As well as a full solution which does not use the multiple choice answers further ideas are given for investigation.
UKMT Extended Solutions
Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem solving skills at all levels. On the outstanding Diagnostic Questions site you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)
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, @EJmathshas 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.
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.
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 Investigationwhere 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.orgis an international research-based initiative which sets out to explore various aspects of integrating stories reading and writing in mathematics instruction.
AQA – Read All About It
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 Formulasyou can easily check statistics for your chosen text and generate a reading age according to the various tests.
To use the links in this post you 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.”
It is very simple to create a quiz of your own using the Instant Quiz Facility. The following slideshow shows how I created a quiz on logs and exponentials. To create a new quiz I make sure that the Instant Quiz has no questions currently in it so have got into the habit of clearing it out once I have created a new quiz. The instructions for doing so are included here.
Checking Insights for my Year 11 class I can see that students have completed many of the diagnostic examination questions. Two students in particular have been rather busy completing 253 and 484 questions, they both got 9s in their mock examinations! (We used AQA Practice Papers set 3).
There is also a mobile app which students can use to complete quizzes assigned to them by their teacher. Testing this recently it works on both my Android tablet and phone.
To use the links in this post you will need to be logged in to the brilliant Diagnostic Questions site. 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. If you scroll down the page you’ll see that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”
Diagnostic Questions provide a way of assessing your students’ knowledge and understanding, they are excellent for identifying misconceptions. Try for example the collections of GCSE 2017 examination questions from AQA, OCR and Pearson Edexcel.(scroll down each of the pages linked to for numerous quizzes on different topics on the GCSE syllabus).
Diagnostic Questions GCSE 2017 Collections
Diagnostic Questions – GCSE examples
You will find excellent coverage of topics new to the GCSE specification. You can also search all questions for a topic of your choice, for example a search on iteration will lead you to the whole collection of Trial and Improvement and Iterative Methods questions.
When you are logged in to Diagnostic Questions, you can easily return to the menu using the icon on the left.
Returning to the collections, there are many – scroll down the page and you will see collections such as GCSE Maths Takeaway – 111 mini topic-specific quizzes covering all the content on Higher and Foundation GCSE (keep scrolling down the page for all the quizzes). These quizzes are ideal to use as baseline assessment before revising a topic, or as a measure of progress following the teaching of a topic.
For schools teaching AQA’s Level 2 Further Maths specification, the AQA Level 2 in Further Maths collection has 12 sections of very useful questions for this specification.
You will see choices for each quiz including the very useful option to download the questions as a pdf.
For example I created a quiz on Circles and Tangents, downloading this as a pdf creates this file. See the guide mentioned below for instructions on creating quizzes.
I wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications I believe thissite 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.
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.