295. I know how to integrate, but which rule to use?

You know that point when you’ve covered the Integration content in A2, the class can do all the different forms and then you set mixed questions … it’s like it’s in a different language. All that wonderful knowledge seeps out like water in a sieve. There must be a help sheet or tool that gives students a starting point, until their confidence and experience grows?

core 4 integration flowchart

Rewind to proving an integration rule. I was discussing a textbook proof of an integration rule with a student and I just didn’t like it. It niggled in my head that I’d been shown a better method when I was first learning this stuff. After a quick dash to the stockroom and a climb up a step ladder, I found a later edition of the textbook I’d used at A-Level. I was right – the Bostock & Chandler proof was far more elegant and comprehensible. Problem solved!

While I had this book out I had a flick through the pages. A flowchart caught my eye – not a fancy infographic, a proper ‘get the flowchart stencil out’ chart. It basically talks students through how to choose an integration strategy. I could have photocopied the page, but it was rubbish quality when I tried. I believe the book is now out of print, so I have recreated the flowchart page with full credit to it’s source. I hope it helps your students as much as it has mine.

C4 Integration flowchart (pdf)

294. Rough guide to new AQA GCSE Maths course

If you are using the new AQA specification for GCSE Maths, you might want to know that I’ve edited the Rough Guide to new GCSE Maths post to include an appropriate AQA version. It’s a collaboration with the splendid @missradders. Click on the link to view the post with all the versions.

293. Boxing Bounds

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!

291. Elves and Trees

elf-clip-art-elf1

Image credit: www.clipartpanda.com

 

Here is a quick festive probability resource for you covering elves, outcomes and tree diagrams. The task starts with logically listing outcomes, before looking at working with tree diagrams in the extension.

Elves outfits tree diagrams (pdf)

290. Alcoholic Percentages

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:

image

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?

289. The secret formula for success

You may remember this advert for Frosties cereal (US Frosted Flakes) from your childhood. If you do you’ve been around as long as me:

What was Tony’s secret formula? We never found out!

Enough reminiscing I hear you cry! How does this help anyone?

Well, in the new GCSE exam specifications the formulae sheets have gone. Specific formulae may be given in an individual question, but due to the lack of a working crystal ball we don’t know the frequency with which this will happen. To help with this I have typed up the Edexcel formulae into a PowerPoint. You can print it out and put it around the room, you could have a formula of the week, you could leave a slideshow running while students work, you could even print it small on card and make a pack of flashcards. Mine are laminated and hanging from a washing line, I’m going to move them around so that students have a varied view.

Whatever you do, increased familiarity improves retention – just think back to the posters you regularly saw as a child. I have made different versions for different situations – Edexcel vs no exam board, white background vs pale blue background, pdf vs pptx. Download whichever version you need:

Edexcel No Formulae Sheet blue (pptx)

Edexcel No Formulae sheet wihite (pptx)

Edexcel No Formulae Sheet blue (pdf)

Edexcel No Formulae Sheet white (pdf)

GCSE No Formulae Sheet blue (pptx)

GCSE No Formulae Sheet white (pptx)

GCSE No Formulae Sheet blue (pdf)

GCSE No Formulae Sheet white (pdf)