Starter of the Day

Colleen Young:

This week I have been updating and tidying up a companion site to this one: Mathematics Starters and Plenaries. I have added some new sections, including Bell Work which seems appropriate here and I will update in future with any more ideas. If you have not fully explored Transum’s excellent Starter of the Day site then do have another look, there are some gems here – more details below.

Originally posted on Mathematics - Starters and Plenaries:

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…

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WolframAlpha – a little fun!

So – it’s the holidays – time for some updating and tidying up. With Easter approaching I thought I’d update the WolframAlpha slideshow with the non-chocolate variety of Easter Eggs!

…and a reminder of what a fantastic resource WolframAlpha is for checking work – see the recently updated series of WolframAlpha pages.

Calculators & Tools

Calculating FinancesI have been busy putting together many of the very useful calculators and tools for checking work. These have previously been on a site of their own but I have now decided they are more appropriately placed on Mathematics for Students. I have also added a link (Calculators & Tools) on the right hand side here in the Links section. I have taken the opportunity to do some major updating and I will develop this further in the coming months.

I like to use tools like this in class to encourage students to use them independently for checking their work. I know this strategy works – one of my Year 13 students announced during a homework discussion earlier this year that she knew the answer in the text was wrong (it was) because she checked it on WolframAlpha! Happily I have had many similar comments.

 

Colour in Mathematics

I have written before on how the use of colour and highlighting can add clarity to mathematical explanations. I use colour a great deal in my everyday teaching and also when writing solutions for students to use online. With written solutions I often use a colour to indicate a part of a question and then use that same colour for a partial answer as you can see in the examples presented below. Interestingly some students prefer a series of still images (no sound) to a video as they can control the pace more easily. I present just a few examples here. Note the Algebra – factorisation example, this has proved very popular with students.

Desmos

Desmos Graphing Calculator

Desmos Graphing Calculator

Earlier this year I completely reorganised  my WolframAlpha pages and at the time decided I should do the same with all my Desmos Graphing Calculator posts and notes. Desmos is something I use so often I decided it should have a dedicated series of pages which you can now see in the menu bar across the top of the page. I will continue to add to this series.

Desmos Photos on Facebook

Desmos Photos on Facebook

I have taken the opportunity to update and add to these pages, so for example the Inequalities slideshow has been updated – each page with a graph links to a Desmos page. I have added a page with useful links – this includes a link to the photo stream on the Desmos Facebook page – some rather nice starters there I think – I do like the Mental Maths Monday series. (You do not have to be a Facebook user to view these). If you have not come across Daily Desmos before you will find plenty of challenges.

Hopefully the clear list of pages should make any resources easier to find. There are several slideshows giving examples of Desmos graphs and syntax on the various pages, I have also put them all one one page here.

Thank you to the wonderful team at Desmos for this outstanding application.

Revision Time Again

UK Department for Education Examinations Timetable

UK Department for Education Examinations Timetable

Once again – examinations draw near; with the timing of the Easter holidays the number of lessons left with our examination classes is small! My lower school classes also have tests coming up, so I find myself yet again thinking about revision. I do try and build in regular review and revision into our everyday lessons and I thought it would be useful to note various ideas and resources for review and revision in one collection. Where I have written on a resource before I have linked to the original post where you will find further details.

Short Basic Recall Questions
These are ideal for use anytime as perhaps a lesson starter.
Dynamic Maths from David Watkins

Dynamic Maths - David Watkins

Dynamic Maths – David Watkins

MathsBox has an extensive collection  quality resources, the settlers and Bingo activities are ideal for a series of short recall / revision type questions. Also note these Year 11 revision starters (UK age 15-16) I do like the attractive presentation of the resources on this site (as well as the content of course!)

Bingo from Mathsbox

Bingo from Mathsbox

There are thousands of diagnostic questions available on Craig Barton’s and Somon Woodhead’s Diagnostic questions site.

Diagnostic Questions - vectors & lines

Diagnostic Questions – Craig Barton & Simon Woodhead

As shown in this post it is possible to create a slideshow of the questions you want for your class. Note the ever growing collection of questions, including a section for post 16 students.

Mega Maths Quiz from Ben Cooper

Mega Maths Quiz from Ben Cooper

Further sites with a series of short questions include Maths Teaching – Higher Level Revision Activities and on TES resources, also on his own site, Ben Cooper’s amazing (and huge!) collection of multiple choice questions covering many topics.

Other Suggested Revision Activities

  • Here’s the diagram – what’s the question
  • The Collective Memory resources on TES can make an excellent revision activity, students look at posters and then have to understand and recall that information. These can be used in a variety of ways which are fully described in the article. (A further set of resources is available here). Last year my GCSE students created several posters of their own which they found a very useful revision activity.
  • Mini-tests (or self checks)
  • Treasure Hunts – see the resources on Mathsbox for some lovely resources. These will get students moving round the room. On the subject of moving round the room, you could try an activity using post-its; see for example this Surds post-it challenge on TES.
  • Tarsia puzzles, these are available for all ages including post 16.

Examination Questions
Of course! You do not have to just work through a paper though – try questions on a theme or all A* questions! As usual there is no need to reinvent the wheel because there are generous teachers out there who have shared their resources. Steve Blades has an astonishing collection of 100 hard GCSE questions - all with fully worked solutions (and note all the other lovely resources on his site). Dan Walker on TES has created a mock paper which has only A* questions! You will be pleased to know that Dan’s resource includes model solutions!

SearchingOn TES I really like Tom Riley’s resource – exam questions and solutions but also with clues! Students match up the clues to a collection of exam questions on 10 higher topics, then use the clues to answer the questions. Something I do in the run up to exams is try questions in timed conditions as I think that is valuable – even for very short sessions. I work out how long they should have according to the number of marks (telling them to start another question if they finish or are stuck), it strikes me that I can make this an even more valuable exercise if I provide clues on the back of the questions that they can look at (or not!)

Team Challenges

Working Together Teamwork Puzzle Concept If you are looking for some problems to use for Mathematics Team Challenges in school or just for class activities with a difference which will help develop mathematical skills there are some excellent sources of materials.

The United Kingdom Mathematics Trust have annual challenges for junior : UK years 8 and 9 (ages 12-14, I have also successfully used these with Year 10) and senior: UK years 11, 12 and 13 (ages 15-18). UKMT publish materials free online for use in school, these can of course be used for all students and make an excellent class activity for individuals or groups. The junior materials can be found here and senior here. I have found the crossnumber puzzles an excellent activity for the end of term, these are crosswords with a difference as lots of the clues depend on other clues! Which clues to solve first?! All materials needed and full instructions are provided. Note the Supervisor’s booklet with answers and instructions; this includes the complete crossword grid and clues. I have used the Group competition and relay race problems very successfully in class.

staircase GVSU challengeAnother great source is Math-Team-Matics – a competition from Grand Valley State University, you can see the 2013 problems here so you could try any of these activities in class. The individual test has multiple choice questions. I like the look of the 2013 team challenge – a combination of staircases and painted cubes with surface area thrown in as well- I’ll definitely be using that!

Writing Mathematics Online

I first wrote a post on the available tools online some considerable time ago and the post has been one of the most popular on this blog since then – time for a revisit and an update.

Something I use a lot. I should explain my requirements - I want tools to communicate Mathematics online, perhaps to give some model solutions or answer students’ questions. Writing mathematics can be a pain (and yes I know about LaTeX). Note that there are various possibilities – sometimes just a static picture is required, sometimes you may want to display how to solve a problem in stages as in my first example here, or perhaps you require a collaborative space. You will also need to consider if you want the examples to be permanent or whether you just want a collaborative space for discussion. A graphics tablet is essential.

There are as always several options:

Illustrating how to simplify an algebraic fraction : simplify-algebraic-fraction

Having said there are several options my own favourite for creating the moving pen / step by step solution and the one I return to every time is screenr. It does exactly as I want – it is very easy to use and plays back as I want it to – send straight to your chosen application or get the url (or both). The screencast can be published easily to YouTube. I think the reason I return to Screenr, apart from the fact that it just works is that the creation of a screencast is what I can only describe as ‘smooth’ – using a graphics tablet, there seems to be no lag / no jerky writing – my scribbles with my pen are recorded with no delays. It is also possible to record a commentary.
For a training video on using Screenr – see this by Russell Stannard.
(From his Teacher Training videos site).

Just in case you try Screenr and get a Java not detected message even though you have an up to date version of Java installed then the solution is hereBasically you need to Configure Java (see your programs list) and under the Security tab add an exception site: http://www.screenr.com/ I left my security setting as high and this did solve the problem.

My other favourite methods for illustrating Mathematics online (and in fact the ones I use most often) when I just need a series of static displays is to either turn an interactive whiteboard flipchart (or a PowerPoint) into a pdf file 

flipchart to pdf example

flipchart to pdf example

or upload a PowerPoint to Slideshare. There are many examples on this blog of my SlideShare slideshows – see this for example

I should mention that I find Slideshare excellent – I use the free version which offers me everything I need – it works every time – I use it a lot!
I created the above slideshow by writing on the interactive whiteboard software using my graphics tablet and taking a picture of each page using the Windows snipping tool - this takes seconds – the snipping tool is something I use every day!

I see that I am not alone in my use of the both screenr and Slideshare, they are both in the Top 100 Tools for Learning 2013.

If you do not have access to interactive whiteboard software there are alternatives, one could use Windows Paint for example; there are also various free online tools available; see some of the resources below.

The following resources offer various ways to write Mathematics online:

If you wish to record a screencast and save your work, then as I have stated above, my own choice would be screenr in this category as it is so easy to use and for me is sufficient. I know that a very popular screen capture and screencasting tool is Jing, to use Jing you will need to download (free) software.

Another alternative is Screencast-o-matic which is very easy to use to capture the screen. I tried capturing myself using the interactive whiteboard software. Simultaneous Equations example here! It is interesting to note that the example is still there even though I created it in August 2009! 

For a collaborative board, try twiddla which seems excellent for collaboration – voice as well if you want. Twiddla offers some very sophisticated features including the ability to use mathematical formulae and upload files and images. Use of the board with all it’s features is free but you cannot save any of your work (possible with a subscription). This would be good for working online with a group of students.

Scriblink - for a collaborative space

Scriblink – for a collaborative space

Scriblink seems to work well, files can be saved, an email (which takes a while to arrive) provides a link which you can send to others. Scriblink offers a collaborative space and an in-screen chat is available. You can see the features Scriblink offers here.

Another to try if you want a collaborative space is Board 800 which is an interactive multi-user (shared) whiteboard application. You can see the features here; the basic whiteboard is free to use. Note you can have several pages – see the page numbers at the bottom of the board. A session lasts for 90 days. Interesting that although one is invited to follow Board800 on twitter – the last tweet was June 2012.

doodle.ly

Doodle.ly

Doodle.ly offers a very easy way to have a quick scribble and then share your thoughts! See quadratic example (and note that I created that just to test Doode.ly three years ago – a good sign that it’s still there!) Select Doodle Now, doodle, then if you want to publish you will need to sign in. You can sign in with Twitter or Facebook. I like the different pen tools available, the full screen option and the ease of publishing. I must experiment more with this in school – demonstrate an example and send it to twitter or Facebook!

AWW Like Doodle.ly provides a very easy way to easily share a whiteboard sketch – no sign up or installation required – just write away then share!  this is really easy to use and you can post to Twitter or Facebook.

Glencoe - virtual manipulative

Glencoe – virtual manipulative

If you are looking for more online whiteboard applications then you could try the interactive whiteboard manipulative from Glencoe  (I came across this in a Google search). Note the various backgrounds and manipulatives available.

Bruno Reddy - Geometry Toolbox

Bruno Reddy – Geometry Toolbox

I can’t mention online whiteboard tools without mentioning Bruno Reddy’s lovely Geometry toolbox - this is great for demonstrating constructions and is on the teachers’ section of his excellent site.

If you want to draw some pictures and like the idea of more crayons and pens then you might enjoy these tools!

Have some fun with Crayola!

Have some fun with Crayola!

writing repeater
Finally – your students may find this amusing – the Writing Repeater – write something and play it back – now this is a lovely tool for little ones learning to write but I’m sure we can think of some uses!

ClassCharts

Class Charts - example student report

Class Charts – example student report

For behaviour management and seating plans an outstanding and easy to use system is Class Charts.

I have written previously on the system Year 7 and I are using for recording learning behaviours, my aim is to document their learning behaviours; it is absolutely not a traditional ‘reward’ system which I think can be a minefield! I want something accessible to all and is clear to us all that it is about each student being the best they can be. In deciding on the points we should have we had some excellent discussions on being a good learner. We have very few negative behaviours, just a few such as forgotten books / calculators and so on that we agreed will really not help learning.

Having used our system this year I would say it is essential that all understand when and how each behaviour point will be awarded. I have simplified our system slightly which I believe will help ensure consistency; in our enthusiasm I think we created a few too many points – some of which are hard to measure!

Thinking ahead to summer examinations I have created a Revision point but to earn that they have to answer some questions on their chosen topic to provide some evidence! In fact I want them to be generally proactive in letting me know what they are doing to help their own learning.

We have been using ClassDojo as you will see in my earlier poststhis works really well but I have found that a real strength of ClassCharts is that each student can log in to their own account and see their complete record (currently ClassDojo allows students to view just the current week and whilst it is possible for me to print a complete report for them I have decided I want them to have their own complete online record).

My own primary reason for using Class Charts is to record learning behaviours – I may well experiment with the seating plan aspect later.

To get started create a free account (note that upgrades refers to SIMS integration, all the functionality you need for recording behaviours and creating seating plans is completely free). You can then create classes and customise the learning behaviours to suit you needs.

In case it’s useful I made a note of some instructions here and there is plenty of help available on the website.

The following document provides a summary from Class Charts: class charts summary

MATHCOUNTS

MATHCOUNTS dog

At a pet store, there are 23 animals. Among the animals in the store, 15 are white, 5 are white dogs and 7 animals are neither dogs nor white. How many dogs are at the pet store?

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Mathematics competitions can often be an excellent source of resources for problem solving and the competition series from MATHCOUNTS is a wonderful example. For US students MATHCOUNTS are currently running their third annual “Math Video Challenge”, a competition for 6th to 8th graders that encourages student innovation as they create and star in their own math videos. Entry to the competition is for US middle school students only (see full rules here) but we can all enjoy the resources. Entrants must create a video based on one of the problems in the 2013-14_MATHCOUNTS_School_Handbook; students entering the competition make a video teaching the problem and showing a real-world application of the math concept on which the selected problems is based. Teams will be able to submit videos until 5:00 PM ET on March 14, 2014.

The 2013-14_MATHCOUNTS_School_Handbook is a great collection of problems; I have seen many in this collection that would make ideal starters. All the answers are provided (page 56 of the pdf) and the index (page 62 of pdf) makes the document really useful because the problems have been assigned to a category such as Algebraic Expressions & Equations (though as the authors note many problems fit into more than one category) and given a difficulty rating from 1 to 7, with 7 the most difficult. The difficulty ratings are explained just before the answers (page 56 of pdf). Note that the references are to the US Common Core State Standards. The question categories are: Algebraic Expressions & Equations, General Math, Number Theory, Problem Solving (Misc), Statistics, Probability, Counting & Combinatorics, Proportional Reasoning, Solid Geometry, Percentages & Fractions, Coordinate Geometry, Plane Geometry, Logic, Sequences, Series & Patterns and Measurement.

MATHCOUNTS ice cream problem

MATHCOUNTS – Problem 102 – Warm-Up 8

I like the look of the combinatorics problems – I could use these with Year 7 or more formally with Year 12! One of last year’s semifinalists License Plates, Questions, and Arguments could be good to show Year 12!

MATHCOUNTS offer the materials from their resources in an interactive format which students can use through NextThought; this platform allows access to all the problems from the Warm-Ups, Workouts, Stretches and competitions. It is free to create an account. Solutions to all the problems can be checked online and full explanations for all solutions are available. To return to the pet store problem which is from Warm-Up 3 the solution available on NextThought is as follows:

NextThought - MATHCOUNTS

NextThought – MATHCOUNTS

As well as the latest handbook two previous editions are also available as well as numerous competition questions. The NextThought platform looks excellent and something I wish to explore further – it allows students to discuss problems and I see it has a whiteboard tool available.

All material is copyrighted by the MATHCOUNTS Foundation.