Data - Averages Resources

Here are some resources I use when teaching Averages.

I find the word 'average' fascinating. Used in everyday language, and as a mathematician, I immediately think, "well... which average?"

I always wonder this when entering an "average speed check" section on the motorway. Which seems to be everywhere in the north west now.

Here is an activity linked to Speed Cameras, and some real life application.

The powerpoint with questions on slides is available here: Law Abiding Drivers
It links well with SDT topics too.


Here are a mixture of questions and projects including some that take longer than others.

Mixing Numeracy and Literacy

Football related averages - could be easily changed to Rugby

Quick question which is certainly seen in real life

Another interesting Football study - prizes for top predictions

This last one I have used for nearly every class I have ever taught. Every time I have done it, boys have outperformed barring the odd outlier. I have also done this with a target Velcro game in class. If a big class, then can be used for mean from a table as well.

Another project I did last year and will do probably every major football tournament is based on Yummy Math's World Cup Draw

I have written up my own task which is available here. Bit dated now but the idea can be used for the future : Fair Draw

Oh and the obligatory averages puzzles: (I think from Don Steward)

Answers via the link - Problem averages

Other useful links for averages worksheets

Maths Sandpit - Splitting The Steps average from table

Resourceaholic - lots of good stuff



Crack the Lock Activity

Here is an activity I use to encourage the students to work through some question in class.

It does require some initial monetary outlay, but it can be used for a very long time.

You will need some sort of locking mechanism, a padlock or safe, that requires a three (or four) digit pass code to unlock.

It should be visible to the class, It works better than a virtual one, although if you could find a digital one professionally done then that might be quite interesting.

Have a prize inside, and sometimes wrap it in an extension activity, in case they crack your code early.

I have a lock which can be reset to different combinations, you can get them for under £4 from Ebay or Amazon. I have also been trying to find a safe deposit box that works with a padlock, but yet to find one, so I bought some chain links from Homebase, for about £2. I then wrapped it round a normal tin and this is what I get:

The worksheets are then designed to give three numbers which relate to the code. I do not check their work until after they have tried the code. If a student tries to guess the code, we can have a discussion on permutations and chance, and the only rule is that you have to wait three minutes before your next guess.

The worksheets cover many misconceptions as they include true or false statements. So some are straightforward, whilst others can encourage debate.

Of course, locking the safe back up so other finishers can guess the code is fairly straightforward.

Those that finish first are asked to note down in their books three key facts that helped them solve the code, and then they can support other teams. So far I have seen relatively little cheating.

Here are the link to some sets of questions, starting with percentages and fractions, I will add more as I do them in lesson. Please feel free to create and share your own.

The worksheets


I actually think you could use a plastic bag as a safe: Put a box in the bag that is big enough so that if the bag handles were locked together, you couldn't get the box out. Sure, you could rip the plastic bag, but if you have nice students I don't think that would matter!

Santa's Route - Lines of Equation

I haven't posted for a while - I will be uploading a resource soon that I use as a way to keep interest in practising and perfecting work.

For now, here is a simple Christmas resource.

Maths is always fun, so doing fun lessons in the last week of term doesn't really change for me. (although I do let my prize winning class from the mistakes chart watch Flatland)

I do like some Christmas themes to my work though. Just like this post from solve my maths.

Here is a simple task on working with and finding equations of lines.

There are two tasks, and the first one is differentiated to allow easy entry.


Basically, Santa needs to plot his 2D Cartesian route between houses (obviously) and does it by plotting equations.

In the harder task: you are required to find the houses, having been given some information about the lines that need to be plotted.

All the documents are available here - including answers for the harder task.

Percentages with Dragons!

I don't have many differing resources for Percentages. It's probably up there with basic operations as the most important part of Mathematics to our learners, but since this is the case, there are bags of resources online to support with this.

I have two resources to add that are a little bit different:

Some higher level thinking and problem solving with percentages:

Next is my Dragon's Den percentages: It is for reviewing / revising percentages and there is a difficult one (with various compound interest calculations) and a more simpler one for practising basic increase and decrease.

Basically - the students invest a portion of their 10k into a choice of three companies. They can choose to invest in two if they like, but not all three.

After everyone has written in their investment choice on the attached sheet, they then work out the money they have made or lost. There is an example on the sheet, but I think it relates only to the higher powerpoint. Also, be warned that I teach to a point where we use multipliers, so if you don't do that you might have to tweak your answer sheet.

The biggest obstacle I have run into when running this activity is that students don't carry over the money correctly into the next round. 

All the companies exist (or have been pitched in the den) - and if I have given them a green, then they have had investment and may have been successful.

I trust my students to check each others work each round, and we take time to go through the workings at the end of each round. They will also never run out of money - as they just lose a percentage of their investment.

The best round is number two - none of the investment opportunities are worthwhile. The students did not need to invest in any if they don't want!

All the bits are available here:

Percentages - Dragon's Den and Other Problems


Finally - I'm sure you all know this clip: but it is a great plenary. The teacher doesn't know - but does anyone in your class?

The video is available via the link above as well.

Prime Numbers, Factors and Prime Factors

Here are some resources and ideas I use when teaching topics involving Primes and Prime Factors.

There are a few ways of spotting prime numbers - including Sieve of Eratosthenes, which I still think is a bit forced.

I like the links to Area (which they may not make straight away, depending on ability). I recommend doing this using multilink cubes: Idea taken from Don Steward

I give 25 cubes and ask the students to record how many ways they could rearrange cubes to represent the numbers from 1 - 25:

Then this leads to discussions about Factors, Square Numbers and what it takes to be a prime number.

If you want to go onto Prime factorisation, then try it a different way - show how powerful prime numbers can be. Set a target - make it a game - after a while allow them to choose one more number to add to the list. Ask them why they wanted that number..

Then comes lots of different activities:

Follow Me Cards - Squares and Primes

Rally Coach for HCF and LCM

Collective Memory - have the students copy the image down from memory and then fill in the numbers when done.

I can't believe I have never heard of Shikaku until this week. It is also referred to as rectangles. It's so perfect to consolidate factors (i.e. knowing that 10 could be one strip of ten or two strips of five) and also help with Area too.

This website allows you to choose loads of different levels of difficulty, meaning differentiation is easy! Also can be done on the website (with timings for extra competition) or printed. There are also a bunch of apps too with the game.

My last resource this post is Factors bingo - if you haven't played this before I will be surprised, but nevertheless here are the rules:

Other places to look for resources on this include, as usual, Don Steward's median blog.

Also check out some good Factor resources on resourceaholic

My last comment is really about selling this topic, particularly primes. There are lots of interesting research and books about prime numbers, and whilst much of it would go over many student's heads, I still think there is value in you discussing that these things are out there. Sound enthused about things you have read, the fact that there are monetary prizes for finding primes, or that internet encryption is based on the idea that no-one has found a quick way to check if a number is a prime number.

Thanks - any other good links then let me know!

Number - Place Value Resources

One of the easier topics in the curriculum - Place Value - can still perplex many students, particularly when talking about the values of the digits after the decimal point.

I still have students who struggle with ordering decimals and calculating which is closest to a certain value. I also come across students who struggle with the terminology.

Place value is one of those topics than can be addressed through mini activities throughout the year, and it always helps to reinforce the topic - even with high ability students.

I like this as a starter:

The discussion is important afterwards - question their strategies. There is also a harder set as well, which involve decimals. Hopefully some discussion about place value will occur.

Link - Place Value Starter

Another useful way to introduce some 'fun' (of course it is all fun) is with the 'Place Value Game' . There are many variations of this, I don't claim this as my own by any stretch. Mine has a full class version (which I usually play last lesson of term) and a two player version.

Link - Place Value Game


I move onto a Prezi which zooms into a unit to show that it can then broken down into smaller denominations.

We talk about notation then - which one is called what, and why. I think it is super important to explain what 1/10 is. It is a wow moment to many that 0.1 actually shows one tenth. 0.6 is six tenths so 6/10.

One way to consolidate is to play Place Value Bingo. This is a sneaky resource I made. Its a fairly straightforward Bingo - but great for assessing progress. If you play to Full House - which isn't long at all - then you'll end up with 1 in 7 of your class winning at the same time. If you then play one more slide - everyone will win.
So... if there are any students who don't have Bingo - make a note, tell them unlucky, and you know they need some support.

Link - Place Value Bingo

Don Stewards Blog as always, has some good resources with place value and decimals, but the best are found under Decimals labels rather than place value.

I particularly like Decimal Nim:

Finally, two worksheets I use, mainly for lower ability - or an easy early in the year homework.

Rearranging decimals given the text, or spotting the missing place value - is actually done quite poorly in a lot of cases. Something different to many other questions.


Comparing decimals worksheet - not particularly all singing or dancing - but it does a job. I like the extension at the bottom of this sheet - and the rearranging letters section spells out MR HILL SMELLS, so you might want to change that. I tell my class that I got the sheet from a fellow teacher, and that I don't know the answer. Bit of acting when I hear the answer and it generates some cheap laughs :)

Any other ideas out there?

Maths Across The Curriculum - English

All teachers are now under pressure to include some elements of basic English and Maths across all subjects. Let me be clear here - this is not about improving spelling or reading within the maths scheme of work. My aim on this section of blog is to give some ideas to actually team teach for a few lessons, giving equal space to, in this case, English and Maths.



Idea #1

Debating Maths

This is great for a mixed class - or one where you have students who often say things like "what is the point in doing this?" "when will I use this?"

Debate Questions:

Is maths useful when you leave school?
Is maths the most important subject at school?
Is maths fun?

I'm eager to hear of any other ideas, but the first one is what I will be leading with. By giving the students time in English to learn about persuasive argumentative writing, allowing them to research and find out themselves exactly why maths is important, can not only lead to good collaboration between subjects, but will hopefully encourage them to find all the reasons why maths rocks.


Idea #2

A new education minister has decided that Maths will be scrapped from the curriculum as it was his least favourite subject. By using examples of real life applications of maths learnt in school, write a formal letter to the minister against the plans.

Idea #3 - could link in to Food Tech as well

For a cook book, explain with clear instructions how to chance the recipe ingredients for4 people to 6 people, or to 10 people, or to n people. It should be clear enough for anyone to understand. With an example.

Idea #4

Pick a persuasive argument that can be backed up by statistics, Chelsea are the best team in Europe, One Direction are better than the Beatles, Films with female heroes are worse than male heroes. Hollister is overpriced for it's market, Beats headphones are selling faster than Dr.Dre's music etc. The school is getting better because grades are getting better etc..
In the Maths lessons, find and analyse data, understand data representation. In English, create a presentation, letter or whatever to highlight the statistics.

Idea #5

Maths fun with English language

Pick two or three novels, pick a sample page in each. What is the average word length on these pages? What average is better to use? Does Charles Dickens write more, longer words than JK Rowling? is their a difference because of the market audience?
How many similes in a chapter? How many uses of adverbs etc.
What about lengths of books, does that have an effect on popularity? If you wanted to write a classic novel, what length should it be?
Just for a bit more fun - Classics Vs Modern, UK v US, who uses the letter z more often? and so on.....

Idea #6

It's a bit obvious, but writing a newspaper article from the point of a mathematical discovery - or just
about a revelation on how to answer fractions.

 

 

 

But then again, who reads newspapers now anyway?

 

 

Why not some successive tweets from Pythagoras, or a facebook profile etc...

 

Idea #7

 

My colleague @MissArcherMaths ran a cross curricular activity with English involving promoting their own supermarket chain. They included offers and promotions and linked it to their presentation.

The Yr7s loved it - they had their own stalls and I played the Inspector, grilling them about their supermarket offers.

 

 

As usual - please fill me in with any ideas you might use to link the subjects together.