New Cur 14: Moving the Decimal Point, and Other Sins

The Year 6 Number stream of the new mathematics Curriculum contains a notable content descriptor:

multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers (AC9M6N06) 

Yep, we’re just like Singapore. Continue reading “New Cur 14: Moving the Decimal Point, and Other Sins”

New Cur 5: Non-Reoccuring Decimals

Last year, we held a competition: What Are the Arguments FOR the Draft Mathematics Curriculum. The winner was officially no one, partly because everyone was too cynical to take the competition seriously, and partly because everyone’s cynicism was very largely justified. Still, we decided to declare John Friend the winner, for his suggestion in a different competition. John’s suggestion was an elaboration from Year 8 Number:

investigating the use of pronumerals to represent recurring decimals as their equivalent fractions, for example, let \color{RawSienna}\boldsymbol{x = 0.\bar7} then \color{RawSienna}\boldsymbol{x = 0.77777..} and \color{RawSienna}\boldsymbol{10x = 7.77777...} therefore  \color{RawSienna}\boldsymbol{10x \mbox{ \bf - } x = 7} and 9x = 7 so \color{RawSienna}\boldsymbol{x = \frac79} (old AC9M8N03)

This elaboration has been removed for the approved curriculum.

Continue reading “New Cur 5: Non-Reoccuring Decimals”

WitCH 4

Well, WitCH 2, WitCH 3 and Tweel’s Mathematical Puzzle are still there to ponder. A reminder, it’s up to you, Dear Readers, to identify the crap. There’s so much crap, however, and so little time. So, it’s onwards and downwards we go.

Our new WitCH, courtesy of New Century Mathematics, Year 10 (2014), is inspired by the Evil Mathologer‘s latest video. The video and the accompanying articles took the Evil Mathologer (and his evil sidekickhundreds of hours to complete. By comparison, one can ponder how many minutes were spent on the following diagram:

OK, Dear Readers, time to get to work. Grab yourself a coffee and see if you can itemise all that is wrong with the above.


Well done, craphunters. Here’s a summary, with a couple craps not raised in the comments below:

  • In the ratio a/b, the nature of a and b is left unspecified.
  • The disconnected bubbles within the diagram misleadingly suggest the existence of other, unspecified real numbers.
  • The rational bubbles overlap, since any integer can also be represented as a terminating decimal and as a recurring decimal. For example, 1 = 1.0 = 0.999… (See here and here and here for semi-standard definitions.) Similarly, any terminating decimal can also be represented as a recurring decimal.
  • A percentage need not be terminating, or even rational. For example, π% is a perfectly fine percentage.
  • Whatever “surd” means, the listed examples suggest way too restrictive a definition. Even if surd is intended to refer to “all rooty things”, this will not include all algebraic numbers, which is what is required here.
  • The expression “have no pattern and are non-recurring” is largely meaningless. To the extent it is meaningful it should be attached to all irrational numbers, not just transcendentals.
  • The decimal examples of transcendentals are meaningless.