Questioning a ‘Theory’



My colleague who is a 2nd grade teacher shared her students’ theory about the pattern which they found in multiplication.

I can’t recall exactly the sentence which she wrote on the board but the idea sounds like this: When you do multiplication, you can get the same answer when you half a number and double the other one.

So I thought it’s interesting to share with my students who are exploring the 2-digit multiplication.  My colleague told me that she would ask her students to prove their theory. 🙂

The students in my class were excited when I told them to prove if the theory is correct.

They tried and started using different numbers.


In the middle of the ‘experiment’, one said, ‘How can we half an odd number?’

That question led to the previous maths unit they had about fraction.

‘What is a half of 7?’ I asked.

This boy who always seems to have the answer for everything said, ‘three and a half.’

The girl ,who had the initial question, replied, ‘But then how do you multiply three and a half?

This conversation provoked them to think more deeply about fractions and decimals which I would introduce them some time in the second semester.

I asked them to rephrase the theory based on their finding and this was what they got.

When you do multiplication, you can get the same answers by halving one number and double the other one but this does not work when both numbers are odd.

I said, ‘OK, we’ll keep the new theory based on your current finding but perhaps we can revisit this and prove if it would be still relevant as you learn more later on.


I thanked my colleague who shared this ‘theory’ with me as it got the students in my class thinking and making connection.  It does encourage students to continue developing their critical thinking skills.


Let’s keep the thinking ball rolling.




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