As a member of the TES maths panel, every so often I’ve given a set of resources to review. Here are some highlights from this batch!

Level 2/3 Perimeter Homework Question by Ayliean MacDonald @ayliean

Such a simple idea but really pushes students to think about what they’re doing. It’s important that we (and students) don’t assume that Grade 2 or 3 automatically means ‘easy’.

Level 3 CORE Maths Lessons Ch1-4 by tpayne89

I’m going to be teaching Core Maths (level 3) next year for the first time at my school. It’s a reasonably new/niche course and there isn’t much out there yet so a bank of investigations like this is great.

Quadratic Sequences 2 (Treasure Hunt) by David Morse @Maths4Everyone

I’m usually not a massive fan of treasure hunts but this one is very well presented and has an extra twist to make it worth using.

Algebra Assessment – Simplifying, expanding, factorising (100 marks, Grade 1-7) by askmrarya @my2pennies

This is pretty straight forward and while it doesn’t break new ground, it is *perfect* for revision for my year 11. Loads of questions with variety and challenge.

Factorising 3 (Treasure Hunt) by David Morse @Maths4Everyone

Similar thinking as my previous treasure hunt comments above. This is really nicely presented, has good questions and an extra twist.

Maths Word Search with something extra (Names of Shapes) by David Morse @Maths4Everyone

I would never have expected myself to give a wordsearch 5 stars! This one is a bit different though as it doesn’t have the words to be searched for but the shapes instead. Given the trouble I’ve had recently trying to get my year 8 students to deal with shape properties, I’m going to put this one in the file for next year and use it as a way in to a discussion about how to describe/name/categorise the shapes.

In case you haven’t noticed, David Morse has made three of these resources so he’s obviously on a roll!

Why not take a look and see if you agree with my 5 star rating? I don’t give them out easily (I had 33 resources to review in this batch) so I think you’ll like them. You’ll obviously need a TES login to access them but it’s free, and frankly, if you’re reading this sort of blog you probably should have a login to the TES!

Just for a change, a busy week 🙂 Some really nice things happened though!

#### Mock marking

Marking mock exams obviously takes a long time. One of the aspects of that is the constant moving of the papers so that you have one in front of you at a time so I thought I’d try putting the papers in a row and then moving around between them. I wondered if that was more efficient and/or more interesting!

I can’t really tell if it was quicker as I had to stop and continue them at home (where I don’t have the space to lay them out) but I can say that it didn’t feel like it was taking longer. I did like moving around more – I’m not keen on sitting in one place for a long time. Next time, I’ll see if I can make it possible for a wheelie chair to move around between the papers as bending over the tables did pull on my back a bit!

#### Mail Merge Parents’ Evening

We had year 11 parents’ evening and, having marked all the mocks and putting the results into a QLA document, I was able to print out a mail merge document for each student with their individual question-by-question results. This made a great conversation point and clear revision guide for the immediate month or so as they can use mathsgenie to look up the topics they did less well on and work on improvements. If you don’t know how to mail merge, I can highly recommend asking around for someone that can show you!

**Scratch – for quadrilateral properties**

In the never ending quest to help year 8 understand the properties of quadrilaterals, I tried to go for the ‘to the point’ approach of simply giving them a list of the properties of each shape. I also asked them to use the sort of revision techniques they use in other subjects when they simply have to learn facts. Mostly, this involved highlighters.

Later in the lesson, I asked students to ‘write a computer program’ that would guess the shape you were thinking of by asking you about its properties. As we were doing this, one of them mentioned Scratch. I checked our system and it was available for me to use so it was a great chance to let some of the students teach me how to use Scratch and for them to see me learning something! Plus, we also had to think about the properties of quadrilaterals and how yes/no questions would lead us to different shapes.

**Joint Planning**

I’ve been working with a couple of other KS5 teachers to jointly plan the topic of Trigonometic Identities and Equations. It’s something I don’t have much experience of teaching so I was happy to pull together resources from TES and other places so that, in discussion with the other teachers, could put together a resource we could all use. I know it is glaringly obvious that sharing ideas and collaboratively planning is a good idea but actually carving out the time and consciously doing it is another matter!

On top of that, the sort of satisfaction you can only get from solving trig identity questions was fun to share with year 12!

I was unwell on Friday and the weekend, hence the delay in this post.

#### Pythagoras

Year 8s are continuing the tilted squares investigation but, the investigation has pretty much run its course so I’ve been looking for other pythagoras tasks to do. As ever, Nrich has the answer with a great selection of challenging problems, including ones about which bits of wood would fit through certain doorways.

Some of the year 8s have shown that they are still unsure about finding areas of triangles. Given that this is the second project that’s involved them this is surprising and frustrating. When individually asked and prompted, they are able to say how to find the area of a triangle so I’m not sure why some aren’t managing it in the short test. I am going to try increasing the pressure and pointing out that it is their job to make sure they know and can recall the topics we’ve done in class and I think that some might need a prompt by contacting home.

**Trigonometry**

Year 12 are moving on to more complex aspects of trig. We’ve looked at how the calculator will only give you one solution and how the graphs can help you find the others. Our KS5 coordinator is strongly opposed to using CAST diagrams (I’m no fan either) but it’s surprising that they seem to be everywhere with many websites and textbooks using it. I’m not yet sure if I might introduce the CAST diagram during revision, once I’m sure the principles have sunk in and I can offer it as a quicker route for those that really ‘get’ how the graphs work.

Even more interestingly, I’ve set up a shared folder where I and the other two trig teachers can pool resources. I really want us to collaborate more effectively and also reduce workload in the long run. I think I’ll have year 12 again next year and want to the same resources I used this year but with improvements and suggestions from my teaching and the other teachers’ suggestions. Sounds easy and obvious but not something I/we are particularly good at (yet).

#### Number puzzles

Year 9 have been looking at factors and multiples as well as some calculation refreshers and I’ve been using this number puzzle with them. It’s interesting how quickly students want to talk to others, share ideas and work together. It’s been an actual battle and I’ve had to tell them to ignore the Brain, Book, Buddy, Boss poster in the room I’m in with them and to think of it more like a Brain, Brain, Brain, Brain poster. They need to experience being stuck and deciding what to do for themselves otherwise they’ll never practice getting unstuck!

#### Staff welfare

I’m part of my school’s staff welfare working group and we had our first meeting last week. The focus was on communication and emails. If you have ideas for how you or your school has reduced emails I’d like to hear them!

#### Number puzzles

*what*they have to do, but it’s the

*how*that’s the challenge. This is a classic example of maths where it isn’t the answer that’s interesting, it’s the puzzle of trying to find out how to get to it that’s the reward. I enjoyed having that conversation with students as it really doesn’t come up as much as it should.

#### Tilted squares

#### Constructions

I’m not a fan of teaching constructions as it seems to take forever and there’s a lot of different techniques to remember. Having said that, this year, my year 11 students seem to be really good at using pairs of compasses. That’s practically unheard of but it did mean that the lesson went really well. I’ve had some of the best ‘centre of a circle’ constructions I’ve ever seen from this class and I might be coming round to liking constructions a bit more!

#### Odds and Ends

We had maths teacher interviews this week and have selected a great PGCE student from a strong field. One of the comments made was that it was obvious that the teachers in the department really loved maths. I already knew that was true and you might assume that all maths teachers love maths but I can assure you that it isn’t the case. I was pleased that this fact about our department comes through even to relatively brief visitors.

I marked the mechanics questions of my year 12 mocks this week. I’ve decided that I’m slightly warming to mechanics. If you know me and/or listen to the Wrong, but Useful podcast, you’ll know that’s quite a breakthrough.

It’s quite common at my school for students to say “Thank you” at the end of a lesson as they’re leaving. I was particularly struck by one student who, last lesson on Friday, left the room, realised they hadn’t said “Thank you” so made a point of coming back to say it. If you haven’t picked up on it yet, I’m in a rather nice school!

Busy week as always. Some nice finds and experiences this week.

**Magic Gopher**

In the 1089 project, we prove that the process always leads to 1089 for a 3-digit number. As a precursor to that, another teacher showed us all a nice website that has a simpler ‘think of a number’ effect that really impressed my students.

It was great to work through the algebra with them and for them to really ‘get’ why the trick was working. There were some actual jaw drop moments, especially when the gopher was right twice in a row with a different symbol each time!

As an aside, I kept catching myself referring to the gopher as ‘he’. Must stop doing that.

__Shape Sorting__

__Shape Sorting__

The battle to correct misconception about shape names continues.

**Positives:**

Our head of maths showed us a nice standards unit that has a lot of scope for playing around with classifying shapes. I didn’t bother printing the grids out and some students thought to just use pens/pencils to recreate the grid on their page. There were good discussions such as:

*Should the circle go in the ‘has no right angles’ group?**Does a square have two pairs of equal sides?**Can a shape have ‘one side equal’?*

I incorrectly named an angle as obtuse when it was really reflex and a normally fairly quiet student felt happy to correct me. That was good to see.

I also used this site in a computer room and it does a lot to work on these sorts of categorisations.

Students have suggested I should write a ‘My First Shapes Book – a Maths Teacher’s version’ and I honestly think there’s some scope in that. One for the ‘to do’ list.

**Negatives:**

When discussing trapeziums, two separate students said:

*My primary school teacher said that’s the one that if you turn it upside down, it looks like a flower pot.**It’s the thing that elephants stand on.*

Probably some more to do here then.

## Indices

Had a really solid lesson where students just practised the skills of multiplying, dividing and raising a power to a power.

Some year 9 students were able to get their head around rewriting powers in a different base. eg rewrite 8³ as a power of 2. This was a good stretch for those that had solidly understood the main points.

## Vectors

Year 11 students are finding this either easy or very hard. There isn’t a middle ground. I need to find some ‘prove that these are a straight line questions’ that are more structured.

Mock year 12 exams this week so that will be interesting to mark. More to come next week.

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.

Hi all. I’d imagine that many people have new year’s plans to blog more often/differently or something else and I’m well aware that it’s easy to make plans and not stick to them. I’ve clearly not been blogging that frequently recently and much less than in my early years:

I think this is probably to do with my change of approach. In the early days, I would send a quick email to Posterous (the host I used before WordPress) and it would be automatically uploaded, making it easy to put up quick thoughts after a lesson. More recently, I’ve been planning my posts more carefully and trying to think about creating more polished content. While I do like this approach, it does appear to mean that I just haven’t been posting anywhere near as much.

So, the plan is:

- Post more frequent, short thoughts,
- Focus more on things that happened in my lessons and/or lessons I’ve seen,
- Record (in writing) some of the frankly, great conversations that happen amongst my maths team.

I think it’s time to go back to being a blog about a full time teacher with more day-to-day thoughts. At least, that’s the plan!