Time to Tidy Up!

Tidy UpIt’s holiday time so time for a bit of tidying up – my house and my blog!

During the holidays I’ll be checking and updating New Academic Year Resolutions for Mathematics Teachers and will publish the updated version at the end of August.

In the meantime I’ll be doing some tidying up and updating in the never ending quest to make useful things easy to find! I’ll post my weekly tidy ups!

This last week I destroyed and recreated the UK Assessment Pages, a completely new page, Assessment without Levels KS3  gives details of the packages of the winning Assessment Innovation Fund. The principles here may also be of interest to non UK readers. On the subject of assessment I rather like the student rubrics I found on the US site, Exemplars, particularly the Jigsaw Rubric. Actually I think some teachers would probably appreciate rubrics like that – plain and simple language!

The GCSE & A Level Reform page has also been checked and updated with new links added, including the chart showing the old and new GCSE grades and subject content.

The Reading pages have also been updated recently including the addition of a new page Blogs – Learning and Teaching, these are on learning and teaching generally and are not Mathematics specific. It’s a short list, these are my personal favourites – so much common sense here by such open-minded authors!

Excel spreadsheet for symbols & charactersFinally for this week, in response to a query I had on last week’s post on symbols, I have updated that post (at the end) with a spreadsheet you can use to see which key on your keyboard will give you each symbol in a symbol font.

If you have just broken up for the holidays or have been on holiday for a while, wishing you a lovely break.

Thank you for reading this academic year.

Symbols

From the MathCentre this very clear nine page leaflet describes symbols and notation in common use in Mathematics, for each symbol we learn what to say, what the symbol means and where appropriate an example is given; it is also possible to search the Math Centre site for further details.

If you are wondering how to pronounce any symbols, this chart of common pronunciations should help. I am pleased to see that the pronunciation of sinh x is given as shine x as there have been a few arguments over this one!

If you are looking for a particular character you could use a WolframAlpha query, or check this comprehensive Wikipedia entry on Mathematical Symbols. There are some very useful documents here and also links to external sites.

To learn more about symbols, try Earliest Uses of Various Mathematical Symbols, from Jeff Miller where you can learn for example when the equal symbol was first used.

From the University of Nottingham Sixty Symbols (there’s actually more than 60!) has a collection of videos about the symbols of Physics and Astronomy.

Mathematics Symbols from Penn State

Mathematics Symbols from Penn StatFFe

From Penn State you can find many symbols here, I found that I can just copy and paste the symbols, for example:

μ

∫   ∲

ℝ ℂ ℕ ℙ ℚ ℤ

∀ ∃ ∧ ∨ ∩ ∪ ∊

∣ ∡

One can of course also insert a symbol in a program like Word: ≅ ∴ ∮ R

copypastecharacter.com

copypastecharacter.com

A very easy to use site is copypastecharacter.com, just click to copy a character. Several sets are available,  note the drop down menu. It is possible to save your favourites from the sets here by creating an account; I created a set which you can see here.

calculator font

From subtangent,com resources

If you want some calculator buttons in your documents, the Calchux font is available on the resources page (scroll right down to Miscellaneous) of subtangent.com

ES03 Font from Casio

ES03 Font from Casio

or from Casio a variety of Fonts to download for teachers.

Excel spreadsheet for symbols & characters
In response to a query I have created an Excel spreadsheet which lists ascii characters.
You can then copy the first column as many times as you wish  and then simply change the column to your desired symbol font.
The spreadsheet has EOS3, EOS4 and the Wingdings fonts.

Characters & Fonts

 

 

Standard Form Resources

Coming across You’re Getting Old, it struck me that the numbers generated by the site would be perfect for standard form exercises; put in a student’s date of birth and even the young ones will have some big numbers reported! For example, for a 12 year old, the following figures are generated, some updated while you watch.

You're getting old

You’re getting old!

Some other resources for standard form:

I have been interested in Astronomy since discovering Patrick Moore’s books in the library as a child so enjoyed Richard Byrne’s post on resources to help students understand the size of the universeI particularly like 100,000 Stars, a visualization of the 100,000 stars closest to Earth. All those lovely big numbers in Astronomy are excellent for teaching Standard Form; I wrote some time ago on the excellent mathematics resources available from NASA, see this on Scientific notation for example.

From the excellent Standards Unit, N4 on Estimating Length Using Standard Form works very well as a class activity. (You can find all the Standards Unit Resources here).

For the start or end of a lesson (or any time!), you could try some Diagnostic questions on Standard Form

diagnosticquestions.com

diagnosticquestions.com

 (See these posts for more information on the excellent Diagnostic Questions site).

standard form calculator - subtangent

Standard Form Calculator – Subtangent

Practice standard form with this calculator from Subtangent.

Students could be shown how to check their work on WolframAlpha
standard-form WolframAlpha syntax

and finally some more great links including some rather good animations:

Scale of the universe. 

Magnifying the Universe

Secret Worlds: The Universe Within

breathingearth.net

You can find lots of data with very large numbers using Gapminder

Staying with world statistics, you could try Jonny Griffiths’ World-wide Statistics task from his Making Statistics Vital. You could use the figures from his spreadsheet – write the numbers in Standard Form and explore some real world Statistics at the same time.

 

End of term activities

With the end of term (UK) rapidly approaching I thought I would check and update the End of term activities page. All links have been checked and updated where necessary and some additions made, including:

  • Learn the syntax for WolframAlpha, perhaps a chance for students to explore WolframAlpha, using the various slideshows, note the questions on the worksheet
  • Explore the Desmos Graphing Calculator
  • the addition of a Desmos page illustrating how to draw line segments and/or parts of circles – get your students creating pictures

    Art Elements

    Get creative on Desmos

  • the addition of a Desmos Spirograph page and an excellent Autograph activity by Owen Elton to a post with more information on Spirograph
    Spirograph

    Spirograph on Desmos

    Spirograph - Autograph Activity

    Spirograph – Autograph Activity by Owen Elton

  • Try or write your own Sporkle Mathematics quiz

    Sporkle: Find the missing primes in two minutes

    Sporkle: Find the missing primes in two minutesA

And to finish – perhaps a song or two!

Lesson Endings

Thinking about lesson endings, which perhaps we don’t always give enough thought to I have updated this page on Mathematics Starters and Plenaries.

An interest of mine is in creating presentations and inspired by Nancy Duarte and her Slidedocs thought I’d experiment with designing some new slides. I took the Endings page and turned it into the following slideshow.

Note that links within a presentation do not work when uploaded to Slideshare, if you would like a version where you can navigate from or return to the Contents page then download this PowerPoint version: Endings – Mathematics lessons or as a pdf: Endings – Mathematics lessons

 

Statistics again …

CensusAtSchool 2013/2014

CensusAtSchool 2013/2014

I wrote last week on the excellent Experiments at School, part of the CensusAtSchool project. To add some information to that post, note that the 2013/2014 CensusAtSchool questionnaire is now live. I like the superpowers question – I think I’ll survey the school on that! Looking at the previous questionnaires (note that a pdf copy of each is available) I see that question was also on the 2008/2009 questionnaire, so the Database Interrogation Tool  could be used to retrieve some data from the results of that questionnaire.

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If you wish to take part in the CensusAtSchool project and retrieve data for your own class register your school herenote the option for schools outside the UK to register by contacting CensusAtSchool directly. The email address is in the paragraph at the foot of this page. Whenever I have contacted CensusAtSchool I have always received very prompt and always helpful replies.

Returning to Experiments at School if you have an LEA code and school code you can retrieve any data that your students enter for any of the experiments yourself. Use this form, the 7 digit school code is the LEA code followed by the school code. I have used it successfully this last week to download data that Year 7 and Year 10 have entered.  I have been very pleased with the discussions students have had when analysing the data and am convinced that collecting the data themselves such as the Angle Estimation data from ExperimentsAtSchool made the whole exercise far more meaningful.

England - trafficFinally – on a topical note, from The Wall Street Journal – The World Cup of Everything Else!

 

Experiments at School

Experiments at School - Online Experiments

Experiments at School – Online Experiments

I have mentioned Experiments at School before, an outstanding resource from The CensusAtSchool Project run by the Royal Statistical Society Centre for Statistical Education. I used this successfully with Year 8 (UK age 12-13) last year; this year I want to do some work with Year 10 (age 14-15. which means of course we will be able to compare Year 8 and Year 10 data!).

Choose any of the online experiments which are items 14 to 21. Selecting any experiment takes you to an introduction giving full details of the experiment as well as teachers’ notes and pupil worksheets. UK schools can get their LEA and school codes and actually try the experiments which will generate data for the school, however anyone can use the Database Interrogation Tool and choose a random sample of data from the database.

Database Tool - Experiments at School

Database Tool – Experiments at School

The best way to become familiar with the tool is to launch the tool, select the logo as in the image above then the follow these very clear instructions from task 1 on page 2. This will take you step by step through how to use the tool including selecting a random sample of your choice from the database. (Note the the info buttons as shown on the right of the above image do not currently seem to work, however you can get full details and all the resources for each experiment as described above on the Experiments at School page).

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My Year 10 students successfully tried all the experiments (with the exception of 16: Candle Combustion, I thought candles in the IT room might not be a very bright idea!). As they were doing the experiments there were some great conversations going on which will lead into interrogating the data very well. For example all the students tried the angle estimation and I heard discussions for example on the type of angles which are easier to estimate and that the flat diagrams are easier to work with. Note that even if your students cannot access the online experiment they could use the worksheet provided as an introduction to the activity or an online angle estimation activity such as this from Nrich.

This site is very comprehensive in that there are many suggestions for activities. For example we can use our own data and data from the database to answer questions such as those suggested in the teacher notes. Interestingly many of these questions came up in discussions between the students: ‘Do you improve with practise?’ ‘Is it easier to estimate smaller angles?’ ‘Is it easier to estimate the angle from a flat or a 3D diagram?’

There was much amusement and discussion generated by the All About Me activity. This worksheet fully explains the genetic traits used in the data and I suspect they will enjoy seeing if they can find out if they have a double somewhere in the world!

This will also be an opportunity for students to use Excel as I will provide them with a spreadsheet of the class data with data filters added so it is easy to sort by any column. They could also create charts, scatter diagrams for example, using Excel.

excel

All resources mentioned here are from TheCensusAtSchool Project run by the Royal Statistical Society Centre for Statistical Education. See this page for information on Copyright and Permissions.

Functions

Thinking about teaching functions in the next few weeks (to UK Year 12 ages 16-17) I realised that I could use Desmos to illustrate composite functions; the following slideshow illustrates the syntax.

We can also use Desmos to illustrate a function and its inverse. To create the page below (select the image), I started with a graph already online illustrating the general case of a quadratic function and its inverse and simplified it. f(x) and g(x) can be changed to a different function and its inverse. Note that the domain of f(x) can be changed.

Inverse

Further examples: exponential function and basic quadratic (where we need to restrict the domain for an inverse function to exist).

Staying with Desmos, as I have mentioned before, the function notation is excellent for transformations:

(See this page for all Desmos slideshaows).

IFunctions two argumentst is also possible to define a function with more than one argument and use Desmos as a calculator

For some clear examples and a resource to point students to, Functions from The University of Plymouth Mathematics Support Materials is useful. The format used in this series makes the examples clear and all the exercises given have answers.

Functions - Plymouth University

Functions – Plymouth University

Other useful resources (requires Java) include the Wisweb applets, algebra arrows could be used to demonstrate functions and their inverses as shown in the following images.

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World Maths Day 2015

Colleen Young:

World Maths Day 2015 – date announced ….

Originally posted on Mathematics, Learning and Technology:

Update
2015 dates

Note the latest announcement and new look – The World Education Games will be back in October 2015.

The exact dates for 2015 have now been announced. You can read the announcement on the World Education Games blog and you can pre-register now.

Perhaps time to remind everyone who enjoys these mental arithmetic games that there are plenty available they can still enjoy all year round.

Note the comment from Shane Hill below, for 4 to 10 year olds he has made Core Skills available.

sum-sense

Sum Sense from Oswego City School District

Sum Sense from Oswego City School District. for example is a little different – arrange the given numbers to give a correct statement. If you like this game note that Sum Sense games are available for other operations, scroll down to the bottom of this collection.

I have been looking at Sumdog again recently, I like…

View original 103 more words

Robocompass

Robocompass - simple demonstration

Robocompass – simple demonstration

Draw geometric constructions using the very attractive interface that is Robocompass.

demo commands

Robocompass is easy to use, simply type in commands. Select How to for a list of supported commands. Robocompass How To

Select the triangle image to go directly to the Robocompass file. Selecting play allows you to easily see each step. Note that you can select the page to rotate it in any direction.

Robocompass - play

Note that you can also look at individual steps,

demo 2

easily change colour or play speed:
demo 3

Reflection example

Robocompass – Reflection example

Experimenting with Robocompass made me realise that it can provide rather good demonstrations for transformations; see the above example (select the image for the file). Having set this up it is easy to change the line MN:

Reflection example 2

Or we could try a rotation.
rotation example

 

 

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examplesLearn more about Robocompass by following their blog and/or follow Robocompass on Twitter.

You can learn how to use Robocompass by studying examples; note the given examples or perhaps have a look at this on a Pythagoras proof.

Pythagoras