answers to these questions? What strategies would they use? How would they represent their information?

Basic equipment I will need - 

Students made a short list of equipment they were going to use.

Running the Inquiry

So, we launched into the inquiry. 

Our chosen data source was the World Fact Book on the CIA website - lots of data on lots of countries, and population data had age categories including 0-14 years. Convenient huh? You would almost think Tina had organised this...

Anyway, lots of discussion, lots of planning, lots of collaboration and lots of fun.

Here are a few work samples from the kids:

We started by collecting data and putting it into a table

A bar graph  - courtesy of Microsoft Excel

A simple column graph - the simple things in life are often the best

A line graph - this generated lots of discussion. Is it the right type of graph for this data?

A pie graph - took ages to work it out but looks very busy.

Can too much information be a bad thing?

Reflection - What did the kids say?

All good inquiries allow space for reflection. We had a few questions as prompts to get the kids to write about some of their experiences - the choices and decisions they made. Here are a few comments from them: 


Which graph was the best type to represent our data?

"I think maybe a bar graph would have been the best choice because you can accurately see the results of the data."

"I found that a column graph was the best to represent my data as it was easy to read and simple to make and information was clear to represent. Here's why: the height of the columns are identifiable and variable, while the vital points on the side containing numbers and/or percentages as a part of information extending knowledge of the topic."



Why is one type of graph better than another?

"All types are good in their own way and it depends on what data you have. Different graphs are useful for different things."



What would you do differently next time?

"I drew a bar graph. This was a good decision because people will understand and interpret my data better. Next time I would do nothing different. I am proud of my decision and I will stick with it."

"I drew a pie chart. This was probably not a good choice because there was too much data to be shown and it would not give the person reading it a fast, visual impact. Next time I would draw a bar or column graph because it would be easier to compare the data and it would be clear and quick to read."

"The column graph was much clearer to read than a pie or line graph in the situation we used it but it depends on what sort of information you need to show."

"The graph I represented my data with was a line graph. This was not a very good choice because line graphs are supposed to show results over time. Next time I would use a bar graph because it can clearly show the data."

So what?

Well, you heard it from the kids. They know that different graphs have different purposes. They know that their decisions will determine how effectively they communicate their data. And it all links back to the learning intention.

Great stuff.

Can't wait for next week...