This isn’t your imagination: ✨complex numbers✨ are now live in the Desmos scientific, graphing, and 3D calculators!→ Learn more in our help center: help.desmos.com/hc/en-us/art…→ Keep up with What's New 🎉 at Desmos: help.desmos.com/hc/en-us/art…#iTeachMath #MathSky
For an introduction to complex numbers, try these very clear notes with exercises from Plymouth University. Sections are available on Basic Algebra, which includes Complex Numbers, Graphs, Trigonometry, Calculus, Vectors, Logic and proof, Matrices and Determinants, Vector calculus, Units, and Applications including Forces.
Try out the new table regressions in Desmos. This is so easy to use; I copied data from a spreadsheet and pasted it into a blank expression line. To create a regression, simply click the Add Regression icon to the left of your expression. I tried the Desmos table regression using a data set from this new Transum Activity, Odd Scatter Out, where students have to identify the odd one out from a set of 5 scatter diagrams. Link to Desmos page.
This GeoGebra applet allows students to move points and watch the effect on the line of best.
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.
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.
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 – 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.
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.
I have so many favourites on Underground Maths, here’s one – Scary Sum!
Following on from an area model for multiplication, for your older students, try Divide it up from Underground Maths, a resource designed to help students to make links between multiplication and division of polynomials using multiplication grids. The problem is presented in the image here, but also provided is a warm-up activity and further notes
A favourite Underground Maths resource I have used many times – To log or not to log? This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. I have always found that in addition to working on indices and logarithms this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!
Students are often used to problems being posed in such a way that they have all the information that they require in order to start, and no more. Problems (especially from the real world) are very often not like this, and so resources of this type will give students the opportunity to develop the skills needed to deal with this. Some problems might not contain enough information, so students may need to decide on classifications, make assumptions or approximations, or do some research in order to move forward. Some problems might contain too much data, so that part of the challenge is to identify the useful information.
When students are familiar with concepts and ideas they often benefit from exploring them further to improve their understanding. These problems aim to allow this further exploration, and for example, might bring different techniques together, highlight interesting or unusual cases, or probe the definition of mathematical terms.
A resource I found very useful for the matching functions with their gradient functions is Gradient Matchwhich can be used interactively online. See this post on introducing gradients at GCSE. Note that you can simplify the task by giving students the set of six functions and the six gradient functions separately.
Can we fully factorise x4+4y4? Starts with a Show that…. And then we factorise and will need to recall the difference of two squares. We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.
Can we simplify these algebraic fractions? Review algebraic fractions, simplifcation including the difference of two squares and quadratic equations. We could of course also talk about functions (including domain and range.
