Jun 25 2016

Review Questions – Underground Mathematics

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.

May 18 2016

Systematic Listing Strategies

Transum – Combinations resources

Number

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 Combination Starters

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. There is alao a whole section on Systematic Listing Strategies with activities from level 1 to level 7. Note Transum’s clear index for teachers and for students, Maths Map with numerous activities to support their learning.

On Corbett Maths, see Product Rule for Counting.

Nrich – Fraction Combinations

Nrich has a sophisticated problem, Fraction Combinations which not only asks students to systematically list possibilities but work with fractions too.

benmossmaths – area problem

Ben Moss has a rather nice area problem which it seems to me will involve students in some systematic listing! I tried this with Year 7 and it worked very well.

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).

AQA Teaching Guidance

And finally (for now!) Don Steward has this bracelets or necklaces problem.

Don Steward – combinations

Have a look at this post on Just Maths: Product Rule for Counting which includes Pearson / Edexcel exam questions and solutions.

Just Maths

Bobbie Bear – from NCTM Illuminations, whilst aimed at younger students, how many ways can you give Bobbie Bear a different outfit? An excellent example when thinking about systematic listing strategies!

May 1 2016

Fractions Resources

For a copy of the presentation: Fractions Resources (PowerPoint) or pdf: Fractions Resources

Apr 5 2016

Is That A BIG NUMBER?

Twitter (quite rightly!) suggested I might like to follow IsThatABigNumber. The aims of the site are as follows:

Put numbers in context
Promote numeracy
Share number facts
Develop Number Sense

Exploring the menu at the top, note as well as the home page, we have other options, we could ask for example how big is 5km? The question returns a very comprehensive answer with comparisons to many other numbers! I do like the various quotes that appear randomly, as I was exploring I saw (very appropriate for someone responsible for Assessment) from Charles Babbage: “Errors using inadequate data are much less than those using no data at all”.

Other options as you can see include conversion, we could convert 1cm to 1 m (though I can already do that with WolframAlpha which returns rather more comparisons, and can also do it myself, I hasten to add!). Alternatively look at some random Number Facts or an interesting option – try a quiz.

On the home page we can the site is in its early stages, (the authors welcome feedback). Numbers in the News is a good idea. I wish the authors well – promoting numeracy just has to be a good thing!

On the subject of big numbers, I have recently completely checked and made major updates to my post on Standard Form resources.

Sep 20 2015

Long Division & Multiplication – Formal Methods

The UK National Curriculum now specifies that:
Pupils should be taught to:

Year 6 (UK KS2 age 10-11)

multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

Appendix 1 of the KS2 document includes the examples below and states that “the examples of formal written methods for all four operations illustrate the range of methods that could be taught. It is not intended to be an exhaustive list, nor is it intended to show progression in formal written methods. For example, the exact position of intermediate calculations (superscript and subscript digits) will vary depending on the method and format used. For multiplication, some pupils may include an addition symbol when adding partial products. For division, some pupils may include a subtraction symbol when subtracting multiples of the divisor.

And at KS3 (UK age 11-14) we are reminded that students should be able to “use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative”.

The Mathematics documents can all be found on this page.

Mathsonline long multiplication
From MathsOnline, comes a clear step by step demonstration of long multiplication, (uses html). Each step is clearly explained. Long Division is also very clearly illustrated and for your older students we can extend to Algebraic Long Division. Refreshing the page generates a new example each time.
Mathisfun explains long division very clearly and additionally offers questions and worksheets. Similar resources are available for Long Multiplication and for Algebraic long division.