Creating data by learning your prime numbers

Here’s a little idea for a team activity that could get quite competitive and hopefully “fun”. I haven’t tried it yet, and it might be a while before I use this. When I do, I’ll try to update this post with any tweaks depending on how it runs.

It’s based a on this really simple website Is This Prime created by@christianp which I saw on Jo Morgan’s MathsGems.

It presents you with numbers and you click YES (i.e. it is Prime) or NO.  It’s not an app so it can be used on a laptop / desktop although it works really well on browser on a tablet.  I’ll be doing this in a computer room as a group activity.

I reckon this could work with classes from Year 5 to Year 8, but most pupils in the class will need to have a reasonably good grasp on their times tables or it could be frustrating. It provides consolidation of times tables and primes but I think the real objective here is actually to use this as a lead in to various data and averages topics.  I always try to teach KS3 Statistics using data that the students have created themselves as they are far more engaged and care about what the data is telling them. This not only provides that meaningful data, but does so in a way which consolidates some fundamental number facts at the same time

I plan to use Google Sheets to collect the data which we will then analyse in a later lesson.  Google Docs in general is great for this type of collaboration.  I have created a template for a group.

Each group has a separate sheet that they fill in as they go.  Just duplicate the sheets for as many groups as you have, making sure that each group is working on their own sheet before you start.

Talking of groups, here are my general rules for planning any group activity:

1. I chose the groups.  I have nothing against pupils working in friendship groups but I know who to avoid putting together and the process of self-selecting can be painful for some.
2. Everyone has a role. Some pupils will see group work as a chance to sit back and some will naturally dominate.  Assigning specific roles reduces this.
3. Everyone contributes equally. By rotating the roles I will try as far as possible to make sure that everyone ends up doing the same activities by the end of the session.

 

To get some excitement going, I’ll keep a running commentary on the highest score.  I also plan to write up the “Errors” that the Error Recorders give me as we go. I want to make sure we have some time at the end for reflection on how it went, i.e.

• Did you work together as a team? How did you support each other?
• What was a good strategy for a high score? (When I play it, I rarely use all 60 seconds as I am trying to go too quickly and so I am often tempted to guess ones I don’t know)
• As a team what did you do to make sure your scores were improving (Write down the errors on a big piece of paper? – I didn’t say you couldn’t!)

I would definitely leave the data analysis part until the following lesson.  There is lots you can do with this and it could form the basis of a series of lessons on Averages, Data representation including Box plots. We can start with the question, “Who was the winning team?”,  which in itself is open to interpretation.

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Nix the Tricks – essential, reflective CPD

I’ve been teaching for 3 years, I’ve learnt a lot, but also appreciated that the learning never stops.  CPD doesn’t mean going on courses, it means spending a reasonable portion of your time looking at new ways of doing things, never just accepting that you are going to teach things the same this year as you did last year.

This wonderful tome written by a group of fabulous Amercian teachers is something that I think might become one of those sources I go back to again and again.

The basic idea is to replace “Tricks” with a proper teaching of deep understanding.  There is a wonderful array of unhelpful mnemonics, cute stories and memorised procedures in here including such gems as “Ball to the Wall” and “Make Mixed Numbers MAD”.  For each one, the authors suggest a better approach to instil deep thinking.

On reading this, I was relieved that I don’t use a lot of these bad tricks in my teaching, but there were a few that made me stop and think about my own practice.  Including:

1. 2.8 BIDMAS (usually PEDMAS in US schools). The first problem is that Divide doesn’t necessarily come before Multiply. The authors suggest an alternative, GEMA, but I’m not sure that this is all that helpful either. I’ve tended to teach this early, in Year 7 and 8, but the problem is that the second item you come in the list, call it Indices, Powers or Exponents, is not something known at this stage.  So I just say, ditch the acronym until much later.  Just start with saying multiply/divide happens before add/subtract unless we use brackets to indicate otherwise.
2. 3.5 Dividing fractions.  Whilst I have never said “Ours is not to reason why; just invert and multiply” I must confess that I do use Keep Flip Change (KFC) a lot!  So I like the idea of getting common denominators first and then dividing the numerators.  The idea being that once students practice a few they will discover the short cut. This takes a confident teacher, though.  I can think of some students who would just feel that I have wasted their time showing them a long method and might even think I didn’t know the short-cut!
3. 4.5 Pythagoras.  Instead of a² + b² = c², leg² + leg² = hypotenuse².  Interesting, but I’m looking for a better word than “leg”…

Anyway, that really is just scratching the surface of this wonderful resource. It should just make you stop and think about the fundamental way you explain maths concepts.  Because it doesn’t matter how many wonderful resources and activities you plan into your lessons, a significant part of students’  learning will still come from your explanations.

You don’t get many grey elephants in Denmark, do you?

This is a classic that I’m sure most maths teachers will know. I’m just hoping my Year 9 class won’t have seen it when I try it on them next week as part of a probability lesson.

In looking for some images I came across an on-line survey that Transum had done following an enquiry from a TV show. The results were interesting and worthy of a few minutes of discussion in class once the “trick” itself has been revealed.

If you haven’t seen this before, you essentially ask the following questions (respondents keep the answers in their heads):

The first part uses the fact that the sum of digits of multiples of nine is always 9, so that you always end up with a 4 which then turns into D.  Most people think of Denmark and then Elephant, but not everyone does as demonstrated by the results of Transum’s online survey.

This is a nice intro to Tree Diagrams but also gives some scope for discussion of these figures, i.e.

• What’s the overall % of people that this trick works on?
• 68% seems low – would it be higher if it was a UK only audience? (rather than a global Internet audience)
• What were the percentages in our class?
• What percentage of people does it need to work on to have the desired effect in the room?

You could even follow this up with a homework to survey 10 people.  Just don’t call it the “Elephant in Denmark trick” as my son did.  Oh dear…