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



Select image for problem on Brilliant

Select image for problem on Brilliant

A site which I believe lives up to it’s name! Signing up to Brilliant allows users to join an international community and get free weekly, personalised problems. Questions at various levels are available, including questions suitable for younger students.

Many of the problems such as the one illustrated here would make ideal starters.

Create an account (free) to use the site, or Facebook users can log in easily via Facebook. Once you have signed in you will see a menu option to practice which offers a variety of problems at various levels. If you find a problem you like you can bookmark it. See Lucky Remainder for example or Keep your operations ordered.

(Post with link to Brilliant for students).

In an IT Room

Padlet - select the image to see this wall

Padlet – select the image to see this wall

In an IT room Padlet is an excellent resource for a starter or a plenary. Students can be asked to post a sticky note with something they have learned in the lesson or perhaps to ask a question. Students can simply o link to the wall, an account is not necessary. See Interesting Ways to Use Padlet in the Classroom where teachers have contributed ideas for inspiration.

Another possibility in an IT room is to ask students to create a word cloud of any vocabulary they know on a topic at either the beginning or end of a lesson.

Starter of the Day

From Transum Software, the well known Maths Starter of the Day has just that, a starter for every day of the year. What makes the site particularly useful is the index by topic and note the link to Quick Starters, Random Starters and Substantial Starters. There is also a complete index of starters which includes the topic of the starter.

Many of the starters would make ideal Bell Work; there are several starters here which could be written up on the board whilst you are waiting for any IT – or maybe if you don’t have IT!

Some of the Shine and Write activities would also make good lesson starters. For example are these statements true, sometimes true or false? As with many of the activities on this site you can refresh the page for further statements, you can also change the level. Or perhaps some Mathanagrams?

Know Your Place - Transum SWoftware

Know Your Place – Transum SWoftware

Checking the National Curriculum (UK) section I came across this really useful mental calculations activity which you can refresh for a never ending supply of such questions. I then discovered the same activity in another format, using the topic index, under Mental Methods, we see that Know Your Place is one of the activities, this time a timer is included as are the answers. Further investigation of this section, led me to this rather nice starter on algebraic notation. As you can see each section has suggestions for activities, with additional suggestions such as the algebraic notation starter at the end of the section. This site is well indexed, from the algebra activity mentioned here, there is a link to other algebra activities

Well worth exploring for your favourites – this site is a rich source of starters and plenaries.

Christmas Starters

Advent calendar Alex Pett

Advent calendar by Alex Pett

See Christmas 2013 on Mathematics learning and Web 2.0 if you are looking for Christmas activities generally. Here I will concentrate on those activities suitable as December starters.

Perhaps use an advent calendar such Alex Pett’s very beautiful version complete with history and problems for each day (and turn the sound on!). It is an ActivInspire resource but Alex has also provided a pdf version or use as a Google document.

Nrich secondary advent calendar

Nrich secondary advent calendar

Also worth checking for starters are the various Nrich advent calendars. Look at problem 1 on the secondary calendar for example; Special Numbers would make an ideal starter. The calendars link to posters of Nrich problems but you can easily search on Nrich for the problem if you want to look at the teachers’ notes and solution. Take problem 1 for example – Special Numbers. Go to the Nrich website and enter special numbers in the search box, the first entry is the required problem.

If you want number properties for each day in December then you could of course use WolframAlpha, eg 19 or Tanya Khovanova’s wonderful Number Gossip site. A good starter can be to ask students to come up with a question which has an answer of 19 and then go on to look at properties of that number.

Transum Software who provide the popular Maths Starter of the Day activities have some Christmas Starterstry ChrisMaths for example.

From TES Resources these Christmas grid puzzles or Operation Christmas Tree would make rather nice starters. Back to the subject of calendars. this very well presented PowerPoint advent calendar could easily be adapted for your students. You could use it to plan your December starters!

Happy Christmas!

MEI GCSE Starters

MEI Starters - fit eight to a page!

MEI Starters – fit eight to a page!

MEI have an excellent free collection of GCSE starters. Designed for the start of a GCSE lesson, the diagrams and questions are very clear and will display well on the IWB. There are several starters under the following headings: Mathematical Reasoning, Number, Algebra, Geometry and Measures and Statistics and Probability. Files with the answers and teachers notes are also provided.

It is not always possible to have the IWB up and running, particularly if you are coming from a different room and I do like to get students working straight away. Experimenting, I found that I could tale a screenshot (I do like the snipping tool in Windows 7) and fit eight to a page! I used a Word document with very small top and bottom margins and a two column layout.

For more ideas on a calm start to lessons – getting everybody working straight away – see Bell Work.


Arithmagons can make ideal starters or plenaries as well as being used for a main lesson activity.

Mathematics, Learning and Technology

What is an arithmagon? 

Clearly, the numbers in the rectangles are the sum of the numbers in the adjacent circles. Of course, there is no need to use addition and no need to use triangular arithmagons!

A revised and completely updated post can be found here.


View original post