Efficient Calculations : Addition and Subtraction

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I was going through my old PowerPoint slides looking at my column addition and subtraction stuff. Which was fine, I guess. But I’ve abandoned using slides for a lot of that stuff and set up examples using mathsbot’s place value counters. They’re awesome. (Although I’d like to be able to save an example for later use). I then use loads of randomly generated questions. Usually I’m a fan of writing my own questions, but randomly generated addition and subtractions, especially if you put them in a crossnumber are where it’s at.

What I like talking about, though is efficient calculations. I’ve extracted them and made them into their own lesson here. I really believe in talking about this stuff. My year 7s will sit for ages and work out a calculation left to right without even thinking about number bonds.

We’re sometimes so tied to hitting examable objectives that we forget this stuff can be really powerful. My ideal year 7 scheme of work would move away from these skills and move onto covering things a bit more nebulous like ‘Tricks’ or ‘Diagrams’ (drawing bar models etc) so by the time we’re in year 8, we are all efficient and able calculators. I’d also add loads of binary and bases stuff. I don’t really care that it’s not in the GCSE. Stuff can be valuable without being a examined skill in the GCSE.

Parallel Vectors

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Probably the last resource I will do on vectors, because I’m not sure how much more value I have to add on this topic. I think a lot of it just comes down to practice.

There’s only 4 slides here. A little exercise about identifying when vectors are parallel, which I haven’t done enough of before

Then there’s an example (but no ‘your turn’ as the differences between questions are simply too extreme to make the comparison worth it) and some exam questions that I took off exam wizard.

It’s a bit lightweight, but I found isolating the skill pretty tricky.

If you do this in an awesome way, please tweet me @ticktockmaths.

Introduction to vector geometry

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Ok, so I found a bit of time today and put this together.

It’s very basic, but covers finding ‘routes’ using vector geometry. It also covers midpoints.

There’s not enough practise here, but that was deliberate. I would set them key skill K652/K653 on Dr Frost Maths to reinforce this skill. Those randomly generated questions are much better for loads of practise than my slides will be.

There’s no parallel line chat, nor co linear chat in this PowerPoint. I’m saving both those skills for the next PowerPoints I make. I’m trying to split the skills up as much as possible.

As always, comments and suggestions and stuff to @ticktockmaths on Twitter.

Magnitude of a vector

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There’s two nice tasks here, and some presentation that I’m proud of.

For instance, I tried to build up the difficulty here pretty gradually. There’s also room for discussion on the magnitude of vertical and horizontal lines.

Moving to the skill we really want

I thought this was a clever way to combine two things I like. Code breaking exercises like this one and also questions where we do two different calculations, but get the same answer.

It all comes with example problem pairs and a nice plenary.

I probably won’t upload a PowerPoint for more than a week as

  1. I have half term starting Thursday
  2. The next resource on my list is vector geometry and I think that’s going to a massive amount of work. I’ll have to think how I can break it down into nice chunks. Otherwise the PowerPoint will be 700 slides long.

As always, comments to @ticktockmaths on Twitter.

Column Vectors

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Three example problem pairs, and three exercises covering the basics of vectors. Notation, adding and multiplying.

There’s probably two lessons here.

No real vector geometry, which I find so difficult to teach. I’m going to need to do a bit of research before I tackle that.

I quite like these questions that I wrote

I stole the following idea from Don Steward.
Quite a nice little thing to do, though.

I really struggled to present this nicely. Grumble grumble.

As always, comments, suggestions, corrections and obsequious praise to my Twitter @ticktockmaths.

Next time : magnitudes of vectors.


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Both simple and compound here. I couldn’t make simple a full lesson.

I’d separate this into two lessons.

Also some nice little one slide questions.

I love this style of question. It’s only 8% needed to double a 10 year investment.

Pupils should use trial and error.

There’s also a blooket for lots of practice picking between simple and compound interest.
One number as a percentage of another

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One thing that redoing some of my percentage PowerPoints has driven home is just how subtle the language around percentages is.

We can have the percentage of an amount, the percentage change, changing by a percentage and one number as a percentage of another (among others). No wonder pupils get so confused!

I think next time I teach this topic I’m going to have a long hard look at being more clear with the language that I employ. Maybe that involves picking the wording of some questions apart. Maybe that means looking at some questions and doing some highlighting. Picking from some correct and incorrect solutions.

As always, chat to me @ticktockmaths on Twitter.

Percentage of amounts [calc]

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I’m going through and updating my percentages PowerPoints so that I have all of percentages done and ticked off. Here’s the percentage of amounts with a calculator one, I’ll upload percentage of amounts without a calculator next. I like to separate the two skills.

I also make a blooket. You can find that here. I’m currently loving blooket. It’s basically like Kahoot, but with games. I think the games are really well devised, and it’s great for getting kids doing simple, procedural questions. I also like how the best mathematician doesn’t always win. I know that seems counter intuitive, but often with Kahoot, the same person wins every time. Which can demotivate some. It’s also great for getting them doing work over a longer period of time than Kahoot is.

Again, I’ve actually been really busy updating all sorts of resources. Use the menu at the top to see what I’ve got.