March Maths @ Sharp Newsletter

Every month or two we send out a newsletter to our subscribers. This is our March 2018 issue. Please do subscribe and let us know what you think 🙂

 

Dear Reader,

 

As I sit here and write this, the thunder has been rolling through. It’s crazy to think that the official change into autumn has begun, and that the school holidays are just around the corner. There are so many public holidays over the next couple of weeks that make me excited to think about late mornings in bed with a cup of coffee and a good book 😉

 

To all those that celebrate, we want to wish you a wonderful and special Easter.

 

Have you signed up for the AMESA 2018 National Conference taking place in June this year? For those of you who haven’t been before, the national conference is taking place in Bloemfontein, at the University of the Free State this year. Teachers from around the country gather together and share their thoughts and ideas for teaching with each other. This is a great way to network with your fellow teachers, and to learn about new trends and products making their way into the South African maths space. If you would like more information please visit the AMESA website.

 

If you are looking for an Easter themed exercise for your students – try this link. These activities are particularly designed for older students. There is even a math “murder mystery”, where students need to use their logical thinking skills to figure out the solution. If you need some down time to collate marks, this is a great activity that will keep them busy for a while. For the primary school teachers, try this link. It has different Easter themed worksheets across the grades, and is grouped according to grade.

 

I am sure we have all covered prime numbers in the last couple of weeks. And the question of “where will we use this in real life?” has come up at least twenty-three times. This article looks at the largest prime number found to date: 23 million digits long! It explains why it is important that we know these prime numbers and what we use them for – particularly encryption in banking. It’s a great way to give students a taste of what is out there. Those students who have a taste for the super spy will particularly love its applications. (As an interesting side note: did you know that it was a mathematician that cracked the German code in World War II and helped turn the war in Britain’s favour).

 

I recently spent some time writing the 2016 matric maths exam papers as well as the supplementary exams. I was curious about the difference having a scientific calculator would make to the possible marks and time I spent on the exam. The results are rather astonishing. Apart from the fact that a whopping 20% of the exam relies on an answer from the calculator, the calculator also gave me a fifteen minute advantage in paper 1. To read more about this click here.

(If you have been having trouble registering or logging into the website please note that this issue has been fixed – we are very sorry about the inconvenience.)

 

I absolutely love this visual representation of Pythagoras. This is a great way to show it to your students, and you can even get them to prove it themselves.

 

After a very interesting discussion with some teachers at a school I visited recently, where we were discussing the method of teaching factorising, I found a great way for factorising trinomials with a value for “a” other than one. It is very well explained in this article, and the analogy to an airplane will make it easier for students to remember. I love it because it coincides with the method that I use for teaching factorising with a = 1. Let me give you a brief overview:

 

Our example will be:

Step 1: Write down your brackets and put  into the front of each bracket (in our example 3x:

(3x          )(3x          )

Your students should automatically question why you are doing this based on what they already know about factorising.

Step 2: Multiply a and c together: 3 x -8 = -24.

Step 3: Here I would use the calculator to find the factor pairs of -24

1. Go to table mode – press mode and choose either 2 or 3 (depending on the type of EL-W535 you have).
2. Type in – 24 a/b RCL RCL (this will give you:

Press = four times until you reach the table:

               3. Scroll through the table until you find the X and ANS that add up to b: -5 in our example:

Here we can see that it would be + 3 and -8.

Step 4: We are going to place these two numbers into our brackets:

(3x + 3)(3x – 8)

Step 5: We now divide the brackets by 3 (I would call this taking out a common factor for both brackets:

 

And this gives us:      (x + 1)(3x – 8)

Which means that we have factorised the trinomial.

 

What do you think?

 

The last newsletter’s riddle was:

Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.

This is really a matter of playing with the number until you find a solution that works. For example, if we wrote down the number:

9 000 000 000

• There are 9 zeros, but then we would need to put a 1 where the 9’th digit is represented, which would mean there are actually only 8 zeros, and so we would have to put an 8 in front and a 1 for 8:
• 8 000 000 010, but then we need to add 1 in the 1’s holder place, and that means:
• 7 100 000 100, but now there are 2 ones and so
• 6 210 001 000 is the final solution.

Did you find any other solutions?

 

Here is your riddle for this newsletter:

How can you add eight 8’s to make 1000?

 

Have a fantastic break and we look forward to seeing you in the winter term.

Best maths wishes,

Tal and the Seartec Team.

 

Ps – In honour of Stephen Hawking,