I just got out of my 6th grade Math Skills class. We finished up the Proportions project (something akin to THIS) and spent half the class getting their final papers printed and putting the project papers up in the hall. I thought it would be hard to really have an engaging lesson afterwards as they were a bit hyped up but we refocused and got started on our lesson on converting percents.

Being that it was our first lesson on percents, I had a few opening questions just to get their minds geared into thinking about what percents actually were:

Lately I’ve been reading quite a bit on math education. Lots of stuff on having students have mathematical debates/dialogues as well as making math inquiry based; pique their intrigue from the start to give them a reason to want to learn. All stuff that I’ve always heard but have struggled with exactly how to do it.

So back to the classroom. Gave them a few minutes to write and then discuss w/ one another what they did. Several of them shared why they felt 50% off of something meant half off. “50 is half of 100 and percent is out of 100 so it would be half off of the item” was a common thought that was shared.

The second discussion sparked one of the best discussions I’ve ever had in class. I’ll try to recall some of the conversation bits:

**AE-** ‘well it’s when something grows to it’s full self because 100% is like full and completed’

**IP**– ‘so if something were like only 25% grown and then grew 100%, it would be more than it’s full self…it would be like 125%’

Several comments like this were coming around. They were focusing on this word ‘grow by’ and I think they were reading it as ‘grow to.’ I decided to make a change in the wording:

If something has increased by 100%, what does that mean? How do you know?

A few students: ‘…oh…OH!…’

**WJ**– ‘ok so if 100% is the full…it’s like 1.0 as a decimal, then lets say our unit is 1. If it increased by 100% then it would be 2! But then let’s take 2…if we increase that by 100%, then it would be 3, and so on.’

**GO**– ‘I might be wrong but I see it as 100% is all that you have…so if I were to have 1, then if that increased by 100%, then that would be like adding 1 more. If I have 2, then if it increased by 100%, then it would be like adding another 2, so I’d have 4.’

Another student echoed what WJ had discussed (I wish I had a recording of the discussion)

**CS**– ‘ohh…so, OK…100% isn’t like a number it’s like…it’s like a percent! So if you have 100% of something, that’s just having all of it…I’m not sure how you would write that as a decimal, I guess it would be 0.100…but…I don’t know how to explain it.’

The above were bits I remember but the discussion had gone on for about 20 minutes by this time. I interjected near the end and shared how it seemed there were two different definitions of 100% going on; a few were thinking in terms that 1 was the whole and 100% of it would continue to be 1 while others were thinking of 100% of whatever they were working with at the time. 5 more hands went up.

Meanwhile WJ and ES were continuing their own discussion while whispering. I heard things like ‘yeah so it’s like the whole!’ ‘Yeah that’s exactly what I was trying to say!’ ‘It’s like we have the same brain!’ ‘Man can we just keep talking about this forever! It’s so interesting!’

We unfortunately had to end the discussion. As I as erasing the board and preparing to debrief the discussion, WJ yells out IT’S OVER 100! IT’S A FRACTION OVER 100!’ I waited at the front like you normally do when you’re waiting for the class to get quiet but a few kept arguing. I let it continue. Eventually they brought their attention back.

I told them that they were having the discussion of mathematicians; that they WERE mathematicians and turned our classroom into a mathematical workshop. I shared with them that the more I learn about what the best math teachers in the world do, the more I kept coming up on teachers doing exactly what we did in class today. I told them that we’d discuss converting between percents, fractions, and decimals next class but that I loved hearing the discussion they had today.

As they were leaving:

**WJ**– ‘man that was the best discussion I’ve ever had.’

**Me**– ‘in math?’

**WJ**– ‘ever!’

Probably a bit of an exaggeration but I’ll take it 🙂

This is exactly how I wish maths was taught; discussing the CONCEPT rather than how to find an answer.

Honestly, I find that I learn better when I learn the concept itself, rather than how to apply it to get a question. I’m sure that this is how a lot of other people learn, and I think that we need more teachers just like you.

Thanks for the encouragement 🙂 Will continually share as I learn how to further develop this sort of classroom environment.

I strongly agree with you. If you hold the concept, then you will grow very very able to apply it to get questions.