What happens when it not only rains but it pours. 

26 03 2017

My brother lives on a farm in central NSW. Tuesday morning they had over 100 mm of rain in the order of 4 hours. Wednesday afternoon there was a further 63 mm in half an hour and Thursday afternoon it started raining heavily about 5. By about half an hour later there’d been just under another 50 mm.

Some of the water from the local to distant area runs past their house and into a creek.

When the last fall of rain came the water running past the house was about 20 m across and 400 mm deep and running at about 40m/min. My brother watched a moving leaf to get the rate of flow. As the runoff from the rain increased, the depth of the water increased to about 700 mm.

If calculations are made on 40 m/min X 20 m X 400 mm, you get 320 cubic metres per minute which is 19200 cubic metres per hour which is 19200000 litres per hour or 19.2 megalitres per hour.

It has been running at least this deep for the last 48 hours which calculates to be 921.6 megalitres or 921600 cubic metres of water.

At the times where the depth raised to 700 mm the rate of flow would have been faster- it was dark so we can only estimate that it was possibly at least half as fast again. This calculates to 50.4 megalitres per hour or 50400 cubic metres of water per hour.


That 3 day rainfall is half the average annual rainfall.

All in the day of being a farmer!





If Students Begin to Drift, Instruction Must Shift by Elizabeth Stein

6 03 2017

There are some good ideas here for reaching each student in the class, even if you are the only teacher.





Proving a Conjecture with Steven Strogatz

19 02 2017

Here’s a video outlining the procedure of proving a conjecture. This comes from the youcubed site.






7 Ideas for Kindness in the Classroom by Rebecca Alber

18 02 2017

Here are a number of suggestions for helping students feel a valued member of the class.





Extension 1 Mathematics Teaching Tips

17 02 2017

Last week I was asked for tips for teaching Extension 1 Mathematics.

It has been my intention to blog on this for ages, so here they are, in no particular order – just as I think of them. There’s nothing in particular that I do, just lots of little things to encourage deep and comprehensive learning.

  • Use a variety of sources for content and activities and methods – textbooks, revision guides, conference presentations etc.
  • Use games to reinforce instruction and content – tiles (these may be cardboard or paper. Foam fitness mats can be cut into rectangles say 3cm by 2 cm and written on with a felt pen. One side has the question like “nth term AP” written in one colour, say red. Another tile has the answer written in say black. The flip side has another question written in red. There have to be enough tiles for at least one per student. The first student will have START or the topic name in red . They say I have START. They turn their tile over and say who has “nth term AP”? and so it goes from student to student until someone has “The End”) and postits etc
  • Regularly use a single question quiz at the beginning of a lesson, without warning. I may record results or may not.
  • Finish a topic by the end of term or be prepared to completely reteach it the following term – which there is not time for. Mathematical Induction would be an exception as there are numerous categories of question which really are quite separate from one another. Mathematical Induction takes a lot of practice so having it experienced in 2 terms reinforces and consolidates the understanding of the students.
  • Leave the predominant focus of HSC questions until Year 12. Focus on strong concept understanding in Year 11.
  • Use regular review sheets in Year 12. These could be past HSC questions. There are sources for these. Edudata is the one I like because it has the questions categorised by topic. I have been using it for years and have not had reason to look for alternatives which I think exist. I have the answers to past HSC questions back to 1989 which can save enormous time when writing solutions. After I have sighted how much and how well the student has attempted the review sheet, I upload the solutions to the intranet and get the students to mark their own responses-it is possible to have this automatically released at the end of the learning session when the task is due and checked. Students learn far more this way because they get instantaneous feedback which is pertinent to their stage of learning. I can also focus on marking other components of their learning. I collect short scripts to mark very regularly and spontaneously, so that I can gain a good understanding of where their current learning is at.
  • During each topic give study tips and summaries etc. The MANSW site has some good resources too, which I ensure students have seen.
  • I aim to finish the bulk of the teaching by the Trials – this allows commercially available Trials to be used if that is desirable and permissable at your school. There are a couple of topics that are never finished – Harder Mathematics Questions and the HSC Geometrical Properties.. These are what I focus on after the Trials as well as  Trials from other schools. The more sight unseen resources the students experience in the last days of Year 12 the better. I often give 1 or 2 sight unseen questions during class, at this stage, to help with timing and confidence building.
  • As the course is never finished, I don’t tell my students that we have finished. The Harder Mathematics Questions topic is endless. I believe that students relax and lose focus if told that the teaching has ended.
  • When I mark in-class quizzes, I do not give marks. I detect where they have started to digress, circle this and often write a one or two word comment giving direction towards accurate completion. This is based on the ideas of Jo Boaler. I aim to hand back in class-quizzes the lesson that they are done.
  • Drill working and setting out.
  • Check home learning every lesson if possible. On my roll – Excel grid sheet with copious columns taped to the front of my textbook- I simply mark if it is done or not. This is very quick to check and record.
  • Be alert to resources that go beyond the syllabus. I only believe in teaching to the syllabus. This can be hard to maintain with some very eager and capable students.
  • Look at the Band 4 etc responses on the web and share these with the students to help develop an understanding of what is expected when answering a question.
  • Look at the markers feedback for the last HSC in the final lesson of Year 12, to give tips for being best prepared for their HSC. There is often a poorly attempted response from the last year or so, which is addressed. There are some aspects of questions which are regularly less well attempted.
  • Attend the Markers Feedback Day at Macquarie University, which is held each February and organised by MANSW.
  • Keep challenging students to answer questions efficiently. My motto is speed, accuracy and excellence without feeling pressured to rush. Its the proficiency development of the spinning of the pen on the tip of the index or middle finger that I do not encourage. I tend to have a similar but different slogan or focus each year, as I discern what is pertinent to the cohort I am teaching.
  • Keep watching Jo Boaler to stay abreast of her new strategies.
  • Access a copy of every study guide that you can find and use them randomly so that the students have no idea where you will next access information to create an activity for the lesson.
  • I advise students to be regularly using one or two study guides by the Year 12 Half-Yearly and perhaps another by the Trials – depending on how much they have used what they have.
  • Resubmits are magic. Have an expected achievement level for a class task. This could be built into examinations too.  It may be that they students need to come to you at lunch to be supervised as they resubmit or you may allow it to be done at home. The student then needs to mark their work. Obviously, the solutions need to be not released prior to the resubmit. This helps to encourage students to learn the work adequately, initially. Similar to this, is expecting students to always correct mistakes on any examination, prior to the release of the solutions. This is also imperative in building a development of expertise.
  • I teach by asking questions rather than telling the students how to do something. This helps them to process the method and if faced with a similar question during assessment conditions, they have done the processing at least once. Otherwise, it is too easy to tune out and not develop understanding. Students find this hard but learn better when they join the process.
  • Keep abreast of trends – blogs, MANSW, Jo Boaler etc.
  • Try flipped learning with every group. When it takes off you’ll be amazed at the understanding and level of the questions asked. I’ll blog on my technique soon.
  • Boys like competition, girls like order and special attention. All students like encouragement.
  • After each examination I have students complete an Error Analysis where they look at the types of mistakes – silly errors, lack of knowledge, misunderstood question etc. That’s been a blogpost several years ago as I spoke about it at a conference. I also categorise marks to look for topics needing most attention for improvement.
  • Record student goals prior to an examination (get them to predict their result) and give them feedback after the examination.
  • I give awards after Half-Yearly and Yearly Examinations, especially in senior classes. I even try to get someone from Senior Executive to issue them with a certificate. Funky postits, special pens, engraved pens are cheap and special etc.
  • I buy a heap of exercise books at the beginning of the year when 40 or 80 page ones are very cheap. I issue one to each of my senior students as their revision book which is not to come to school to be used as they choose. I suggest that they summarise each topic on a double page. If they get time to come back and then summarise it onto a single page, they will deepen their learning and understanding even further.




Imaginary Oil Spill Mathematics Lesson by Nanci Hutson

3 02 2017

Here’s an idea connecting Measurement to its applications in the adult world. 





New Online Course: Mathematical Mindsets With Dr Jo Boaler

2 02 2017

Read all about it here.