Thread by @blatherwick_sam

Factorising non-monics

I had read about doing this before factorising monics.

So I gave it a go.

Fans of #donsteward 's boxes (donsteward.blogspot.com/2019/02/boxes-…) will like this!

This is y10 set 2 aiming for grade 6/7. Some of them will do A-level.

#mathschat #mtbos #mathscpdchat

I appreciate this is leaving nothing to chance, direct teaching. This took four lessons in total.

I was a little delayed, when, halfway through the week almost half the class got put into self-isolation and I was teaching it blended with 13 at home and 16 in the classroom.

I'd written about this approach here in theory logsandroots.wordpress.com/2020/10/11/way…

based upon a tweet by @DrStoneMaths here:

https://twitter.com/DrStoneMaths/status/1281276558351773699?s=20

so this week has all been about putting this plan into action.

I started with skirting round what I intended to avoid; explicitly teaching monic factorisation

We multiplied some brackets out. I didn't specify a method. We noticed stuff. Some students were caught "speeding" (eg not writing out all four terms). We discussed how they did it.

Then worked onto a hook. These had a pattern but it wasn't so obvious. We could write down the next one in the sequence, but it wasn't as straightforward as the last to see what the coefficient of n was going to be.

I didn't go over the top at this point.

I wanted to highlight the importance of the four term expansion to these and we'd got that. I specifically asked for the four terms here. Four terms is important for where we are going to so they needed attention drawing to it.

We have done loads of practice at "boxes" over the year. I had been doing loads of practice because I knew in September it would come to this.

I gave them a sheet of A4. The top exercise was boxes the bottom exercise was expanding double brackets.

I forced the grid method

Because the students' attention was drawn to the procedure they hammered their way through all of this.

Then I asked them to step back and look at the numbers.

WOAH!

What do you notice? All about the wow here!

There's a lot of hard work still to go

Worth mentioning at this point that a student had recalled the diagonals property of boxes (as we had investigated it earlier in the year) and had shared with the class that it was a v good strategy in this case where it was hard to see the ratios as well.

I hammered this for the rest of the week. I kept coming back to this student and saying it was his method.

I emphasised how important it was that he had remembered it.

We are doing "Student X's method" - all about the ownership.

ps I started putting product in the middle

Now we had made that connection I needed to put some ground work in. We started with two mini steps. One was working with algebra in boxes. The other was putting four terms into the grids.

Big variance in performance here.

Because of the variance in performance I looked at my assessment and put some scaffolding in place here. I went back to whiteboards and did some work on both of these.

Students at this point were keen the emphasise how important the diagonal property was here. (as a coincidence I saw @StudyMaths using this method in a worked solution this week on another type of problem)

They put this and would explain it like this.

I made a point of still talking about horizontal and vertical relationships. So important to still spot those in the answer and PRAISED students who weren't following the crowd method and were seeing alternatives.

All about diversity of thought and listening to those thoughts

Then I looked at the four term problems. Some students struggled with knowing where to put the terms. So I did another expansion and then highlighted the positioning.

At this point students are happily factorising these four terms and we get to the point where if they are given four terms then they can *easily* factorise it - 100% success rate.

I now go back to a theme that we have talked about before (many months ago) and we begin to explore the sum of a diagonal.

So we do the sum of everything, and then start to specify it with problems.

Then moved it onto thinking through these with algebra, before finally going for it.

I need another lesson of practice but I have confidence that this has been more successful than I've taught it in the past.

I am also much more happy with this method!