Mathematics Starters

All the content of this blog can now be found on Mathematics Learning and Technology and any future updates and additions will be made there. All sections have been updated and checked, additionally, there are many new activities and some new sections also.

Resources for the beginnings and endings of lessons can be found in the Lesson Planning series of pages, in particular on the following pages:

• Starters
• Starters – Blog Posts
• Vocabulary

The Starters page includes an Index of starters to jump to a particular section.

• Collections
• Retrieval Practice
• Challenges
• Number
• Algebra
• Advanced Level Starters

Bell Work

Starting lessons quickly and calmly…

Mathematics, Learning and Technology

At the beginning of a lesson I like to get everybody busy straight away, making a calm start to the lesson and very much like the idea of so called ‘bell’ work. Give students a task that is simple to understand and requires nomore than a simple instruction, question/s and/or diagram on the board (no technology required – unless you are in the room ahead of your students which offers more possibilities). This is a particularly useful idea if students arrive at different times. Students are expected to get to work as soon as they enter the room.

In current times, the students may well be in the room before their teacher, so could be given instructions at the end of a lesson on what they are expected to be working on at the beginning of the next lesson.

Some ideas

• A short question or questions on a topic studied…

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Here’s the diagram…

Mathematics, Learning and Technology

What’s the question?

(This post is an update of my post from 2013 and now includes the more recent, excellent resource Goal Free Problems from Peter Mattock.)

Using diagrams as prompts like this is excellent for Retrieval Practice.

Seeing this well-received resource, GCSE Question Prompts on TES reminded me that I have successfully used this idea myself before. For example for GCSE revision I have given students a selection of various triangle diagrams and asked them what the question might have been. This proved to be a useful way of revising several topics – some of which students sometimes mix up! For several of these triangles there are many possibilities and students can be asked which lengths and / or angles they could work out.

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Further excellent examples come from Mark Greenaway – GCSE Visual Prompts for both Higher and Foundation. Mark’s resources (Prompts 1) show the diagram first…

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Numbers – Visualizations

A great vizualisation or diagram can make a very good starter…

Mathematics, Learning and Technology

I have several references in various places on this blog to some great visualizations.
Time to put them all together!

Jeffrey Ventrella’s Composite Number Tree

From Jeffrey Ventrella this wonderful Composite Number Tree – I have used this successfully with many students. It makes a great starter. Students can work out themselves how the tree is being formed and comment on any patterns they notice.

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Stephen Von Worley

Brent Yorgey

Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dance which tells the tale of the animation. Noting his reference to Brent Yorgey’s factorization diagrams led me to Brent’s own later post, More factorisation Diagrams. I love Brent’s use of colour here. If you want even more on these great diagrams he has more information and links on this page on his blog, The Math Less Traveled

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Topic Test Starters

From the very busy Jonathan Hall! Jonathan has added this to his excellent mathsbot.com under his Activities section.

Topic Test Starter – Jonathan Hall

Note the other options in the Activities section too.

This site really is excellent, I mentioned it a while back. I and my students like his GCSE questions.

Happy New Year – 2017

New Year always provides us with January starters!
2017 – a prime year!

Mathematics, Learning and Technology

When 2017 starts around the world!

New Year Map – showing when cities round the world enter 2017.

2017 Year Game from mathforum.org

It’s that time of year again and we can play the 2017 Year Game in our January lessons.

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MathsClass

On Simon Job’s MathsClass, he suggests writing a number sentence under the date; as you can read on his blog he endeavoured to write the number sentence using the digits of the date in order in 2016. It strikes me this idea could be used as a starter, ask the students to come up with such a number sentence.

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2017 is a prime number and as we see from the WolframAlpha properties below, in particular a Pythagorean prime, so another source of starters and investigations perhaps? The last time the Year was a Pythagorean prime was 1997.

We can always turn to Number Gossip from Tanya Khovanova for information…

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Tools for Maths Teachers – MathsBot.com

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

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 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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Yohaku

These puzzles be good starters, note the Algebraic version.

Mathematics - Games

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.

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These 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.

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