Introduction to stats in Y9

Three big ideas we want to get across to students at this stage are

1. Distributions describe variability in data
2. Bivariate distributions describe patterns and trends between two variables
3. Statistics can be used to summarise the features of a group 

We want to develop students statistical content knowledge in an "experiential active learning environment that focuses on the problem solving process and makes clear connections between statistical reasoning and notions of probability" (SET p.25).

The problem solving process is the PPDAC cycle where we

• Formulate statistical questions
• Design strategy for data collection
• Collect data
• Explore analyse and summarise the data
• Draw conclusions from the data

Statistical software should be used to aid in data analysis and interpretation

NZGrapher: dynamic data analysis https://www.jake4maths.com/grapher/

Data Viewer on census at School http://new.censusatschool.org.nz/explore/
It is not too late to take part in the census


Examples of quick data 

1. Use post-its or paper squares and create data cards &then make graphs from them on the board (had a photo but can't find it :-()


Make sure  "data cards"  have a mix qualitative and quantitative variables
Give the students some control over what variables go on the data cards
great opportunity to revise measurement skills & unit conversions cm-mm etc
Google maps could give them a walk time to school

 2. How long is it ?

we want to find out how good they are at estimating

• Use a piece of rope or maybe a piece of wood ( both good tools for measuring other things)
• Collect the data quickly by handing out small squares of paper & have students write their estimate of the length in cm or mm
• collate data 
• Create a dot plot & discuss what they see 
• Summarise findings from 1st estimate

 An interesting extension to this is see how much better /worse they are at estimating if the wood/string isvertical rather than horizontal

3. In the same vein - how many dots? 

take an A3 piece of paper 

Put 36-38 dots on it with a white board marker

• Give students 3-5 seconds to look at the paper and then without talking to anyone else write down their estimate.
• Collect and collate data 
• Create a dot plot & discuss what they see 
• Summarise findings from 1st estimate

(Do not tell them the answer by the time they find the centre & IQR and have the option to adjust their estimate they will as a class almost always come up with 36-38)

"The eyes have it"

 when describing the distribution

I see....

I notice.... 

                  which makes me wonder .....

4. On census at school there are a few data sets that you can use to make "populations" from which students can grab a handful (a sample)

• Koala
• Kiwi
• Stick Figures
• Trout

Students can use these to take random samples from the "population" make "dot" plots on their desks 

I call this the "grab" method

By comparing samples with each other they  will see all samples are different and start to develop their understanding of variability of samples

5. Estimating the Ages of famous people

 

https://mathbits.com/MathBits/PPT/EstimateAge.htm

1. Question – do year 9 students at ABC College tend to over or underestimate the ages of people ?
2. Data Collection : use powerpoint online here https://mathbits.com/MathBits/PPT/EstimateAge.htm
3. Analysis: Plot results on a scatter plot actual vs estimate and put in a line of best fit ( y=x)
4. Describe features what patterns do I see?
5. Summarize and answer the question asked