G and T - New syllabus 2019
The new Mathematics: Applications and Interpretation syllabus is out and published on the IB website. Log in to your MyIB account and head to this link . It is a new course with a new name and renewed focus on understanding the relationship between mathematics and its application and interpretation. It is still intended very much that the SL course will cater for the same group of students that might currently opt for Mathematical Studies. It is hoped that some of the current SL students will opt for the applications HL. Clearly all sorts of permutations are possible. Read more about the development of this course through the links in the New Syllabus section of the website. This page will focus on the Geometry and Trigonometry unit and evolve over time as the new applications site is built.
Geometry and Trigonometry
The following is just a quick comparison between the two syllabi for the benefit of overview.
- Equations of lines, intercepts and gradients.
- Right angled trigonometry.
- Non - right angled trigonometry.
- 3D Geometry
- Volume and surface area of 3D Solids
- Distance between 2 points in 3D space. Volume and surface area of 3D solids. 3D geometry.
- Right angled and non right angled trigonometry.
- Applications of trigonometry.
- Circle sectors area and arc lengths.
- Equations of perpendicular bisectors.
- Voronoi diagrams
Points of Observation
- The syllabus looks very similar indeed to the current maths studies syllabus
- Worth noting that bearings will make a come back.
- There is an explicit mention of circles, arc lengths and sectors.
- Perpendicular bisectors are explicitly included as a build up to....
- Voronoi diagrams are going to be new to most of us and an interesting challenge?
An SL Scheme of work
Based on these guidelines, here is an idea about how we might spend the time. Remember that the Toolkit hours can come anywhere we want them. Clearly there are a number of ways in which this can be done, but this is just a suggestion to get us started.
A note about assessment - Each week shows a suggested assignment and there are a number of ASSESSMENT points through the unit. Many teachers like to use regular quizzes and clearly, all of this can be weaved in and out as the teacher chooses.
Week 1 - Circles and Geometry of 3D shapes
Much of this is likely to be reviewed from previous experience, depending on what experience students have had before. Essentially though, students need to understand about
- The distance between 2 points
- Areas and lengths of parts of circles
- Surface area and volume of 3D solids and related compound shapes
3 lessons might go like this.....
- For conceptual understanding, we might use the Making Cones and Pyramid Volume activities. These can be good ways to re-engage students with previous experiences with these shapes. This Piece of Cake activity is a nice way to look at the parts of circles. Crow Flies invites students to think about the distance between two points.
- Formal definitions and exposition of formulae might follow
- Then a lesson looking at broader applications and associated interpretation of some of these ideas.
Assignment - ....
Week 2 - Trigonometry part 1
Again, right angled trigonometry will likely have been seen before, which means this week allows us to look at some conceptual links and review the key ideas.
- The Trig Calculator is a good exercise for understanding the key calculations.
- Re-arranging relations might help to deal with the problem solving schema needed to approach right angled trig problems.
- A third lesson might focus on practice OR begin the Non right angled trigonometry (see next week)
see resources on the Focus on SOHCAHTOA page.
Assignment - A practice exercise that puts right angled trigonometry problems in to context.
Week 3 - Trigonometry part 2
This week the focus will be on Non right angled trigonometry.
- The Sine Rule activity is a good opportunity to follow the mathematical path from SOHCAHTOA to non right angled formulae (Sine rule and area of a triangle).
- A second lesson might focus on the cosine rule and practice of all of these non right angled ideas. The activities Impossible Triangles and Which Rule? could be useful here or next lesson
- A third lesson could make use of the two activities above and/OR move on to the solving of problems in context.
see resources on the Focus on Non-right angle trigonometry page.
Assignment - Students should get a chance to spend time with exam style problems for non right angled trigonometry.
Week 4 - Bisectors and Voronoi diagrams
The next two weeks should be devoted to these key ideas. this first week would likely review the construction of perpendicular bisectors and the introduction to Voronoi diagrams
Assignment - This is another opportunity for students do work on a review exercise from a previous unit to keep older ideas fresher.
Week 5 - Voronoi diagrams
This week would focus on Voronoi diagrams in context.
Assignment - Practice questions involving Voronoi diagrams
Week 6 - Review and Assess
After this unit, this week is available for general practice and review and would culminate in an end of unit assessment.
ASSESSMENT POINT - A 60 minute assessment based on the geometry unit.