Yes, another algebra post.
Today I was teaching a new (to me) Year 7 middle group algebra. This was their first experience of algebra – at Secondary anyway. I was sadly not surprised that when I announced we were doing algebra for this lesson, the ENTIRE class groaned and booed. Consider that for a moment. They’ve NEVER done algebra at this school, they’re 11 years old, and yet they already have this preconceived idea that the lesson was going to be shite and boring because it has the word algebra in the title. Where does that come from and why??
So battle 1 was to fix it. I asked students to draw a smiley face in their books because algebra is smiley. They had no idea what I was doing, but obliged, because “it’s maths but we’re drawing SMILEY FACES!!”
I asked how many smiley faces we had. One. So far so good.
Then underneath we drew a single smiley face but with a 2 in front of it. How many smiley faces? One student thought there was only one (quite literally correct), but picked up the notation soon enough.
Then I posed a question. The build up and the question are below:
They all got it correct straight away, although a few wrote 🙂 + 🙂 + :), which we discussed and accepted that a more efficient way to write it would be 3 🙂
The point is that for some reason, students seemingly found using smiley faces more accessible. “I thought algebra was about letters?” Not necessarily.
We then looked at the need for different notation for different groups of unknown numbers that have the same value. That sentence alone is confusing, and so it’s no surprise really that students find the concept baffling.
I ditched the smiley faces and went for question marks.
“The question mark is an unknown, hidden number. What do you think it might be?”
Simple enough, no wrong answers.
Now, assuming that the question mark has the SAME VALUE, what is the answer to this:
Again, no incorrect answers. Everyone said 18. I’ve never taken this approach to basic algebra before (apart from the smiley faces bit) so this was a bit of an uncertain venture.
Now, if we know those two question marks are both worth 8 each, what’s wrong here:
Again, everyone acknowledged that something must be wrong, if each question mark is 8, then you don’t get a sum equal to twenty (incidentally, we spent a few minutes considering what ‘equals’ means, reiterating that it doesn’t mean FIND THE ANSWER or GIVES, but means IS THE SAME AS, or EQUAL TO).
We established that one of these ?’s is a bit of a traitor. A liar. It isn’t an 8 at all. Treacherous question mark! A student suggested we wrote it instead as this:
Now we’re getting it. The symbols are now differentiated. The blue question marks are one value, and the red one is a different value. They also correctly said that the red one must have the value of 2, assuming the blue ones are still 8’s.
I then told students that I didn’t want two different coloured question marks. So the red one is going to be our smiley face from earlier.
No complaints. Then came the killer question to test understanding. Seeing as the smiley face is worth 2, and we also have a 2 at the beginning, how can I write this whole thing differently. I want to write the symbol for a smiley face and a question mark just once each. Make this WORK:
A few students were a little puzzled, so I worked briefly with them and looked back at the very first example of how we can write different amounts of smiley faces in different ways, and the cogs turned, I swear I heard audible clicks and ding noises… and then…
They practised collecting like terms using various symbols after that, yada yada yada, then at the end there was a great moment when I asked how many people were confident about what we’d covered. We went through a few key (increasingly difficult) examples and they got them right – a few dropped off when I pushed my luck with 3a + 2b – a + 3, but MOST were still ‘getting it’. At that moment I asked them to reflect on their attitudes when I announced it was an algebra lesson, and compare themselves then, to right now. Because in this moment, with students reaching their hands as high as they could, supporting one arm with the other, desperate for me to pick them to tell me the answer, it didn’t feel so scary.
IN YOUR FACE algebra.