With 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 listI found exactly what I needed onMathBits, scroll down the page for polar papers; one of the options usefully provides 4 smaller grids to one 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. 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.
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.