Happy New Year 2018

Update: Happy New Year 2020!


Looking at my blog statistics I see Happy New Year 2017 is popular, so time for a quick update!

New Year Game

It’s that time of year again and we can play the 2018 Year Game in our January lessons.


We could also look back and use the excellent MacTutor History of Mathematics Archive from the University of St Andrews, Scotland. We could check any day for example for Mathematicians who were born or died on that day or check the Mathematician of the Week. Or we could look at the Theorem of the day!


 

Number GossipWe can always turn to Number Gossip from Tanya Khovanova for information on properties of a number. We see for example that 2018 is square free; I have found students are usually interested in these number properties and we could certainly usefully revise prime factor decomposition and come up with some more square free numbers.

wolframalpha-historical-number-formsWe can also look at WolframAlpha which provides further information including what 2018 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. Some possible starters for January lessons here I think!

The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.

babylonian-2017

For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.

Calendar

Teacher Resources on Line

We should make a calendar for 2018.
From trol, Teacher Resources on Line.

 

Wishing educators and students everywhere a very Happy New Year.

 

Diffy

Diffy
Diffy

Relaxing at Christmas, it must be time for a puzzle! To play Diffy, draw a square and label each of the corners with some whole number. At the midpoint of each square write the (positive) difference between the numbers at the corresponding vertices. Then draw a new square through the midpoints and repeat the process. Note we ended up with four zeros.

Change the starting numbers, do we always end up with four zeros, and how many steps does this take?

Diffy Excel

Or perhaps it is rather easier to set this out as follows and use a spreadsheet to explore many possibilities.
I was introduced to Diffy at an excellent lecture by Rob Eastaway and have used this successfully since with students from Year 7 (UK age 11-12) to my Year 13 Further Mathematicians!

Having done a little further research I found an excellent post by Don Steward on Diffy where he has numerous excellent questions for students to explore.

Diffy - Don Steward
Diffy – Don Steward

Note The PowerPoint included in Don Steward’s post. We can practise our Algebra too!

Do we need to start with integers?

Diffy - Irrational
For further reading and extension, a very thorough analysis, try Diffy Boxes (iterations of the Ducci four number game) by Peter Trapa, September 27, 2006 and Joshua Zucker on Circle of Differences in Numberplay from the New York Times.

Correlation & Regression

Studying Statistics with my Further Mathematicians I thought I would put some resources together. The use of Technology can really help with understanding here.

This GeoGebra applet allows students to move points and watch the effect on the line of best.
GeoGebra Correlation

This can be used in class by asking students to plot the points, draw their lines of best fit and then comparing with the computer. This worked really well on my phone, I simply sent myself an email with the link and was able to move points easily. This could also be used with younger classes when talking about lines of best fit.

We can also demonstrate correlation coefficients and lines of best fit with this PhET simulation on Least Squares Regression.

Correlation & Line of best fit

PhET – Least Squares Regression

Choose from a range of examples or choose Custom to add your own points and guess then check the correlation coefficient. You can also draw your own line of best fit and compare it to the theoretical line of best fit. Note the option to include residuals for both your own attempt and the line of best fit.


We can check Regression Calculations using this Linear Regression calculator from Social Science Statistics.

Linear Regression

Social Science Statistics – Linear Regression

On the subject of correlation coefficients, we can play a game to see how well we can guess the correlation coefficient! Guess the Correlation Coefficient.

guess-the-correlation

Guess the Correlation – Omar Wagih

From Cambridge PhD student, Omar Wagih ‘Guess the Correlation‘, a rather addictive game with a purpose – Omar Wagih is collecting the data on the guesses collected and using it to analyse how we perceive correlations in scatter plots. Select About to read the rules and further details.


We also need to look at ranked data and students must be able to calculate Spearman’s rank correlation coefficient from raw data or summary statistics. Again, Social Science Statistics, offers us a calculator which will be useful for checking work.

Spearman's RanK Calculator

Social Science Statistics

Calculation details provide a useful check on work.

Note Social Science Statistics also has a calculator for calculating the Pearson correlation coefficient.