Solving triangles decision tree

Before entering declination and inclination in year 10 I wanted my students to really consolidate how to solve a variety of triangles.

I set up a decision tree on the whiteboard splitting the various methods for solving triangles.
My students are heavily reliant on notes to solve problems but now can see which parts of their notes to use for a variety of problems. They are even labelling triangles correctly!

Obviously the tree has limitations - finding third angles when two angles are given, finding the unknown angle with the cosine rule (when not the central angle) and the "ambiguous angle" with the sine rule.

Another area I have focussed on is providing differentiation for students of varying levels of algebraic skill. For some I have written all variations of the various rules on their notes page and ensured they can find the correct rule and use correct mathematical notation when recording their logic for solving a problem. For more capable students I have suggested only the bare minimum in their notes and encouraged them to identify the subject and manipuate equations to suit (as it is great practice). Some students have worked more on mastering sine & cosine rules, others have experimented with 3D trigonometry.

After discussing the limitations and completing a number of examples, suddenly the lights turned on for many of my students.. for the first time in a while I felt they were ready to move on. This is my cue to run a revision session of mixed and composite examples and check for further issues.

3D trigonometry

3D Trigonometry in year 10 is one of those subjects that lots of kids have issues with. Students traditionally learn just one topic at a time, are tested and then move to the next topic. With 3D trigonometry are all of a sudden faced with using lots of maths all at once.

Topics that all come together:

• Parallel lines (in 3D)
• Alternate/Complementary/Supplementary etc angles
• Polygon properties
• Trigonometric ratios
• Pythagoras' theorem
• Sine Rule
• Cosine Rule
• Oblique and isometric drawing
• 3d visualisation
• Volume, Surface area
• Algebra (in all its guises)

My students have seen some success in this topic through the use of "wireframes" (made of skewers and connected with a hot glue gun) and templates placed in the wireframes to indicate various right angled and non right angled triangles. It also helps them see parallel lines and equivalent lengths/angles. This seems to be the concrete element they need to put all the other stuff in place.

I also try to introduce the topic multiple times throughout the year as new concepts are introduced (eg. parallel lines - > volume -> pythagoras -> trig ratios -> sine rule -> cosine rule)

Also useful is the discussion on solving triangles here.

Burnout Week 5 term 3

As a new teacher we have to cope with a lot of things.. The kid with the difficult home life, the aggressive learner, physically agressive students, bullying and social issues between students, unachievable aspirations of students, students with low self esteem, politics between teachers, goals of the school, TEE, the list goes on.

And sometimes you feel it is all a bit too much. You grit your teeth and look forward to the next break. This is especially prevelent in term 3. You can see it even in the senior teachers as they confide they are not coping. I think to myself if they're not coping, how can I do it?

Then you stop sleeping and eating.. You get a little grumpy.. classes stop responding to your teaching methods. You're not as quick at coming up with alternate responses to poor behaviour and end up being the teacher you said you would never be.

At this point, talk to someone you trust - hopefully a team member that has gone through it all before. Don't pick someone struggling that will reinforce your issues, but someone that is doing well. Listen to what they do and why they are having success. Ask for some time out. Don't talk to your line manager - my past experience is that their responsibility for performance causes an imbalance in their judgement as they look at the now and only have time for a quick fix rather than investing in the whole picture.

I suppose the main thing is not to burn out. Your classes can suffer for a little while whilst you slow down a little. The profession needs you - three years from now you can laugh at what caused you such grief before, even if sometimes you can think it doesn't care. At the end of term four you can reap the rewards and next year be recharged. This is the hump - know this and just get over it the best way you can.

At least I hope so.

Setting difficulty level of classes

I've copped a bit of criticism about the level of difficulty of my classes. Some students have found it too hard, others too easy. This to my mind is an indicator that I'm probably doing ok.

After all it's better to push kids too far and get the difficulty level wrong occassionally than not push students and get the difficulty level wrong all of the time.

I try and manage the difficulty level through a number of factors:
1) Are the majority of kids engagaed in learning?
2) Are mean scores in tests increasing?
3) Can those not engaged be moved next to engaged students?
4) Can I make the course more difficult?
5) Is the top student being extended?
6) Are students endeavouring to pass the top student?
7) How long have we been on the current topic?
8) Where are similar classes at?
9) Have I covered the intended content?

And so on..