Mr. Kendall recommends…

Dear Maths Colleagues,

With the roll-out of the new maths syllabus and my teaching First Years this year, I thought it handy to have an accessible check list to keep track of the exact topics I have covered with my class.

As such, I’m going to use this First Year Maths Progress spreadsheet. I’m hoping it will keep me on the straight and narrow as my school’s textbook presents the topics in a slightly different order than the order presented in the Project Maths Teacher Handbook.

This spreadsheet presents the topics exactly as given in the Teachers Handbook. Along with the sequence of topics, the Project Maths Team provides a recommended number of class periods for each topic. Very helpful.

On my end, I’ll be placing a dedicated copy of the spreadsheet in “the cloud” for my school’s maths department. Ideally, as a First Year maths teacher completes a topic with her class, she will place an ‘ x ‘ adjacent to the topic on the spreadsheet. It should be helpful in planning our common end-of-term tests.

If you think it helpful to you or your colleagues, you are welcome to download it. Just click File menu, Download as…

Regards,

Tom

For one to articulate an understanding of algebra, one needs to be able to speak the vocabulary of algebra. Knowing how to correctly reference algebraic terms helps one to ask better questions and to describe methods in a more meaningful manner.

In this series of short video clips, Virtual Nerd revises the meaning of Constant, Variable, Coefficient, Like Terms and Simplest Form. Review these video clips as the vocabulary represents the building blocks of algebraic expressions. Thank you Virtual Nerd!

It is my understanding that 2011 will be the last year for the Ordinary Level Linear Programming Question as we know it. Project Maths will integrate elements of linear programming into the syllabus and exam, but not as a full question.

As such, this post is for those 2011 Ordinary Level Leaving Certificate students considering  linear programming for their Options question on Paper 2.

Below, Patrick JMT walks us through a linear programming problem that is used to maximise profit in a farming scenario. After introducing the problem, Patrick gives a general overview of the approach to be taken and then works through the problem step by step.

Many thanks to Patrick JMT!

For more helpful maths video clips from Patrick, visit http://patrickjmt.com

Imagine your parents took a photo of you everyday of your life from birth to 10 years old and then compiled the photos into one large digital flip book? It might look pretty cool.

Well, J A Magic Films did just that, or near enough that, with little Natalie, and A LOT of people have viewed it. In fact, J A Magic Films’ time lapsed video has gone viral and, as of 30 Dec 2010, it has been viewed on YouTube nearly 4.5 million times.

What questions come to mind when you watch this clip?

Here are some of mine:

1. Over 4.5 million YouTube views; how big is that number? What might I liken it to?
2. If I was J A Magic Films and I received 1 cent for each YouTube view, would I be financially content? Might the sum pay for Natalie’s university education?
3. The term “Time Lapse” is part of the title of this clip. I can visualise “time lapse”, but can I describe it in words?
4. Did J A Magic Films really take a photo of Natalie every day for 10 years? In my correspondence with J A Magic Films, he explained that as Natalie got older it was more and more difficult to get a photo of her each day. He comments on his YouTube channel that 1,254 photos were taken in total.
5. 1,254 photos taken over 10 years. That would mean Natalie had her photo taken – on average – every how many days?  Hmm… would I be that patient of a subject?
6. 1,254 photos displayed in 1 minute 25 seconds. On average, how many seconds is each photo displayed?
7. 1,254 photos. Might the original 1,254 photos fit on a memory stick? To estimate this, what type of assumptions will I have to make?

You can use the Sine Rule to solve any non right triangle when you know (i) a side and its opposite angle and (ii) at least one other piece of information about the triangle.

In this video clip, Conquer Maths provides an introduction to using the Sine Rule for finding an unknown side of a given triangle. Three specific example problems are provided that will allow you to pause the clip, workout your solution and then check your work.

Thank you Conquer Maths!

Here’s a 3 minute clip to help you visualise the proper substitution of values into the Cosine Rule.

I like how the author uses simple text boxes to “drag” the labels into their correct place in the formula. He also colour coordinates the angle-side pairs. A big thank you to the author from all of us visual learners out here!

Watch Hans Rosling tell a story of 200 Countries over 200 Years in 4 minutes. As Hans says, “pretty neat, eh?”

Now imagine Hans telling the same story, but without the use of his graph. Pretty b-o-r-i-n-g, eh?

Want to get a message across to an audience? Use a graph!

In this clip from www.examsolutions.co.uk, the instructor uses common sense semi-circle and quarter-circle examples to introduce the general formulae for finding arc length and the area of a sector of a circle.

The current syllabus for Higher Level Junior Certificate Maths requires you to be familiar with a number of constructions. The complete list of required constructions is as follows:

• Triangles
• Bisect an angle
• Perpendicular bisector of a line segment
• Circumcircle of a triangle
• Incircle of a triangle
• Divide a line segment into a number of equal parts

You will find links to animated step-by-step instructions, as well as printer-friendly guides, for all of the above constructions on the Math Open Reference Constructions webpage. 

While there are number of other online construction tutorials, I especially like this website’s tutorials in that the authors use an animated compass and straight edge to show proper positioning when drawing arcs, circles and lines.  

You’ll note that in the “Divide a line segment into a number of equal parts” tutorial, the author uses a different approach as to what is often presented in math textbooks here in Ireland. Feel free to use the construction method you are most comfortable with.

Congratulations to the team at Math Open Reference for putting together such an excellent resource!

On The Right Triangle and Applications page of  Interactive Mathematics, Murray Bourne provides us with visual explanations of what the terms Angle of Elevation and Angle of Depression mean as well as a few problems (with step-by-step solutions on demand).

This page will provide us with a tidy revision exercise in the run up to exams.

Thank you Mr Bourne!