# WHTW? 1089 and classifying quadrilaterals

Last week, I wrote about returning to the title of my blog site and being a ‘reflective maths teacher’. I haven’t figured out exactly what format I want this to take yet, but for now, I’m going with What Happened This Week? (WHTW?)

**1089**

In year 7, our project this term is 1089 and there’s a very brief description here if you’re not familiar with it. It’s a nice little project and really flags up who isn’t comfortable with adding and subtracting.

#### Positives:

Students are doing really well at making conjectures:

- I think that after the subtraction, the middle digit is always 9
- The difference between the first and third digit, multiplied by 99 is the answer to the first subtraction

And, after moving into 4 digits, students are productively amending previous conjectures:

- Student A: If three digits are the same, you get 10989.
- Student B: No, you only need two digits the same.
- Student C: Not quite, the two the same have to be in the middle.

- Student B: No, you only need two digits the same.

I’m really pleased about the conjecturing and that the students seem to be fairly comfortable with having their conjectures shown to be wrong. However, I think I still have a way to go with this as there are some students that are reluctant to share their thinking. I may well force this point and individually ask them for a conjecture 1-to-1, then put it on the board.

Two students particularly impressed me. Some of the three digit numbers lead to 99 after the subtraction and you have to discuss whether to treat that as 99 or 099. If you choose to treat it as 099, then you end up at 1089, if not, you get 198. As part of the class discussion, one student said that you’d like a reversed number to reverse back to itself (eg 192 to 291 to 192 to 291 etc) and for that to happen, if we start with 990, then we would need to keep the zero on 099 for it to self reverse. This is the nicest reason I’ve ever seen for why to keep that leading zero!

When we moved to 4 digit numbers, I asked whether we should keep the rule about ensuring our first digit is larger than the last digit. One student said, “I think we should keep that rule as we’ve already changed from 3 to 4 digits so we shouldn’t be changing more than one thing at a time.” This was absolutely the most mathematical thing that any of this class said last week and really showed strong progress in understanding how to do a maths investigation.

#### Negatives:

My weakest students are still really struggling with subtracting and adding consistently. I’m at a little bit of a loss as to what to do as they can do it when I talk them through 1-to-1 but then don’t seem able to carry on by themselves. I have contacted one parent and probably need to with the others.

The layout of the calculations is widely variable. I evidently didn’t model this as clearly as I could have. I also need to think more clearly about what to do with students that easily *could* lay it out better but are choosing not to. I think I might use a structured worksheet but I also don’t want to ‘do it for them’ and take the responsibility away.

## Classifying Quadrilaterals

**Positives:**

I haven’t really got very far into this yet but students are clearly (mostly) comfortable with things like right-angled and parallel.

**Negatives:**

Quite a few sadly.

The first one is that I realised this week that I have been teaching a vocabulary word incorrectly. There are a number of ‘named’ quadrilaterals and then, there are the ‘other’ ones. I’ve been calling those ones *irregular* and have even said “Irregular ones are the ones where none of the sides are the same length”. This is simply wrong. I don’t really know how I’ve gotten to this point but it is quite a weird feeling knowing that this relatively simple thing is something I’ve been doing wrong, probably for 16 years now! Obviously it’s good that I’ve spotted this and can correct it now but still…

I don’t seem to be able to get across the nested nature of quadrilaterals. Having gone through with a class what the properties of various quadrilaterals are, I asked whether rectangles were parallelograms, to be met with a slight majority vote of “no”. I’m prepared to accept that quadrilateral classification is a bit tricky/nuanced but it shouldn’t be that bad. Evidently, I need to reflect on how I teach this. Current thoughts include using venn diagrams in future.

My students **still** aren’t all convinced that squares are rectangles. I think this might be part of a bigger battle in society in general and maybe I worry about this more than I should but I’m wondering if I can find out a bit more about how quadrilaterals are introduced in nurseries and primary schools.

## Index notation

**Positives:**

One of my classes have picked up the three basic index laws (multiply, divide, power of power) just from seeing two examples of each. It just sort of ‘clicked’. I’m pleased that I (correctly) judged that a simple example would be enough for them to get it.