An update! Happy New Year 2018!
I have several references in various places on this blog to some great visualizations.
Time to put them all together!
From Jeffrey Ventrella this wonderful Composite Number Tree – I have used this successfully with many students. It makes a great starter. Students can work out themselves how the tree is being formed and comment on any patterns they notice.
Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dance which tells the tale of the animation. Noting his reference to Brent Yorgey’s factorization diagrams led me to Brent’s own later post, More factorisation Diagrams. I love Brent’s use of colour here. If you want even more on these great diagrams he has more information and links on this page on his blog, The Math Less Traveled.
I wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications I believe this site will provide us with rich resources for these new specifications.
Each section includes Review Questions, look at Thinking about Algebra for example; scroll down the different resource types for the Review questions for this station.
Alternatively you can browse all the Review questions.
An excellent feature of Underground Mathematics is the excellent search facility; we could look at the Review questions by type. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.
See the example question below, for each review question you will find the question, a suggestion, the solution and sometimes suggestions for taking it further with for example GeoGebra resources.
Note the star by the title – if you choose to log on to the site (you don’t have to but it’s a very good idea!) you can save any favourite resources to your collection.
I can never resist a quick illustration on Desmos! I think I’ll start an Underground Maths Desmos collection! Note the use of the hyperlink on Desmos to link to the question.
Select the image for the Desmos page.
I think we have a wonderful supply of excellent questions here to challenge our students and help them see connections between the various areas of the subject. These are ideal to use with A Level students; some are also useful for higher level GCSE students aiming at those top grades or Level 2 Further Maths students. Any student who wants to study Mathematics at university should certainly be using this site.
5. apply systematic listing strategies including use of the product rule for counting
The UK GCSE specifications include systematic listing strategies.
Some resources for this topic:
Transum Mathematics has many excellent resources including a section on Combinations, where you will find Combinations starters, activities and investigations. The Transum site includes links to some videos includes The Counting Principle which provides a clear introduction. Note Transum’s clear index for teachers and for students, Maths Map with numerous activities to support their learning.
Nrich has a sophisticated problem, Fraction Combinations which not only asks students to systematically list possibilities but work with fractions too.
AQA have a very clear Teaching Guidance document with many useful examples, I use these a lot in class. If you use or are considering using AQA you can register here (there seems to be a problem with the link on the Teaching Guidance document page).
And finally (for now!) Don Steward has this bracelets or necklaces problem.
Have a look at this post on Just Maths: Product Rule for Counting which includes Pearson / Edexcel exam questions and solutions.