An update! **Happy New Year 2018!**

# Category Number

# Numbers – Visualizations

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**.

On the subject of Diagrams generally I have several **posts on the subject**. You can see Fawn Nguyen’s lovely Visual Patterns in **Diagrams in Mathematics.**

# 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.

# Systematic Listing Strategies

## 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 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.

**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).

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.

# Fractions Resources

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