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This is a quick example of how using Tracker software can generate a nice physics-related exploration.  I took a spring, and attached it to a stand with a weight hanging from the end.  I then took a video of the movement of the spring, and then uploaded this to Tracker.

Height against time

The first graph I generated was for the height of the spring against time.  I started the graph when the spring was released from the low point.  To be more accurate here you can calibrate the y axis scale with the actual distance.  I left it with the default settings.

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You can see we have a very good fit for a sine/cosine curve.  This gives the approximate equation:

y = -65cos10.5(t-3.4) – 195

(remembering that the y axis scale is x 100).

This oscillating behavior is what we would expect from a spring system – in this case we have a period of around 0.6 seconds.

Momentum against velocity

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For this graph I first set the mass as 0.3kg – which was the weight used – and plotted the y direction momentum against the y direction velocity.  It then produces the above linear relationship, which has a gradient of around 0.3.  Therefore we have the equation:

p = 0.3v

If we look at the theoretical equation linking momentum:

p = mv

(Where m = mass).  We can see that we have almost perfectly replicated this theoretical equation.

Height against velocity

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I generated this graph with the mass set to the default 1kg.  It plots the y direction against the y component velocity.  You can see from the this graph that the velocity is 0 when the spring is at the top and bottom of its cycle.  We can then also see that it reaches its maximum velocity when halfway through its cycle.  If we were to model this we could use an ellipse (remembering that both scales are x100 and using x for vy):

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If we then wanted to develop this as an investigation, we could look at how changing the weight or the spring extension affected the results and look for some general conclusions for this.  So there we go – a nice example of how tracker can quickly generate some nice personalised investigations!

One of the main benefits of flipping the classroom is allowing IB maths students to self-teach IB content. There are currently a good number of videos on youtube which allow students to self teach syllabus content, but no real opportunity to watch videos going through IB Higher Level past paper questions. So, I’ve started to put some of these together:

Playlist, Worked Exam Solutions:

The videos above are all around 10 minutes long and consist of talking through the solutions to 2-3 IB HL maths questions. The best way to use these videos is to pause the video at the start of the question, attempt it, then watch the video to check the answer and make notes on the method. Click on the top left hand corner to change the video being shown in the playlist.

The playlists below combine these worked solutions with the syllabus content videos, all grouped into the relevant syllabus strands:

Playlist 1, Algebra 1:

Sequences, Binomial, Logs, Induction, Permutations, Gaussian elimination:

Playlist 2, Complex numbers:

Converting from Cartesian to Polar, De Moivre’s Theorem, Roots of Unity:

Playlist 3: Functions:

Sketching graphs, Finding Inverses, Factor and Remainder Theorem, Sketching 1/f(x), sketching absolute f(x), translating f(x):

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