tales from the chalk face

Multiplication – an important skill.

There’s many different ways to multiply, but I prefer the good old fashioned method.

Whilst not necessarily easy for all, most children do find a method of multiplication that works for them.

But that’s only half the story. Can you work backwards, being given part of the question and part of the answer, can you fill in all the missing numbers?

The question above is not too hard – hopefully (because the unit digit of the answer is 5) you can quite easily find the missing multiplier.

Below are a couple of questions that are not so easy.  Can you solve them and replace all the ?s with numbers?

and a long multiplication:

Every day I get to work with geniuses.  They often don’t yet know they are a genius, and they’ve still to hit the heights of Einstein, but nevertheless, I am, on a daily basis, struck by the brilliance and intuitive thought of those I teach.

I’ve recently been doing some work with a class, encouraging the effective use of a calculator.  I love this as it really forces the pupils to think as we can use the calculator to do the boring donkey work of, well, calculation.

Knowing that some in the class would finish the set tasks first, I had prepared some extension work to challenge them.

One question I devised was:

Two integers (whole numbers)  multiply together to get 1829.  What are the two numbers?

Having picked two prime numbers, I figured that, whilst solvable with a bit of trial and improvement, this was not a simple 10 second question and would need the pupils to think about their strategy to solve the problem.

But I was wrong (not a first!) – one boy solved the problem instantly:  “1 and 1829”

He was working smart, he had the insight of a genius – look for the simple solution!

I love it when pupils come up with the unexpected and show a real insight into the subject.

But don’t worry, I amended the question for the next class:

Two integers (whole numbers)  multiply together to get 1829. What are the two numbers? 1 and 1829 is one solution, can you find another?

And the answer?

Well, I’m not going to tell you – perhaps you can work it out too!