Mathematical Miscellany #14

Years 7 and 8 (UK ages 11-12 and 12-13) Summer Assessments

From the White Rose Maths Hub, (@WRMathsHub on Twitter) Year 7 and 8 Summer assessments.  I have mentioned the White Rose team before, recall their excellent Problem Solving resource.

The GCSE Problem Solving Questions of the Day – Compilation  available free on TES Resources. The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided.

GeoBoard Activities
Answering a question from a reader on unique triangles on a 4×4 GeoBoard, I have updated GeoBoard Activities to include the solution to this and also added several new activities, including the use of GeoGebra.

Staying with the subject of GeoGebra, I discovered some very nice resources by Tom Carpenter,  I do like his Line Graph worksheet which demonstrate how to draw a line graph and/or how to interpret a line graph.

As I mentioned in last week’s post on GeoGebra, even if you are not familiar with GeoGebra, there are so many resources already available ready to use.

I have mentioned the excellent PhET simulations before. This on Least Squares Regression provides a very easy to use demonstration. Try and find the line of best fit then see how closely your line matches the actual line.

On this subject you can also very easily use GeoGebra, Desmos, or WolframAlpha for regression, full details with examples are provided here.

See more posts in the Mathematical Miscellany series. Collections of mathematical goodies!

Mathematical Miscellany #13

From TES, comes a collection of esources hand-picked by the Tes Maths Panel, organised by topic area and selected for their relevance to the new specifications. This is an extensive collection of quality resources. Checking Probability for exmple we see an excellent selection of free resources, including Venn Diagrams for teaching and learning.

This Venn Diagrams post with many resources for teaching this topic has been updated to include the TES collection.

Another update to the Venn Diagrams collection comes from Transum.

Transum

Try Venn Totals 4 different levels of exercises which can all be checked are available. Level 1 – Reading information from a Venn diagram containing two intersecting sets. Level 2 – Reading information from a Venn diagram containing three intersecting sets. Level 3 – Adding information to a Venn diagram containing three intersecting sets. Level 4 – Adding information to a Venn diagram containing three intersecting sets with some problem solving required. There are also exam style questions, to see the worked solutions a subscription is required.

I have written on Transum before, with its very clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning the site is very easy to navigate. The resources are very clear and attractively presented, they display well for demonstration in class as well as being very good for self study for students.
Look at this series on Transformations for example:

Level 5 is on transformations and matrices, very useful for older students studying Level 2 or A Level Further Maths.

This GCSE Exam Preparation resource from JustMaths made me smile, a lovely mix of humour and some very useful reminders.

Mel’s inspiration came from Edexcel’s Maths Emporium Guides to Life: GCSE Mathematics Examinations. Brilliant!

On the subject of student advice, one of my Year 11 students asked me to confirm for her which transformations are examined at GCSE, a slight change here from the old spec hence her question. I answered her question with a post on Mathematics for Students as I thought it would be useful for others. Transformations of graphs includes Desmos pages for reflections and translations as required at GCSE (see GCSE content on Algebra:

13.sketch translations and reflections of a given function.

The post also includes a couple of examples on finding the equation of the transformed graph.

Another query was just a quick reminder on the required constructions.

A reminder from Mathematical Miscellany #12, I am very much looking forward to trying Jamie Frost’s wonderful homework site with my Year 9 group.

And finally another reminder because I think it is such an important resource – just in case you missed the news that Underground Maths are helping teachers everywhere who are preparing for the new A Level. Many brilliant resources suggestions are clearly mapped to the subject content for the new A Level.

Mathematical Miscellany #12

On his outstanding website full of very high quality resources, drfrostmaths.com, Jamie Frost has now launched his new Homework Site.

Completely free this does a lot! Practise questions on National Curriculum and enrichment topics, choosing questions by topic and by diffculty, perhaps choose UKMT Maths Challenge questions as these are in the extensive database too. Students can practise independently and earn points and trophies. Teachers can set and monitor work using the powerful Data Analytic Feature. I will certainly be trying this with my students and easily uploaded my Year 9 class which took moments.

Something I alway do is add myself to my classes so I can get the student view, Colleen Student is a very busy student – she’s in a lot of classes! Jamie Frost has this as an easy feature already provided; you can be Demo McDemoFace (love the name!) in any class.

So here’s Demo McDemoFace practising her Algebra!

DrFrostMaths

What a sophisticated way to choose questions, not just the subject but the difficulty as well and additional skills to include or exclude.

So I can confirm that it is very easy to use as a student, Demo McDemoFace did a bit of Algebra and earned a trophy!

The interface for entering solutions is intuitive and very easy to use,

Explore this site and sign up your students. Thank you Dr Frost from teachers everywhere! This looks superb. More to follow on this.

MEI have published this video (18 minutes) to introduce features of the new MEI AS/A level Maths specs, explaining the decisions made and how they support good teaching, learning and assessment. MEI’s YouTube Channel includes this and other helpful videos. This is helpful in its discussion of the new requirements for Statistics

On the subject of new A Level Specifications I am working on the series of pages on  A Level Reform. There have been several updates recently, a work in progress, there is much to do here and I am very much looking forward to working with the new specification. Using for example Desmos is something I do all the time anyway so I am delighted that the new specifications require the Use of Technology. Quite right too to assess the Use of Data in Statistics and the use of large data sets. MEI discuss their use of Data in the video above.

For schools who use AQA’s excellent Level 2 Further Mathematics Qualification, news from AQA states that this qualification has been extended and will be available for all students in 2019. AQA’s intention is “to redevelop it for first assessment in 2020 to ensure that it still fulfils its stated purpose of filling the gap between GCSE Maths and further studies in Maths at Level 3.”

My Year 11s this year have been studying both AQA’s GCSE 9-1 course and the Level 2 Further Maths; these have made a wonderful complementary pair. Many of the Further Mathematics questions have provided additional practice for the standard GCSE course. The extension will allow us some breathing space to keep working on the new GCSE course and take on the new A level specifications.

And finally..
This has been doing the rounds recently and illustrates beautifully that caution is required in our statistical analysis! Be a little wary of summary statistics! From AUTODESK Research, “Same Stats, Different Graphs… Note that you can download a detailed paper by Justin Matejka and George Fitzmaurice of Autodesk Research.

Mathematical Miscellany #11

Desmos Geometry
An exciting space to watch! Chancing upon this tweet I saw that indeed we have an exciting possibility here as Desmos does Geometry! Early days right now and this is still in early beta.

Have a play – it’s very easy to use. There are some examples to investigate. Excellent to have vectors as an option in the line tool and I like the way that once a line or segment is drawn construction options are available.

See the Desmos blog post The Desmos Geometry Tool. Such a thoughtful post. Reading it reminded me why this is one of the few websites I use on a daily basis to help my students learn.

First, our goals are different than those embodied by most of those other tools. When we design products, we design first for students who struggle with math and we assume they may also struggle with technology. We strive for a student’s first creation with our tools to feel effortless and joyful. For that reason, our geometry tool has a far shorter list of features than some of those above. We will carefully expand that list over time, never trading power for ease-of-use.

I have always said that what I like about Desmos is the ease of use. A young student can just ask for a graph of a straight line and my Year 13s can play with Polar Curves for example.

With revision for examinations very much in mind at this time of year, have a look at Tying it together, a bundle from Underground Mathematics which looks at efficient revision for mathematics; to quote Underground Mathematics: “The resources in this bundle encourage students to bring together their experiences in multiple areas of mathematics, helping to reveal and reinforce connections between a variety of mathematical ideas and problem solving strategies”. (And note the free webinar on April 19th looking at revising effectively and sharing resources for AS revision.)

Being very conscious of our first students aiming for grade 9 GCSE I particularly like the fluency exercise Pick a Card which will be a great way to revise Quadratic Functions, linking together many student experiences in Algebra, functions and graphs. What’s the shared area for these two circles, another resource  in this bundle illustrates so well how a good diagram can help.

Pick a card is a Fluency Exercise, Note that you can search resources in many ways including by type.
(More on Underground Mathematics).

Staying with the subject of exam revision, The Learning Scientists have an important post here on studying with Retrieval Practice. For further valuable resources to support study techniques see the excellent downloadable materials on study strategies. Note how each strategy is backed up by research.

MEI Maths Item of the Month example

From MEI this curriculum mapping for their Maths Items of the month resources is a great resource, both for GCSE and A Level. (This has been added to the A Level Resources page.)

See all Mathematical Miscellany compilations.

Mathematical Miscellany #10

For any of your students studying for STEP direct them to this excellent portal from stepmaths.co.uk which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.

The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.

Note that you can also download a copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core MathematicsAdvanced Problems in Mathematics is excellent preparation for ANY undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.

See also, from Cambridge University, their STEP Support Programme and from Nrich, Prepare for University.

These details are also available on Mathematics for Students.

On the subject of challenging questions for older students and with revision on our minds, perhaps a good time to remind everyone of the excellent MadAsMaths site.

The AQA Mathematics AS and A Level specifciations have now been accredited. Watch the AQA website for further resources on the new specification. Checking Teaching Resources we see that AQA are developing their route maps; I have always found the GCSE route maps very helpful indeed.

AQA Route Map

Something I have used a great deal with my GCSE teaching for both the current and previous specifications is AQA’s detailed and very clear teaching guidance.

AQA Teaching Guidance

An A Level Teaching Guidance extract is available.

We can also see Command Words which reminds me a little of the Exam Terminology document so useful at GCSE. There seem to be versions of this document in various places, I believe the first time I used it was back in the days when there were more Examination Boards, this may well have come from the then Southern Examining Group!

Under Assessment resources we find Specimen Papers and mark schemes; also an Assessment Guide on using a large data set. On the subject of large data sets, for information on all the Examination Boards and large data sets, read Bruce Hampton’s clear and detailed comparison.

I have added an AQA page to the A Level Reform series.

Eduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also  the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

Staying with the subject of Statistics AQA and Edexcel have accredited GCSE specifications; note that coursework is no longer a requirement of GCSE Statistics.

See more in the Mathematical Miscellany Collection.

Mathematical Miscellany #9

Now on the outstanding Diagnostic Quesions site – United Kingdom Mathematics Trust Quizzes – choose a theme or a quiz with random topics. To use the resources will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.” (See this post for Diagnostic Examination Questions).

From AQA, on their ‘All About Maths‘ site see their Further Guidance and Practice Questions for the AO2 and AO3 requirements of the new 8300 GCSE. The 120 questions in this resource have been selected from legacy specifications which, to quote AQA “exemplify each of the strands of these Assessment Objectives and would therefore be suitable questions for the new GCSE as well.” AQA have arranged the questions in approximate order of difficulty andhave also divided them into those suitable for Foundation tier only, common to both tiers, and those suitable for Higher tier only, as well as by Assessment Objective. To

Remember from AQA we also have the excellent, GCSE Mathsematics: 90 maths problem  solving questions. These problems have been designed for use in supporting the teaching and learning of mathematics. There is a helpful intruductory section for teachers and note also the helpful Classification Tables by Strategy and by Content Area. Em,  has a brilliant PowerPoint with all the questions and answers – see it here.

Staying with problem solving, on TES Resources cchristian’s Multi-Stage Problem Solving is an excellent resource. These problems could make great starter activities.

Also, remember the GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team, @WRMathsHub available on TES Resources.

The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning now includes Year 7 material (UK age 11-12); an assessment is also available.

From author Captain Loui a TES resource, BIDMAS – Solve a Scooby Doo Mystery! Note that answers are provided in the author’s description of the resource. The theme is engaging but doesn’t get in the way of doing plenty of Mathematics!  Captain Loui’s resources are all free to use and as you can see have very favourable reviews.

Splat – Steve Wyborney

A resource that caught my eye recently is Steve Wyborney’s Splat! Definitely a resource I wnt to explore further; you can read Steve’s blog post and download the lessons here.

Thursday 2nd March is World Book Day; we could bring books and Mathematics together with some Statistics (at any time); have a look at this resource from TES, World Book Day Maths Data Investigation where students analyse word length and sentence length in some book extracts. UK readers who remember Statistics coursework, this brings back memories of AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability. Note too the launch of a new website, MathsThroughStories.org is an international research-based initiative which sets out to explore various aspects of integrating stories reading and writing in mathematics instruction.

The extension task for the TES resource above considers the reading age of a text, you may wish to consider further readability formulae; if you paste some text to this site, Readability Formulas you can easily check statistics for your chosen text and generate a reading age according to the various tests.

WolframAlpha can be used for Words and Linguistics, note the various examples given, including number names.and document length.

Analyze My Writing

Alternatively, try Analyze My Writing. Simply paste in some text for a comprehensive analysis including basic statistics, word and sentence length and readability. It is also possible to create Cloze tests.  You can read more about this resource on Richard Byrne’s always impressive “Free Technology for Teachers”.

It seems appropriate to check some world records on books!

On the subject of books see the free books information and note in particular Colin Foster’s Instant Maths Ideas – lots of ideas you can try in the classroom.

Mathematical Miscellany #8

It’s Half Term this week and a time I always find useful for a tidy up!
Checked and updated posts include:

Happy Birthday Nrich! To celebrate Nrich’s 20th Birthday they have been digging in the archives and freshening up some old problems. This is still one of the best websites around and one I have been using for a long time! See also their Hidden Treasures. and the Teacher Birthday Feature.

The Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  We even have 9 Maths skills you need to win the Great British Bake Off!

Note the Poster Competition closing in January 2017 for UK students age 11 to 18. The entries will be judges in three categories Years 7 and 8, Years 9, 10 and 11 and Years 12 and 13.

For some brilliant Puzzles and Games resources – see celebration of mind and more resources here.

Find out more about Celebration of Mind.

Mathematical Miscellany #7

Questions Questions..

I have been busy checking and updating various pages on this blog, taking into account popular resources.
See:

Mr Barton Maths
Craig Barton has been working hard redesigning his wesite, Mr Barton Maths. You will find a treasure trove here for teachers and students. Note in particular Craig’s Maths Topic Index Page.

For each topic, you will find information on all the GCSE specifications, a whole variety of resources, questions and more. The pages are very easy to navigate. Note the inclusion of Diagnostic Questions for each topic, a resource which is going from strength to strength this now has over 20,000 Multiple Choice Questions. Multiple Choice Questions when well written like this can be an excellent way of addressing student misconceptions.

Note these free CPD Events from Underground Mathematics including a webinar at the beginning of November.

For more on Underground Mathematics, an introductory post is here and you can view all posts in the category Underground Mathematics.

Suppose you are interested in Quadratics and want to stretch your students – you’ll find an extensive collection here, As always, for each resource, you will find so much more than just the question and solutions but for example all the printable materials you need and suggestions for teaching with the resource.

If you create an account you can easily save and organise your favourite resources. This list of favourites can be downloaded as a csv file.
For some of my recent favourites see this Excel file cy-ugmaths-favourites or as a pdf: cy-ugmaths-favourites Note the handy Excel =hyperlink(cell) command for turning the text to a hyperlink).

The favourites facility is sophisticated – you can create sub collections also.

Note Scary Sum – what a lovely problem!

By Colleen Young

Mathematical Miscellany #6

Another compilation this week, this time of updates to this and some companion blogs.

A consistently popular page on this site has been Rich Tasks – this has now been split into two separate pages, one for age 11-16 and the other for age 16+. The 16+ page has been updated with considerably more detail. With the UK new A Level specifications having a greater emphasis on problem solving and more challenging questions, activities such as those here should be a natural part of our regular teaching.

Do explore the brilliant Underground Mathematics site as well as Jonny Griffiths’ various sites. Further resources are provided in the presentation at the end of the page.

With a new academic year approaching for UK students or just started for students elsewhere, I have updated Transition Time on Mathematics for Students. This is a collection of resources and activities aimed at students changing stages in their studies – perhaps starting more advanced studies at school or heading off to university.
The illustration here is from Jonny Griffiths’ Carom Maths, a collection of forty mathematics activities bridging the gap between A Level and University. Check the List of Activities, for Inequalities for example, illustrated here, choose Carom 1-2: Inequalities. This will lead you to a complete PowerPoint with information and questions on Inequalities.

In last week’s Mathematical Miscellany #5 I included Jonathan Hall’s MathsBot.com site with its many excellent Tools for Maths Teachers. With some great starters and a bank of GCSE questions with solutions more detail has been added to this post on Mathematics – Starters and Plenaries. The Collections page on the same site has also been updated and checked. As the name implies these are sites with a fantastic supply of starters.

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