May 28 2015

Looking for Resources

Pondering a question on Twitter I realised that I always have a few sites I rely on where I know I can always find something. So I thought I’d pick a random example to illustrate.

A3 Constructions
So – constructions, for demonstrations I always use John Page’s Math Open Reference, his demonstrations are so clear and can be shown step by step; students can also be given the website so they can access them themselves. I found this many years ago when I wanted some demonstrations for constructions – a Google search returned it as the first entry!

$bisect angle Math Open Ref$

Math Open Ref – Bisecting an Angle

So obviously we need some questions / activities. Where to look – our textbooks are fine – plenty of questions there, but what else is available?

On Nrich, try a search by topic facility to find all the resources for a particular topic; searching on constructions there are several resources returned.

Nrich – triangle construction

CIMT – I don’t think CIMT have ever failed me! One can actually do a Google search such as CIMT constructions to very quickly find resources. It is worth being familiar with the site so you know what is where; I would always check the Year 7, 8 and 9 material and also the GCSE course. In this case, the Year 9 resources include Unit 12 on Constructions and loci. As well as the text we have all the supplementary teacher resources. Note that for some Teacher Resources you will need the CIMT password.

I often find Nrich and CIMT more than sufficient and

I want to spend time planning my lesson and thinking about my students’ learning and how I’m going to help them understand and make it stick.

And how will I know what they know?

So of course quality resources are key but I don’t want to spend too much time looking for them if it stops me spending sufficient time on the above. I believe it is very worthwhile to have a few key sources so you can find something efficiently and quickly.

Having said that, since this post is on finding resources I’ll mention a few more!

The old Exemplification examples for Key Stage 3 have some very useful example. In this case use the Geometry and Measures document and do a search for constructions.

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free. A search on constructions returns a small number of resources including a good card sort.

I’ll finish with Craig Barton’s and Simon Woodhead’s wonderful Diagnostic questions site. (Select this link for all posts on Diagnostic Questions, these include some instructions for use and other resources for rich questions.) Start typing construction into the search box and various choices will be returned.

Introducing Trigonometry

This week I will be introducing Trigonometry to Year 9 (UK Key Stage 3, age 13-14). I always like to begin trigonometry with students actually measuring lengths in triangles, I believe they get more of a feel for the meaning of the ratios of the sides of a triangle if they have actually measured the length of the sides and calculated the ratios themselves.

I decided what I need is some accurate drawings of triangles of various dimensions that they could work on. It took a few seconds (the third entry in the search results for introducing trigonometry) to discover not only the drawings I wanted but a perfect recording sheet! From NZmaths (New Zealand Maths) – a site I have mentioned before for its excellent resources comes Introducing Trig. As well as the resources, teachers’ notes are provided. (Scroll to the end, past the teachers’ notes for the resources)

This slideshow requires JavaScript.

So after an introduction including a reminder of Pythagoras they met last year, we’ll just need to be clear on the terms opposite, adjacent and hypotenuse, how to complete the recording sheet and the measuring can begin! This is a very able group of students and I suspect several of them to be telling me for example by the end of the lesson that sin 60° is the same as cos 30°.

Checking a few more links in the results of the search I see the excellent Math Open Reference site which I have referred to on several occasions. I also see that I am in very good company in my desire to get the students measuring themselves and using the nzmath resource – see Dan Pearcy’s post.

Something else I like to do when discussing trigonometry is to discuss all the possible types of problems that can come up because whether they are disguised as buildings / trees / ladders or whatever there are still only a limited number of problem types, eg find the angle given the opposite and hypotenuse. The students can work out how many problems there are.

May 17 2014

Robocompass

Robocompass – simple demonstration

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

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.

Note that you can also look at individual steps,

demo 2

easily change colour or play speed:
demo 3

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.

………………………

Learn 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.

Jul 6 2013

Geoboard Activities

National Strategies – Exemplification Examples: Geometry and Measures

I have always found the above task, suggested in the National Strategies exemplification examples (click on the above image for the pdf) an excellent one when looking at types of triangles and their properties. Students are required to find the number of unique triangles on a 3×3 grid. The task can be extended by asking students how many unique triangles there are on a 4×4 grid. A good discussion can be had on being systematic in approach.
The next time I teach it I will certainly use a Geoboard.

For GeoBoard resources and suggested activities continue reading here.

May 11 2013

Scratch

Scratch, from MIT is object-oriented programming language which is very easy to get started with as there is now a new release of the platform availble entirely in a browser; no program downloads are required. The interface is intuitive and easy to use; extensive help is available including a very clear Getting Started Guide and a set of Scratch Cards with clear instructions which will help you learn new Scratch code. Note the Scratch For Educators section.

As you can see from the sprite’s path the above program continues as follows:

Scratch square part 2

Now that’s not a very efficient program! Scratch is a great way to learn programming as well as doing some Maths! We could look at external angles of polygons for example and show how to repeat a set of instructions.

Scratch – drawing an octagon

We could add some sound, change the pen colour or shade, learn about variables and generally have some fun!

Scratch Hmm...

Click the image then ‘See Inside’ at the top of the screen.

Try experimenting with this program which uses variables for the number of lines to draw and the angle to turn through. You will need to sign up to Scratch which is very easy and free.

It strikes me that Scratch could be used for many topics, bearings included.

Stephen Quinn’s dissertation is an investigation into using Scratch to teach KS3 Mathematics and has many ideas as well as useful information on Scratch.

Apps: Scratch Junior for iPad (for young children age 5 to 7)