# Challenge Your Mathematics Students …

To achieve the highest grades at GCSE (taken in the UK by students age 15-16) students will need to be good problem solvers which include being able to make and use connections between different parts of Mathematics. There are many suggested resources in the Problem Solving Presentation.

For older students (16+) I have included Underground Mathematics. I have also used Undeground Mathematics resources with my very able GCSE students; see for example Introducing Calculus. There are many Underground Mathematics Resource Types. One of the types I have written on before is the Review Questions which in the words of the Underground Maths Team:

### These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Checking the Review Question type in this category we see that O/AO-level questions are included.

I see several questions here that will provide appropriate challenge for my GCSE students.
For example:

Can we fully factorise x4+4y4?
Starts with a Show that….
And then we factorise and will need to recall the difference of two squares.
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.

Can we simplify these algebraic fractions?
Review algebraic fractions, simplifcation including the difference of two squares and quadratic equations. We could of course also talk about functions (including domain and range as these students are also studyling AQA’s Level 2 Further Mathematics)

Can we simplify these simultaneous equations of degree 1 and 2?
Solve simultaneous equations, we’ll need simplification of algebraic fractions again and we can talk about the graphical solution of equations. We will also need to factorise a quadratic, 3y2−y−80 with a coefficient which is not 1 for the square term. We have all decided we are fans of the Box Method!

You can also search on the Line and the Station to narrow your search; you can also save and categorise your favourites by creating a (free) account.

# Mathematical Miscellany #5

Twitter can be useful for alerting one to resources / news, note the first two items.

Problem Solving – an open access (free) book which looks at research on Mathematical Problem Solving.

Jonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. Note that you can show solutions for the GCSE questions – there is a link at the bottom of the page for each question.

The page on Apps has recently been updated, there are fuller descriptions of the various apps and note the addition of Summaze2 from MEI and Sigma. A wonderful example of a free app – Maths to make you think, visually attractive and no irritating adverts trying to make you buy the premium edition!

In Mathematical Miscellany 4, I mentioned the excellent Linar Equations Calculator; for an excellent way to illustrate the balance method of solving linear equations, try this manipulative on Mathisfun, this is very simple to use and does not require the user to log in.

UK Results 2016 – a new page has been created which I will update as A Level & GCSE results / news comes in. As I do each year, I will provide links to the results statistics and grade boundaries for the various examination boards.

Note my Twitter Examinations list. Check this for announcements / news. (You do not have to be a Twitter subscriber to use the list.)

Whilst this is Mathematical Miscellany #5 I have been writing these compilation posts for quite some time. They were at one time ‘Thoughts this week…”. Previous posts are all filed under the category (note the Category menu on the right) Mathematical Miscellany.

By Colleen Young

# The Standards Unit – Mathematics

This is an outstanding resource – there are so many excellent activities here for the secondary classroom.

The resources are hosted by Nottingham University, including all the pdf files very clearly indexed. Note that this site includes the complete set of resources including the software; however, this software no longer works on modern browsers and mobile devices, but see note below for HTML5 versions.

Tom Button has rewritten the Traffic Simulations in GeoGebra for A5: Interpreting Distance-Time Graphs with a Computer.

##### See also this post onWisweb Applets HTML5which has applets and lessons using the programs referred to in the Standards Unit. These wonderful applets were created by Utrecht University, they have built the learning environment Numworx around these.

The Professional Development resources are excellent. Look at PD1 ‘Getting Started’ for example, note PD1.4 on page 9 – 8 Principles for Effective Teaching.

IWB Materials This website has come about as a result of the NCETM research project: Enabling enhanced mathematics teaching with some interactive whiteboards (September 2006- September 2008) and was supported by the IWB research team at Keele University and the Spire Maths team.

PowerPoint Files
MMT has written a set of PowerPoint files for almost all of these excellent resources, he has made them – in his own words ‘classroom ready’. MMT has provided the resources in an editable format so that they can be tweaked to your own requirements. Thank you MMT! These files are available directly from Dropbox; note they are also hosted on Craig Barton’s site.

Standards Unit A1:Expressions – MMT PowerPoint

I have used activity S4 many times and created a PowerPoint including all the solutions.

A set of Desmos Classroom Activities by Ben Sparks features some of the Standards Unit Tasks. See also this #TMMathsIcons collection of Desmos Classroom Activities by Kathryn Darwin which features several Standards Unit activities.

Alternatively:
All materials – hosted by National STEM Centre. Including:
Mostly Algebra   Mostly Number  Mostly Statistics   Mostly Shape and Space   Mostly Calculus   Others

# Happy Numbers and more…

Continuing my theme from last week I have added a new page to the Investigations series – one of my all time favourites – Happy Numbers.

I have also added further resources to the Investigations – Links and Resources page. From the National STEM Centre which is an incredible source of resources for STEM subjects we have

Lorraine Mottershead’s book: Investigations a complete book by including solutions to the puzzles and investigations.

Also on the NMoational STEM Centre from David Kirby and Peter Patilla we have Maths Investigations – Pupils’ Workshop together with a comprehensive teachers’ guide.

# Team Challenges

If you are looking for some problems to use for Mathematics Team Challenges in school or just for class activities with a difference which will help develop mathematical skills there are some excellent sources of materials.

The United Kingdom Mathematics Trust have annual team challenges for junior : UK years 8 and 9 (ages 12-14, I have also successfully used these with Year 10) and senior: UK years 11, 12 and 13 (ages 15-18). UKMT publish materials free online for use in school, these can of course be used for all students and make an excellent class activity for individuals or groups. The junior materials can be found here and senior here. I have found the crossnumber puzzles an excellent activity for the end of term, these are crosswords with a difference as lots of the clues depend on other clues! Which clues to solve first?! All materials needed and full instructions are provided. Note the Supervisor’s booklet with answers and instructions; this includes the complete crossword grid and clues. I have used the Group competition and relay race problems very successfully in class.

Another great source is the resources from Math-Team-Matics a competition which was from Grand Valley State University, you can see problems here so you could try any of these activities in class. The individual test has multiple choice questions. I like the look of the 2013 team challenge – a combination of staircases and painted cubes with surface area thrown in as well- I’ll definitely be using that!