New Cur 7: Logjam

This is the sum total of the approved curriculum‘s coverage of logarithms:

Year 10 Measurement

interpret and use logarithmic scales  in applied contexts involving small and large quantities and change (AC9M10M02)

understanding that the logarithmic scale is calibrated in terms of order of magnitude; for example, doubling or powers of 10

identifying and interpreting data representations (charts and graphs) that use logarithmic scales and discussing when it is appropriate to use this type of scale and when it is not appropriate; for example, graphs representing percentage change, a wide range of values or exponential growth

investigating and interpreting logarithmic scales used in real-world contexts; for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of micro-organisms and disease and describing reasons for choosing to use a logarithmic scale rather than a linear scale

investigating dating methods of geological sites to provide evidence of First Peoples of Australia’s human presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales (scientific notation) and measurement accuracy in the dating 

Optional (and Hidden) Year 10 Algebra 

the inverse relationship between exponential functions and logarithmic functions and the solution of related equations

using the definition of a logarithm and the exponent laws to establish the logarithm laws

evaluating \color{OliveGreen}\boldsymbol{10^x} for decimal values of \color{OliveGreen}\boldsymbol{x} and relating this to a logarithm base 10 scale; solving exponential equations algebraically using base 10 logarithms; for example, \color{OliveGreen}\boldsymbol{5\, 000 \times 1.01^x = 10\, 000 \Rightarrow x =\frac{\log_{10}(2)}{\log_{10}(1.01)}\approx69.66}, and connecting to the graph of the corresponding function

6 Replies to “New Cur 7: Logjam”

  1. Logarithms is a small topic in the curriculum. If students do mathematics for 4 lessons/week, that is probably enough for 2 or 3 weeks for average students in Year 9. The quotes above suggest that only base 10 and 2 are used, but it would be easy to tell students about other bases.

    Teachers could also mention the role of Napier. Here is a multiple choice question on an exam that I set recently.

    Logarithms were invented by:
    A. John Napier
    B. Archimedes
    C. Albert Einstein
    D. Isaac Newton
    E. Pythagoras

      1. I agree that logarithms need not be a small topic. I have just finished teaching Year 9 students about logarithms but I had 10 weeks to do it (less a couple of weeks due to various events at school). Most topics in high school mathematics tend to be “covered” in a small space of time. So, it was nice to have time to explore ideas: as I have said before, I have a dream job. Attached is an essay topic that I set for the students.

        log-kat2-2022

  2. Logarithms and their manipulation are essential mathematics. They give beautiful context for problems.

    Reminds me of some people on twitter complaining about rationalising denominators. I said that it is good practise at manipulating fractions and that things don’t need an application to be something you teach to kids. The way they were expressing their dislike for the topic rubs me the wrong way.

    1. Glen,

      Before 1976 log/trig tables were standard issue for GCE O and A levels and calculators were slide rules in the UK

      Steve R
      last millennium dinosaur

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