# Old Maths Textbooks – a Treasure Trove or Trash?

So, like some of you I am at home on holiday and relaxing.

Don’t ask me why, but I am flicking through a 1978 Maths Textbook (Maths Around Us) that was recently gifted to me. 1978, yep that’s 51 years ago probably before you were born.

Anyway, like most other maths text books of any time warp there are a lot of boring pages of drill and kill, repetitious exercises that culminate in a ‘fun page’ or ‘maths puzzle’ just to break the monotony. So pages 274 and 275 are just two such pages. They contain ‘math magic puzzles’ (also called thoans – think of a number) but with a twist.

Before we get to the ones in the book, here are a couple of refreshers to get you thinking:

This one is slightly diﬀerent, but same principle:

So, questions that could accompany this include:

- Will it work for any whole number?
- Why is the answer always the same?
- Why does it work?
- If you backtrack, start at the end and reverse every operation what happens?
- Can you make up a diﬀerent math magic trick that works all the time?

Now for page 274. Notice that this one includes percentages. I think this is the first time I have come across one that includes percentages.

I like the potential of this type of math magic trick because it provides an opportunity to work with benchmark percentages (1%, 10%, 20%) and landmark fractions (25%, 50%, 75%) mentally.

Being able to work with simple percentages is a precursor to being able to understand the formula when it is introduced (usually too soon).

The book gave two variations on this math magic trick.

## Diﬀerentiation

I was pondering how to include students for whom the percentages might be too challenging and considered the possibility of such a student being the checker! A very important job; the checker uses a calculator to check every step, thus making sure that the math magic is correct. Ideally the partners will be explaining their steps as they go.

For example:

“To find 60% of 30, I knew that 10% was 3 and 6×3 was 18.”

and the checker will have windows into the strategies of others, this immersion is important.

Johnny has been looking over my shoulder and wants a turn to show the algebra behind these math magic tricks. I’ll hand over the conch. But, before I do, I just wanted to say:

“Enjoy the rest of your holiday. You deserve every minute of it!”

## Bonus bit …

Thanks Ann, here we go. I’ve put the algebra in for the first two examples that Ann started with (as percentages don’t look good in algebra)!

No matter what value of x you started with, your current value will be …