# 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?

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.

# 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?

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!