Tools for Maths Teachers –

Tools for Maths Teachers J Hall

JHall site

Jonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. 

J Hall Maths Tools

The illustration shows an example from Differentiated Questions; these have an oprional timer.

The GCSE questions bank is really useful; note the choices of topic. It is also possible to choose Foundation or Higher or both and Calculator or Non-Calculator. You have the option to show solutions.


This site has been added to the Collections and Revision pages.

Plenary Tweets

Mathematics, Learning and Technology

Discovering a novel idea for a plenary via Twitter recently, a UKEdChat resource by @grahamandre I thought I would try the idea with my very able Year 9 class (the same wonderful class I mentioned some time ago who gave their views on Good Maths Teachers).

I should mention that “Somewhere over the 2a” is part of some lyrics by one of my colleagues sung to the tune of “Somewhere Over the Rainbow!”

In the first part of this lesson I used one of my mini-tests to review the key points for solving quadratic equations. When we reviewed the solutions I also used Desmos to illustrate some of the answers and for these students, the first year who will tackle the new GCSE course made sure I used function notation! This time I told them that I was using the mini test to review the material we have been studying and…

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A perfect day…

What a perfect starter for 28th June – Perfect Numbers!

Mathematics for Students

28th June is a Perfect Day to enjoy some Mathematics!

perfect numberPerfect because 28 and 6 are both perfect numbers. You can easily check for properties of any number with Tanya Khovanova’s Number Gossip where we learn that 28 does not only have the rare property of being perfect, it is also composite, even, happy, odious, practical, triangular and Ulam! You can browse all the properties here.

28 is also happy! Happy Numbers – a favourite investigation, Dr Who knows about happy primes!

It’s also National Tau Day! Pi is wrong…..
This video provides a short version of the Tau Manifesto (14 minutes)

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These puzzles be good starters, note the Algebraic version.

Mathematics - Games


Additive Yohaku with rule

For a new kind of puzzle Yohakuu is a puzzle that will test your number sense and problem solving skills. Each Yohaku puzzle is either an additive or a multiplicative puzzle. You must fill in the empty cells such that they give the sum or product shown in each row and column as well as satisfying a rule if given.

Choose from 2×2, 3×3 or 4×4 puzzles.



Multiplicative Yohaku with ruleThese could be used as Starters or perhaps in form time.

Follow Yohaku on Twitter. Checking the Twitter stream I noted this algebraic puzzle below, an excellent idea. Try a little logic, where must c be placed for example.

Algebraic Yohaku

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Mudd Math Fun Facts

Mathematics, Learning and Technology


This searchable collection of Mathematics fun facts from Harvey Mudd College Math Department make ideal lesson starters or perhaps useful for those odd moments.
Note the search on the left, it is possible to search by topic, difficulty level and keywords.

For example, try:

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Mobile Puzzles – Algebra

For a wonderful Algebra starter – equations through Mobile Puzzles

Mathematics, Learning and Technology

Mobile Puzzles Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.


Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:
Master Level

Note the menu in the corner of each puzzle page:
Play Menu

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

create equation
Note that you can then drag a heart to subtract a heart…

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Number Operations


Questions such as this can make a great starter for a lesson and provide the chance to discuss number operations and the relationships between them. Manipulating numbers like this can also help with algebraic manipulation.

Looking for some more examples of this type, I came across a really useful resource on TES, “If I know this then I also know …” by Piers Butler. This would make an ideal lesson starter. As it is an Excel spreadsheet, I thought it would be simple to add another worksheet with the answers and created the Excel file CY If_I_know_this_then_I_also_know_ which is a copy of the original, but just adds another worksheet with the answers.

Thank you Piers! Note that this has been added to the Number page where you will find other starters on the Number category.
If I know this..


By Colleen Young Posted in Number

2015 Year Game

Happy 2015

Select image for geoGreeting

From The Math Forum @ Drexel comes the annual Math Forum Year Game. How many numbers from 1 to 100 can you generate using the digits of 2015? Unlike Countdown which uses only the four operations and brackets, additional operations are allowed – you can check the detailed rules.


A totally updated page, reproduced below, thinking about ending lessons well: Endings

What have they learned today? How do we make the important concepts stick?

Of course many / most of the starters could also be used at the end of the lesson!

Note that this is also published as a Slideshow on my main blog Mathematics, Learning and Web 2.0.

From the Essex Maths team see 50 Ideas for Plenaries – Essex Maths team and Another 50 ideas for plenaries

On TES Resources – register for free: Try an Exit Ticket and have a look at Mike Gershon’s Plenary Producer which has many excellent ideas which would be useful for any subject.

Perhaps sum up the key notation and vocabulary from the lesson, see also the Vocabulary page for ideas.

TeachIt Maths (all pdfs are free if you register for this site) have a collection of starters and plenaries.

Diagnostic Questions - Algebra

Clearly you may well want a question or questions to check key concepts from the lesson, two sites that could be particularly useful here are Diagnostic Questions and Dynamic Maths.

Staying with questions and marking, trying an exam question and then checking / discussing the mark scheme can be a very appropriate lesson ending. Or you might want to have a slightly longer ending, with the all important idea of making things stick and give them a mini-test. Reading Make it Stick (The Science of Successful Learning) which discusses the use of testing as a learning tool convinces me even more that mini-tests are a good idea! During a revision week, all three of my Year 10 (UK age 14-14) lessons started with a mini test which seemed to work very well and I was very pleased when two students who had to be somewhere else in the first part of one of  the lessons asked it I would send them the mini test for that day! Students need to recall information and the evidence suggests that testing is a better way of doing this than simply rereading material, a method often favoured by students. I am planning more plenary mini-tests, with the students I’ll definitely use the name I know they like, ‘Self-checks’ which I hope helps them realise they are as the authors suggest a learning tool, not something to be stressed by.

Aristotle apparently wrote “exercise in repeatedly recalling a thing strengthen the memory.”

triangle diagramStill with questions and marking, Here’s the diagram…what’s the question? or Spot the mistake would also make excellent lesson endings.

Set a question and then use WolframAlpha to answer a query on a topic being studied. This is a chance to show students how they can check their work; you may want them to check homework for example. Or you might want to remind them how easy it is to use the Desmos Graphing calculator or perhaps some of the other calculators here

For a novel plenary – plan ahead with a student – let them know they will be giving a vote of thanks for the lesson! This can include what has been learned and refer to any members of the class, perhaps comment on someone who asked a great question for example. This can work really well and the lesson may well end with everybody clapping!

It may be that you decide to use the end of the lesson to discuss what is coming next lesson and perhaps leave them a problem or task which you can tell them you wish to start work on as soon as they come into the next lesson.

…and speaking of the beginning of the next lesson