Just over three years ago I started writing compilation posts, a kind of newsletter-style – a mix of mathematical goodies. I was inspired by Doug Belshaw’s Thoughts This Week – now Thought Shrapnel. It’s been on my blog to-do list to revisit this idea again; how appropriate that Doug’s Thought Shrapnel today includes newsletters he enjoys. I was very happily distracted by some of these great compilation posts this morning and particularly struck by a post from Doug’s first suggestion Austin Kleon – important for any blogger, What to leave out and what to leave in. Some great quotes there including Elmore Leonard’s:
“Try to leave out all the parts readers skip.”
(Wondering which bits you are all skipping here!)
So I decided it was time for a new title for posts of this kind – hence ‘Mathematical Miscellany’. Previous compilation posts can be found under the category (note the drop down menu on the right for categories) Mathematical Miscellany.
In class With my Year 10 GCSE class I used some ideas from a site I often use: Mudd Math Fun Facts. Squares Ending in 5 and Multiplication by 11both made excellent starters, we looked at proofs as well as enjoying the mental Maths tricks! You will find more lightning arithmetic suggestions on the site.
Resources OCR have published some very useful new resources; I have written before on their Check in tests. New tests for Foundation and Higher have been added. The Higher resources include Triangle mensuration, Language of functions and Algebraic expressions; these really are excellent resources and I will definitely be using all of them.
Working with my Further Mathematics students on a work / energy question based on the Jack and Jill nursery rhyme started a lively discussion on what other stories and rhymes we could turn into Mechanics questions! We all immediately thought of Humpty Dumpty! I think the examiner was having fun with this one – the question carries on with poor Jack falling over and hurting himself. Jill seems to get off lightly unlike the original! If anyone is interested this is question 4 on the June 2007 MEI M2 paper.
Staying with the subject of Complex Numbers, with the same students, another discussion we had recently when looking at Complex Numbers was the need to write clearly, a z can look like a 2 for example. See Mathematical Handwriting on Mathematics for Students. Also on Mathematics for Students I have updated the page giving links to A Level Exam papersto include some really useful solutions resources such as David Smith’s worked solutions.
In that presentation, Daisy discussed the use of Multiple Choice Questions, something I have always liked using in my teaching. Daisy’s discussion of making questions harder by changing the number of correct answers reminded me of the, in my opinion excellent, Multiple Choice A Level papers which the then London board included in their A Level Mathematics examinations (London Syllabus B) (see an example below).
In the meantime, happily we do have access to some Multiple Choice questions online and I thought it would be useful to bring them together in one place.
Mathisfun has an extensive library of very clear diagrams and explanations and also multiple choice questions for most topics. Use the Indexto find the topic you want and note that for most topics you will see some questions at the end.
As you can see from the Index all ages are catered for including older students; I have used the clear explanations and questions on finding the inverse of a 3×3 matrix with Further Mathematicians for example. Once you have selected an answer a complete solution is provided. Note the Question Database – some exploring to do I think!
The Who Wants To Be A Millionaire format can provide a fun way to present Multiple Choice quizzes. A Google search returns various resources and of course, provides you with PowerPoint Millionnaire templates you can adapt for your own use. Some highlights from that search, the Primary Resources files use a simple and clear format and William Enemy has described a resource on Great Maths Teaching Ideaswhich also usesthat template; such a good idea to have all students answer all questions and add up their winnings! Another example – Algebra on TES.
There are various options for creating your own multiple choice questions. That Quizis simple but effective – all free and no adverts. There are many quizzes already available on a variety of topics, it is also possible to create your own quizzes. Teachers can register and add classes if they wish. You can search the many quizzes available, searching for Fractions, for example, led me to this quiz.
For an alternative way to set up a simple quiz try Testmoz. No registration is required. This has been written by Matt Johnson, an undergraduate student – the instructions are all very clear and you can check out the FAQ! (I love those FAQ! For example: I lost my quiz URL can you retrieve it for me? Answer: No). Try this test on Directed Numbers– log in as a student, the passcode is cy090610
More to Explore!
In Daisy’s talk mentioned at the beginning of this post she mentioned British Columbia questions in her discussion of multiple choice questions, a quick search led me to this Pre-Calculus paperfor example...
Following a recent test for Year 10 (UK age 14-15) I wanted to use colour to show clearly a way to make sure all terms have been included when three brackets have to be expanded (new to the UK GCSE qualification). (Colour can be so useful in Mathematics – something I have written on before).
I have created this example using Excel. This is just a simple example with positive coefficients only; I wanted to start by being clear on making sure that all combinations are included. There are various FOIL and quick methods available if you search but my own preference is a more systematic approach. An advantage of using Excel is the ability to trace precedents (Formulas menu).
The numbers could be changed and of course any examples could be made up and checked on WolframAlpha.