Category Archives: Number

293. Boxing Bounds

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I thought this would make a nice little starter – address a few different topics, bit of problem solving, all over in 15 minutes. How wrong I was!

The Question: A company packs toys into boxes which measure 12cm by 8cm by 10cm (to the nearest centimetre). The boxes are packed into crates which measure 1m by 0.75m by 0.8m (to the nearest centimetre).
(a) Basic question – How many boxes fit into the crate?
(b) What is the maximum volume of a toy box?
(c) What is the minimum volume of the crate?
(d) Look at your answers to (b) and (c) – do they affect your answer to (a)?

It was a simple question about fitting toy boxes into a shipping crate. It extended to looking at upper and lower bounds, then recalculating given this extra information. Simple? No chance!

Problem One
Not changing to the same units

Problem Two
Working out the two volumes and dividing to find the number of toys. When challenged on this, it took a while to get through to the basics of how many toys actually fit – mangled toys and split up boxes don’t sell well.

Problem Three
Maximising the arrangement of boxes – remainders mean empty space

Problem Four
Using the information from Problem Three to find the total number of toys

Problem Five
Working out the dimensions and volume of the empty space in the box

Problem Six
Trying to convert centimetres cubed into metres cubed. I don’t even know why they wanted too!

Problem Seven/Eight
What’s an upper/lower bound?

Problem Nine
What do you mean that the original answer changes when the box size alters?

Problem Ten
All those who weren’t paying attention when you went over Problem Two and don’t ‘get’ why the answer isn’t 625!

290. Alcoholic Percentages

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The season of gratuitous excess is upon us and the reminders about safely consuming alcohol are popping up in supermarkets … usually next to the massive bottle of brandy, which are on special offer! We educators are counting the days to the holiday break.

But wait!

Keep your eyes peeled for all the alcohol awareness promotions. My local supermarket had information leaflets and these goodies:

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Forget doing percentages about sale prices. How about working out the volume of alcohol in different beverages? Finding out how easy it could be to exceed the recommended intake? A bit of education of the effects of alcohol in a cross curricular lesson?

Now how much brandy soaked Christmas cake is equivalent to one unit of alcohol?

288. Seriously, when am I going to use this?

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Oh, that question … heard often from the mouths of those who will not go on to study Maths at a higher level! But when it’s more able students who can’t see the necessity of fundamental principles … Well, that’s a bit worrying.

M’colleague, Mr D, has nailed the answer to this question. When I say ‘nailed’ I obviously mean ‘stuck’ and he has literally* stuck the answer on the wall.
*Note: Mathematician using correct definition of literally.

Here you go:

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If you zoom in on this student work, on A2 Differentiation, you can see that he has annotated all the skills used and when you first meet them in the curriculum:

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Such a simple idea to tie together seemingly unrelated parts of the Maths curriculum. It also reinforces the need to keep all basic skills sharp.

I’d say it was genius, but then I’d never hear the end of it!

282. Round the Venn

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My next class neighbour, Mr D, has been evangelising about venn diagrams since he did the TAM (Teach A-level Mathematics) course. His lesson on equations and graphs using venn diagrams was brilliant! Then, at MathsConf5, Craig Barton (@mrbartonmaths) shared his love of venn diagrams.

And they are on the new english GCSE Maths syllabus.

In light of all this, I introduced venn diagrams as a vehicle for probability (Y10) and rounding (Y9).

Introduction

First of all I used the films of Tim Burton, Johnny Depp and Helena Bonham-Carter to introduce a triple venn diagram, with the box to represent everything – I like dropping in the proper forms or technical bits early on in all topics.

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We had quite a lengthy conversation about films, including why the Bond film could be on the diagram. The discreet use of IMDB (with my permission) settled some arguments too!

Rounding

I wanted my Year 9s to consider the differences and similarities between different forms of rounding. I created a simple diagram for them to complete where they compare ‘nearest ten, ‘one decimal place’ and ‘two significant figures’. You can download it here:

Rounding Venn Diagram worksheet

Probability

For my probability lesson I used the probability PowerPoint by Craig Barton. You can link to his resources here:

Mr Barton’s venn diagram resources

281. Mathsconf5 resources

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Hi to all those who went to Mathsconf5, in Sheffield.

If you liked the proportion snapdragon you can download it here: Proportion Snapdragon

If you liked the trigonometry snapdragon you can download it here: Snapdragon download

There are instructions for it here: Trigonometry Snapdragon

If you’d like a snapdragon template or instructions on how to fold it click here: http://mathssandpit.co.uk/blog/?p=667

If you want more foldables after the Paper Maths session, run by the lovely @MsSteel_Maths, I can recommend this resource: Foldables by Dinah Zike

(Note: this pdf is widely available and a version of it is free to download from Dinah Zike’s website, however if you represent Ms Zike and there is a copyright issue please contact me in the comments below)

280. BIDMAS & chips – a second helping

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Back in post 231, I discussed using a Fish & Chip shop to introduce BIDMAS. I’ve since taught this topic again and written a resource to go with it:

BIDMAS & chips

There are three different menus – if you hand them out correctly no two pupils should have the same menu. Pupils write their names on the front and fold the menu in half so that they can see the price list.

If you go through the activity in post 231, pupils can use their menus to work out totals without copying from each other. You can then get the pupils to gather into the three different shop groups and argue out the misconceptions.

I used this on my first lesson this year with a shared Year 7 class, in front of five PGCE students and it worked a treat!

269. Snappy Proportion

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Proportion … it comes in so many forms and different students grasp different elements at different speeds. Differentiation hell!

What about a little resource that offers up 4x8x8 variations of question ranging from simple direct to proportion to inversely proportional to the square? It’s not a new app, it’s an old app – a fortune-teller snapdragon:

proportion_snapdragon

Print, cut and fold (see 92. Snapdragon Fun for instructions)

  • The first decision chooses level of difficulty – students pick a number and count through the opening/shutting process.
  • The second gives the information to calculate k (eg y=kx) – the number of open/shut moves is specified.
  • The third asks you to apply your equation to a hidden number.
  • Students increase the level of challenge as they do more questions.

Download the pdf here: Proportion Snapdragon

The editable version is available here: Editable Proportion Snapdragon

You may wish to enlarge the pdf on a photocopier to make it more manageable for bigger hands.