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Is Zero even?

Jo Gledhill (@JoLocke1) asked this on Twitter:

… thoughts on 0 being even or neither!! Some of my dept say neither I say even as a multiple of 2 sorry?!?!?

Here’s my thoughts about what makes something even as it’s something that comes up in my classes often when I’m doing the caterpillars investigation.

Even numbers end in 0, 2, 4, 6 or 8

This one often comes up with students and I’d agree with the caveat that we’re talking about integers. I wouldn’t want to have to say that 1.2 is an even number for example.

Even numbers are (integer) multiples of two

Passes this test. 0 = 0 × 2

Stacking up a pile of blocks

If you stack up the blocks into two piles, the top is level (even). This works with 0.

Sharing it out

When you share an odd number of things equally between two people, you have an odd one left over at the end (remainder one). That doesn’t happen with two.

It fits the pattern

-3, -2, -1, 0, 1, 2, 3

odd, even, odd, even, odd, even, odd

So, in conclusion

0 is even

*******************************************

In other 0 related news:

0 is neither positive nor negative

0 may be a natural number or not, depending on which definition you use!

 

 

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Correlation and line of best fit

Correlation

Soon, I’ll be moving on to the topic of correlation and regression with my Core Maths classes. It’s a topic that I think often makes intuitive sense (you can have a feeling of what correlation you might expect) while also being something that it’s easy to see as being useful.

For me, it’s important in Core Maths lessons that they are more than ‘just about the maths’ when possible so this seems like a good time to talk about spurious correlations and also to have some fun. I’ve made four scatter graphs that relate to some well-known sayings. See if you can figure out what saying each one is!

Bigger they come harder they fall All workEarly bird Empty vessels

They’re just meant to be a bit of fun and a nice way in to the topic. (I’m well aware they are bending the exact meanings of the sayings in some case.)

Line of best fit

I’ve been talking to a couple of the science teachers in my school (this one and this one) about some of the things we do differently in maths in science. It turns out that are just some different phrasings that are used and I don’t think we are going to get a collective agreement. So, it makes sense to explicitly point these out to students so that they just get the idea that we deal with things differently. Here’s a slide from from my correlation and regression lesson notes. You can find the whole powerpoint over on TES. (Along with some other resources.)

line of best fit

30 Second Challenges Starter

Just a really quick post to share a resource that I like. This one is a site made by Christian Lawson-Perfect that recreates the 30 second arithmetic challenges found in some newspapers.

arithmetic challenge

Great for projecting on to the screen for the class to do and is even useful for tutor time.

The link is here http://christianp.github.io/30secondchallenge/

My First Core Maths Lesson x2

I can now officially call myself a Core Maths teacher rather than just a Core Maths Planner. I’ve seen both of my classes now and taught the same first lesson to them both.

The classes have 18 students and 12 students which is a good take up rate and, although there will likely be some fluctuation as they finalise their A level choices, this is promising! It is less than the amount originally signed up so I’ll do what I can to try and find out where those other students have gone.

So, what did I do in my first lesson? I really wanted to start with something that is different to what they’re used to. Estimation seemed to fit the bill and note that you don’t need to know the answers to be able to put these in order, just a sense of the size:

Put in order pic

It went well and there was a good ‘buzz’ in the class. People were willing to suggest ideas and I got an early chance to encourage participation with things like “Obviously, you don’t know the answers here – who would? But, you’ve got an idea of how old a really old tortoise might be haven’t you?”

Things I’ve learnt and to bear in mind next time:

  • Having the two distances in different units was unnecessary and confusing
  • Students often didn’t know where the river Severn was
  • It wasn’t entirely clear that students definitely knew where Edinburgh was
  • EVERYONE was able to get involved in this. It seems like a good starting point

Next, we went in to the main task of the lesson:

how many items luggage

We spent a long time on this (longer than expected) and I made good use of Lily Tang’s (Twitter: @cvcltang) framework for breaking down a Fermi problem. The structure was very helpful in getting students not to panic and to also make them think they could do these kinds of things.

Things I’ve learnt about this:

  • Students often know things I don’t (how are runways used for example)
  • I did this twice and got pretty different answers with both classes
  • Students were expecting me to ‘know’ the answer. I had to explain to them that’s not how these questions work
  • I can probably push this forward more quickly and model ‘not getting bogged down with detail’

Next, I showed them the following slide.

easy to be overwhelmed

It’s easy to forget that just a few months ago, these were GCSE students. They have not magically learned how to take notes so I’m going to help make sure they have decent things to look back on in their course notes. To signpost this, I’m making slides with notes on have a different background to them. Hopefully that will help!

Finally, I set them some homework. Because of the length of time I have to teach the course, I think homework is necessary. None of the students questioned it so I’m guessing they were expecting it!

Estimation Homework 1

The homework includes some of the facts people should know and also two estimation questions. We’ll see how that goes!

All in all, a really great start with a positive buzz about all the questions so far. Looking forward to the next lessons.

Fermi type Estimation Problems

A part of the Core Maths course I really like is the section dealing with estimation. Far too often, maths gets bogged down in unnecessary detail or leads students to think that getting an answer is all that matters, regardless of whether that answer makes sense! 

However, it’s not a topic I’ve ever taught before and it very much seems like the sort of thing that lots of varied practice would help with so I set about finding a list of questions. I could find some but not as many as I wanted so I set about collating a list and creating some more. Lots of people on twitter helped contribute ideas too so thanks for that.

Questions like these are included:

fermi questions clipping

It’s a little rough at the moment and I will do some fine tuning later on but, it’s a good starting point. At the time of writing, there are 61 questions and, if you have any more ideas, please let me know so I can add them!

Link to the full list of questions is here.

Some questions about Core Maths decisions

It’s the day before students start back for my school and, in the spirit of preparation, here are some questions I’ve been asked by @CoreMathsCat that relate to ‘setting up’ decisions. I’ll try to answer them here.

Why have you chosen AQA?

Primarily because I was a proof reader for a book called AQA Level 3 Certificate in Mathematical Studies by Hodder and Staughton which was tied to the AQA course.

I also like the fact that there are different options and although I’m starting with 2A (the stats option) this year, I’m excited about the possibility of running different classes as appropriate for different students with maybe those taking Geography and Psychology doing 2A while the Business students can take 2B (featuring critical path and cost benefit analysis).

Are you teaching the course over 1 or 2 years?

1 year.

A big driver here was wanting to make sure that the exam did not happen at the same time as the A level exams at the end of year 13. It has been a good ‘selling’ point and will also be something concrete to put on UCAS application forms.

How many hours per week have you been allocated?

2.

I’m aware this is very tight and I will be making use of homework to help with this. If it is looking to be too short then I’ll talk to the 6th form team and see what we can do additional sessions. I will be upfront with the students and say that they’ll simply have to do additional work.

Are you accepting anyone with at least a 4?

Yes.

The course is designed for anyone who got a 4 or higher so there’s no reason not to allow those students to take the course. It looks like we will also be having students who got grade 7s as well.

Have you written your own sow or using aqa/other ones?

My head of faculty has a friend who is teaching core maths already so she kindly let me have that as a starting point. I’ve adapted it a little as I really wanted to make sure the course starts with something new (Estimation). The scheme I’m going to start with is this but it’s obviously open to adaptation if needed.

SOW image 1

SOW image 2

Any more questions, please ask!

 

It would be good if people knew …

If you haven’t picked up on this yet, I’m starting to teach the Core Maths course (AQA) from September. Part of the course is estimation questions like “How much liquid would a small town consume in a month?” and this raises the question “Do people know a reasonable estimate for the population of a town?” (Do you?).

This sparked a thought along the lines of what things it might be helpful to prompt students into finding out just so they feel more confident about answering these questions. What is the population of the UK? How long would a car be? And so on.

Next, I realised that this isn’t really something that would only be useful to Core Maths students and I also thought that other people would come up with good ideas too, so I turned to Twitter. Unsurprisingly, there were plenty of good ideas and here’s my collated list. The ordering is somewhat arbitrary and you may well decide that some aren’t that important for your needs. That’s fine – use it as you wish. Perhaps these could also spark tutor time discussions!

Thank you to everyone who contributed ideas.

Population of the UK
Life expectancy in the UK
Average adult height
Average adult weight
Average UK temperature
How many countries are there?
Weight of an apple
Height of a house
Height of a door
How many people fit on a bus?
What temperature would be gloves and scarves weather?
Diameter of the Earth
How far away is the sun?
Population of a large town
Population of a small town
What temperature would be t-shirt and shorts weather?
Population of the world
Average hours of sleep per night
Weight of a melon
Average car length
Average car width
Width of the UK
Length of the UK
How many primary schools in the UK?
How many secondary schools are in the UK?
How many teenage pregnancies were there last year?
What proportion of the UK are over 65?
Volume of water in a bath
Water used per shower
Days in a year
How many people can a theatre hold?
How far away is the moon?
Average car petrol tank capacity
Average car miles per gallon
Average distance an electric car can go on a full charge.
Average family size
Weeks in a year
How many people are unemployed?
How many people fit on a train?
How much water does a flush use?