# 211. Hidden Rectangle problem

Cool vectors can be exciting! They can describe the motion of a particle, they can represent the acceleration of a rocket, they can tell you about the angle an impact takes place at!

Uncool vectors describe lines, they can intersect, they could be perpendicular, they could even describe skew lines in three-dimensions. Not quite as exciting. It isn’t difficult to see that revising standard C4 vectors can be a tad dull. How about an investigation? An investigation without an obvious answer. A question so simple that the answer is a single number. It’s the steps in between that make things interesting…

• I asked my A-Level class to find the area of a rectangle … simple so far, how is this worthy of C4?
• The rectangle is bounded by four vector equations … ok, points of intersection, line segment length, bit of Pythagoras there
• The vector equations are 3D … ooh, that makes it a bit harder
• There are eight equations to choose from … that’s mean, that means finding the angle between lines, checking for skewness, identifying parallel vectors
• There are plenty of ‘red herrings’ … now that is just unfair (great!)

The solution to the problem is a simple surd. If you do ‘Crack the Code’ or ‘Locked Box’ problems you could use the digits under the square root sign as your padlock code.

You can download the worksheet and teachers notes here: C4 Vectors Hidden rectangle (pdf)

Depending on the engagement/ability of the students this could take between 20 and 40 minutes. It would also make an easy to assess homework.

# 210. Most Wanted Percentages

I’ve been looking at how to teach percentage increase and decrease at Key Stage 3. If you can find 20%, you can obviously increase by 20% by adding it on. But does this reinforce the misconception that percentages are an addition, rather than multiplicative, function? I’ve started teaching multipliers for increase and decrease to a wider range of pupils, so it makes sense to introduce the concept earlier. I’ve used finding 120% as a way to increase by 20%. It opens up discussion as to why this works and pupils can form their own ideas on how to decrease.

Image Credit: www.te

To reinforce and practice the idea of increase and decrease by percentages I’ve created some ‘Muppets’ themed Top Trumps cards (not licensed). You can download them here: Muppets Top Trumps (pdf)

There are only eight cards, but you could print out one set per pupil and shuffle them.

# 209. Unforgettable pens

Before signing off for the Easter break, I thought I’d share this nifty little gadget with you.

• What do teenagers always bring to lessons? I’ll give you a hint: it’s not their homework.
• What do teenagers often forget to bring to lessons? I’ll give you a hint: it’s not their homework.

Answers: Mobile phones are often brought, pens are often forgotten.

The ‘Jackpen‘ is a pen that fits into the standard headphone socket on a mobile phone.

It’s a clever little idea, combining two everyday essentials. The multi-packs make them cheap enough to be good classroom prizes too (pick up three pens for less than £3 from Amazon)!

For students it’s a bit of novelty, although it could be easy to lose or ‘borrow’ and is not a long term solution to bringing their own pen!

# 208. Gadget of the week

Anyone who visits or uses my classroom knows that whatever equipment you will need to teach with will be there. I think it’s just good manners to keep everything tidy when you share a classroom.

One of my pet hates is mini-whiteboards, or rather the distribution and collection of them. If you weren’t in that classroom the lesson before, you don’t have the luxury of putting them out before pupils arrive. Some people keep them in plastic wallets with a board, pen and wiper in each. Great, until:
“My pen doesn’t work!”
“There is no wiper”
“There are no wallets left”

Last year I found an easy to manage solution in a supermarket – Kids Garden tidys (£2.50 – Tesco). They are back in stock for Spring.

The long section holds whiteboards, the small section is a perfect pen pot and the middle sized section holds mini sponges. Obviously this will depend on the size of your whiteboards.

If my tables are groups, I just put one of these baskets in the middle. If the desks are in rows I distribute them around the room – it saves a rugby scrum at the front. Collecting the boards in is much quicker and it is easy to have a couple of spare pens in each tidy in case one runs out.

The small size of these baskets makes them easier to store than the full size versions. As they have handles, they stack nicely when not in use. They could also be used for any class equipment: pencils, calculators and rulers maybe?

See what your local garden centre or supermarket has this Spring and have a Spring clean of your teaching space!

# 207. Is it on the formula sheet?

In the Autumn term I put together a booklet of all the Trigonometry and Differentiation rules that you need for the Core 3 (Edexcel) exam. It was a summary of key facts and highlighted what you need to learn vs what is on the formula sheet. The original post was 155.Trigonometry&Differention including links to the booklet.

One term on, at the request of students, I’ve produced the same kind of booklet for Core 4 Integration and Differentiation. Even if you don’t do the Edexcel exams, they are still helpful revision tools.

# 206. Seek a number pattern

So I’m all ready to teach a lesson recapping number patterns from the basics for a lower ability group … then a visitor to the Department arrives and asks if it’s okay if they observe my lesson. They’ve been told that there is usually something ‘off the wall’ happening in my room. Thanks … I think!

Well, I’m not one to disappoint. A little fun with the starter perhaps? The sun is shining and I’ve got whiteboards and chalk …

We’ve all seen fence panel number patterns. Here is a fence:

What can you see?

We discussed the pattern linking number of posts and spacers. We then represented the fence in colour coded symbols (yes, we have chalk in more than one colour!) and annotated it.

The class were then sent off to find their own patterns. They found repeating patterns and made notes on their whiteboards. Once they were happy with their work they could chalk it out.

This group looked at number of slats on a bench with number of benches.

They represented each bench as an ‘L’ and each slat with an ‘o’.

They worked out:
No of benches x 6 = No of slats

Other groups looked at number of windows & number of classrooms and number of benches & number of picnic tables.

We then went back to our quiet number pattern work in the classroom.

This task is easily adaptable for many aspects of number, including ratio and proportion.