Unit 1 - Numbers & the world around us
This unit is right at the start of the first IB diploma year and designed as a short 'induction unit' that introduces students to the course. In practice we know there is likely to be movement between classes at the start of the course and we, as teachers, are required to give some feedback about students as to how well they have started the course. Te unit is a great place to start working on the philosophy of the applications course and getting to grips with the significance of numbers as a tool for understanding the world around us.
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What is this unit about?
The syllabus items in this unit are addressed as follows
Week 1 - Induction unit - Students take part in the IB induction programme in our lessons this week. This is a whole school cross-curricular event. Details can be found here.
Week 2 - Accuracy, estimation and standard form - How, why and when to express numbers in standard form. The mechanics and implications of accuracy and estimation. See SL Standard Form, Accuracy & Estimation
Week 3 - Indices and Logarithms - Working with indices and numbers in standard form. Understanding logarithms as the inverse of indices. See SL Indices & Logs
Week 4 - Practice and test - Test involves work from the induction unit as well as the background knowledge. See below
Why does it matter?
Through out this unit, we will be emphasising the importance of understanding these mathematical ideas and being able to work with them in terms of understanding information that is given too us. For example, take this blog post about Statistics telling Stories which looks at the implications of a logarithmic scale used in graphs in the media. The whole point is that we cant understand or interpret the information we are being given if we don't understand the languages it is being given in.
Example resources
During this unit, students will do most or all of these activities
15 Countries and 200 years - This activity will make up part of the induction unit that all students will do
The 6 million question - This is a profound exercise in putting the volume of the number 6 million in to context
Percentage Perception - Whilst looking at percentage error we will explore this survey that explores the perspective of people in different countries about the percentage of their population that is Muslim.
This new Log Jam - Thinking about logarithms activity is a good one for introducing this new idea.
Further activities might include - Big & Small Numbers , Exactly , Upper Lower Bounds
In addition, we will use the formal explanations and practice exercises available on these pages for the important direct teaching and practising of these ideas.
SL Standard Form, Accuracy & Estimation and SL Indices & Logs
Opportunities for broader goals of education
The IB philosophy as detailed under 'Approaches to teaching and learning' (ATTL and planning) , invites is to always be thinking about the broader goals of teaching these units. It can be really hard to detail all the things that we do, big and small, planned and spontaneous, to do this, but it is important to try and reference some of them so that we get a strong sense of how we are doing against these objectives. Each of the pages and activities referenced above will also include references specific to those activities.
Each of the links above have extensive details about the nature of the tasks and the opportunities within them to address the broader goals of teaching and learning. For example..
- In the 6 million question, students will collaborate to work on an estimation and present their arguments to the class. At the same time they will dwell on the global significance of the chosen number and, in tur, the nature of estimations that are used around them.
- In the percentage perception problem students will address the fundamental issues intuitive responses to questions like this and what informs peoples intuition. At the same time, we will see three perfectly correct ways of presenting the mathematics that each tell a completely different story. This will bring out some key ToK ideas.
As suggested above, these are just examples and further details are available on the activity pages themselves.
Assessments
Students will use the practice exercises listed above as assignments during the unit and build towards an 'Unit test' that aims to test their understanding in exam conditions of the kind of questions they are building towards. This will be marked on an IB scale from 1 to 7 and used in the feedback for induction.
Here is an End of unit test assessment that can act as a summary assessment for the unit. Here are the solutions for marking. Here are solutions with marks assigned. The test is worth 50 marks and we would recommend about 60 minutes for the test.
Help and support
Many of the tasks in the unit have different access points that should help students to engage at all levels. In addition, students have access to their text book and studyIB.net/mathapplications, where they can watch video lessons and get help and support. This is of cousre in addition to help from the teacher during lessons.