Unit Planning

Here are some thoughts and ideas about how to pay explicit attention to the ideas at the unit planning core when teaching and planning this topic.

So I have been teaching these ideas at the beginning of the course as part of a unit I am calling 'numbers for describing' that covers ideas related to standard form, indices, logs, percentage error, accuracy and estimation.  I feel like these are key 'tools' that play a part in many other parts of the course. We have grouped indices and logs together for some obvious reasons about inverse. The following are some considerations for unit planning then...

Conceptual understanding - This is a good opportunity here to consider Equivalence, relationships, representation  - understanding how a logarithms are another way of expressing the exponential relationships. As such they become useful equivalents for solving equations and indeed for representing information using logarithmic scales. Its great to take the opportunity to help students make a note of these key conceptual links.

Contexts - Students are mostly likely to encounter logarithms in the context of needing to solve an exponential equation and the idea of log scales on graphs. There are lots of these to look at and there are some examples in this blog post Statistics telling Stories were I discuss the purpose of and pros and cons of using such scales. These discussions offer a great opportunity for students to enquire and understand the significance of different representation son accurately and usefully representing information. Clearly the context chosen could be looked at from both a local and global perspective. This kind of activity and discussion will draw on many of the learner profile attributes as well.

Calculator - students find it pretty exciting to finally make sense of the 'log' and 'ln' buttons on their calculators and given that there is no use of log laws at SL, this ends up being quite accessible for all students.

All the while, we have lots of underlying knowledge issues at play. The most obvious one is about the different stories that are told by using the different representations - as shown in the Statistics telling Stories post. There are perfectly legitimate reasons for making such choices, but they do seem to come with consequences or at least a need to know and understand those choices and how to factor them in. Then we get to the notion of the logarithm itself as a notion and the extent to which it is a construct as opposed to a natural idea. This of course leads nicely in to discussion of 'the natural logarithm' this can be tricky, but I have recommended elsewhere on the site that students are introduced to 'e' in the context of compound interest since it gives a great way to explore that idea as well. It can be very powerful to get these lovely links between the ideas and really pay attention to the ideas at the unit planning core. Happy to read and include user suggestions about unit planning considerations here. Thanks.