Perimeters of arcs and sectors

PowerPoint here.

I’m kinda on a roll. Not sure how I feel about this one, though. Maybe too close to the last two that I’ve done (in activity terms). Could do with a little more interest in there.

I’ve also made some lovely sectors questions (first pic above) but I’m not sure exactly how they fit into the lesson. There’s a big lesson about using the formula and then some questions at the end where you don’t really need it. Hmmmm. They’re nice questions, though.

Also I think I should have included more questions on half circles and quarter circles. Or shunted some into the circumference PowerPoint. Might have a think about that.

Circumference of circles

Lesson powerpoint here.

The questions here lack a little of the meta tasks I’ve built into other stuff. But I’ve tried to build as much thinking into this as possible.

Here’s a little gallery of what you’re downloading.

Areas of circles next, I think.

I know some of these lessons are ‘prescriptive’. I don’t want people to get the wrong idea. In the lead up here I did a lesson on ‘discovering pi’. Using string to measure circumferences. The pupils found it really hard!

Measuring a circle is difficult!

We then used the ‘wisdom of the crowd’ and collated all our answers to get close to pi.

We got 3.3 ish. Eeeek.

I’m not sure if doing this helped students get a feel for pi. Measuring was so hard that students didn’t really feel like each circle they measured had the same ratio.

But I’m still glad I did it. Sometimes it’s nice to do things like measuring and to let go of student’s hands and see how they cope. Hopefully they’ll also have an appreciation for why it’s better to use the formula than measure when we come to do this lesson on circumferences.

PS : Gonna look through the links at the top and start cleaning up the sections. I’m sure there’s materials I’ve made that haven’t been listed up there.

PPS : It’s worth occasionally redownloading the PowerPoints. I often tweek and change stuff as I teach. Everything is a work in progress. Give me 20 years.

PPPS : Don Steward’s questions on this are, as always, brilliant.

Quadratic Simultaneous Equations

Here is a lesson on Non-linear simultaneous equations. Three example problem pairs. Some questions. Something a bit more problem solve-y. 5 timed questions. Some exam questions. It’s quite basic, really.

I know I haven’t posted much recently.

I will try and post some more stuff.

There’s a big difference between stuff to make for myself and stuff to publish. I usually just find some questions and paste them in for myself. Writing the questions and getting this up to snuff for publishing took a good couple of hours, and it’s quite a basic lesson.

PS I recently subscribed to MathsPad and it’s really good.

New Lesson: Using the quadratic formula

THE LESSON IS HERE.

This lesson was a massive learning curve for me and I’ve massively changed it after I taught my year 10s.

The first version of the lesson presented an example problem pair and asked them to get on with a variation activity. How hard could plugging numbers into a formula be? Well, it turned out the lesson was a little rubbish, and students really struggled.

After the lesson I got to thinking why.

I think I had not thought deeply enough about what can go wrong in the quadratic formula.

Specifically, I did not make it explicit enough that a, b and c contain not just the coefficients of x squared, x and the constant. They also contain their direction. In the equation x^2 -3x + 2 = 0, b is -3, not 3.

I wrote an activity to tackle this and added it in when I retaught it the following day. It went a lot better.

There was also confusion around a negative b going into the -b bit of the formula. It just shows, I’ve been teaching 7 years but there’s always stuff to learn and think about. Often things we think are straightforward are anything but to our students.

I’m also not sure how good the vary and twist activity is [available here].

I have split it into two sections on the PowerPoint, surely a sign it should really be two worksheets. However, I’ve still left it as one, for printing reasons.

I also wrote some questions I thought were lovely.

There’s quite a bit to discuss here. I like the emoji format. Does that middle question need to 5x on the diagonal? I don’t know if removing it makes the problem better.

These proved very challenging for students. I really should have scaffolded more, but I’m not sure how I could have without giving the game away and making the questions trivial. Some students liked these problems. Quite a few didn’t engage. It was hot and after break.

I’m still sharing the lesson here, with adaptations I’ve made. Maybe you’d like to make your own. Again, I’ve tried to go into more depth with things like the number of roots.

There’s also a set of timed questions here. Again, this is picking from a couple of thousand questions. It also picks from a database so you should never see repeat questions or nonsensical questions. I’ve done the four levels like so
Level 1 : Naming a, b and c
Level 2 : Solving a simple one
Level 3 : Introducing negatives
Level 4 : Number of roots

A long time project might be to adapt this resource so you can choose the number in each skill level to display.

Please comment with any suggestions.

New(ish) lesson: Factorising Single Brackets

THE LESSON IS AVAILABLE HERE

This isn’t completely new. I’ve edited and refined a lesson I’ve had on here before. Except I’ve packed it with MORE STUFF. I’eve tried to use Jo Morgan’s idea of going more in depth. So this lesson has:

Some I do you do/examples.

One of my vary and twist activities. Available as a word file here.

Some ‘does it fit’ whole class discussion. Look at question 4. Oh my!

A ‘spotting of mistakes’ activity to really hammer the point home.

Using factorisation to complete calculations. Yes please!

A problem solving task!

Oh. Then I thought. How about a plenary.

On the powerpoint is a quite nicely thought about 5 question mini test thing. It’s quite easy. But Craig Barton has defiantly managed to convince me that chucking a really hard question at the end is a mistake and maybe we should be giving students confidence at the end.

I know what you’re thinking.

What if I want some slop. Or some more timed questions? You can get some here. It randomly picks from…wait for it…over 2,000 questions!!!

Sometimes I think I should plan more lessons like this.

Including coding and stuff for the questions on the timed questions it took me about 5 hours.

Maybe that’s why.

As always give me a shout if I’ve idioted a question up.

Excuse me if the writing style was mad today. I downed a lot of Cherry Coke whilst coding.

Robert Low: Why is subtraction so hard?

Really interesting article and worth a read

Subtraction presents various problems to learners of mathematics, not least with the mechanics of hand calculating the result of subtracting one multi-digit number from another. But that’s not the kind of difficulty I’m interested in: I’m more interested here in the difficulties that arise when computations involving several additions and subtractions of integers are involved, or at the slightly more advanced level where algebraic computations involving several additions and subtractions are required. I’m going to take a look at what I think lies underneath the difficulty.

http://robjlow.blogspot.com/2018/06/why-is-subtraction-so-hard.html