Polar Coordinates – Resources

StationeryWith Year 13 I will be looking at Polar Coordinates this week. The first thing we’ll need to do is understand the meaning of polar coordinates and be able to convert from polar to Cartesian coordinates and vice-versa. So we will need some polar graph paper and Desmos! Checking my stationary list I found exactly what I needed on MathBits, scroll down the page for polar papers; one of the options usefully provides 4 smaller grids to one page.

So now to plot some points, Desmos provides a good solution

Desmos - polar coordinates

Select image for Desmos page

With two points to play with, we can understand how negative values of r and θ are displayed and appreciate that a point may be described in more than one way with polar coordinates.

The Desmos page also shows the relationship between polar and Cartesian coordinates (the Cartesian form is needed to plot the points.) On that subject, Desmos created the page below – match up the two points.
Desmos - polar & cartesian coordinates
We also need to be able to plot polar curves, Desmos is ideal for exploring polar curves; it is possible to use sliders to see how the curve is generated as values of θ increase.

desmos-domain-and-sliders

On the AQA website the Teaching and learning resources page for A Level Further Maths includes three online textbooks under the Resources for students heading. The second book (Unit 03) includes a chapter on Polar Coordinates.

WolframAlpha can also be used for polar plots.

For further examples and resources, see this post on Mathematics for students.

Desmos & Valentines (& fractions and rotations!)

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

Click on the image and move that slider!

Click on the image and move that slider!

In what happily seems to have become an annual tradition Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
valentine-design

Geeky people you could even use the Desmos API …

Valentine’s Day seems an appropriate time to express love for Desmos!
Two happy discoveries this week (thanks to Twitter):
Fractions - multiplying Rotation
Multiplying fractions and Rotation about a point. Brilliant.


Elsewhere – express your feelings for WolframAlpha!

I Love YOU

Transum Valentine Puzzle
and here’s a logic starter from Transum for Valentine’s Day!

Wishing Mathematicians everywhere a happy day and if you are a UK teacher about to start half term – have a lovely week!

Number Operations

Manipulation

Questions such as this can make a great starter for a lesson and provide the chance to discuss number operations and the relationships between them. Manipulating numbers like this can also help with algebraic manipulation.

Looking for some more examples of this type, I came across a really useful resource on TES, “If I know this then I also know …” by Piers Butler. This would make an ideal lesson starter. As it is an Excel spreadsheet, I thought it would be simple to add another worksheet with the answers and created the Excel file CY If_I_know_this_then_I_also_know_ which is a copy of the original, but just adds another worksheet with the answers.

Thank you, Piers!

If I know this..