I finally did it – I ran a session at Mathsconf8, in Kettering! The theme was ‘Why don’t you…?’, inspired by the 1980s UK kids show:
The idea was why don’t you put down the textbook, step away from the worksheet and get your students involved in doing Maths rather than have it done to them. I have to thank the participants for being up for a laugh and getting fully involved. Because it was a hands on session, all the notes needed for the activities are downloadable in a booklet.
Joey? Why yes! Joey Tribbianni from ‘Friends’ (random 90s TV reference). When the friends came to London, from New York, Joey demonstrated his unique technique for navigation:
He jumps into the map! And that is what my students did for vectors.
In the first lesson we started looking at the basics of vectors. I found this PowerPoint from TES resources to be really good for starting discussions: Introduction to Vectors by rhemsley
In the second lesson, we started to solve problems and moved outside.
Objective
To develop problem solving skills with vectors.
To understand how vectors relate to more complex diagrams
Resources
Chalk (coloured is good)
Vector questions from a textbook, worksheet or exam database
Mini whiteboards – optional for working out/calculations on the move
Activity
I drew one side of a regular (ish) hexagon on the wall (I really would like an outside chalk board). We labelled the ends A & B and the vector joining them was a. I decided to use a different colour chalk for each vector to make them stand out.This was followed by vector b (joining B & C) and vector c (joining C & D). To be honest, I had to get a student to draw in D and the line – I’d accidentally* drawn the diagram higher than my arm reach.
(*I’m over 5ft 6in, but my lively lads are nearly 6ft – gallantry meant they felt they had to help and hence engaged with the task very quickly!)
Back to the problem:
This hexagon wasn’t going to draw itself, but which of the existing vectors to use to create point E? I explained that vectors a, b & c are our building blocks, which helped us move on.
The students were quick to identify vector a. They were very picky about the direction too. My gallant helpers added it to the diagram. We used the same logic to finish off the hexagon.
The students then went away with their worksheets and drew out their own versions of this diagram. As I walked around there were some heated debates as to which vector went where and in which direction. They addressed many misconceptions before they even looked at the question – it comes back to the old rule of ‘ Write down what you know’. They’d already answered questions on the diagram that they hadn’t yet been asked.
The questions were based on this diagram:
They started easy and quickly moved on to trickier concepts:
Why can’t you just invent a letter for BE?
Does it matter which route you take around the diagram?
Can vectors be simplified like algebra?
All of these questions can be solved by ‘doing a Joey’.
When I teach vectors I always use the analogy that vectors are like a one-way system of roads. For example, the vector from E to B is drawn in, but has no specific vector – this is like a closed road, you must detour down the other roads to get there.
As you walk down the other roads (vectors), are you going the correct way?
If the answer is ‘yes’, just make a note of the vector and carry on.
If the answer if ‘no’, then a minus sign gives you the permission to go the wrong way – write the the vector with a negative. (This then leads to the follow up discussion of why this works through use of column vector examples)
There is more than one route. What do you chose?
Clockwise or anticlockwise?
EDBC or EFAB?
Walk them both and see what happens – you can see that the vectors are the same, just arranged differently.
Finally, when you start to compare different routes, you can see that vectors cancel out, just like algebra. In fact, it quickly becomes clear that basic rules for simplification still apply.
Student Reaction
The sight of pupils walking around diagrams looked like something from a Monty Python funny walk sketch. As we walked back to class, after half an hour in the sun, I overheard two different groups of students. One group said: ‘That was a really good lesson’ and ‘Yeah, I enjoyed that!’ – that may have been the sunshine though. Another group however said: ‘I get it now. I didn’t get it last lesson the board, but now I get it!’ – and that wasn’t just about the sunshine!
This is a simple compass directions game which can be extended as you see fit. The basic concept was thought up by some KS3 pupils who were designing an activity for KS2 pupils.
Aim
To practise using compass directions (4 or 8).
To develop the concept of bearings (extension)
Set Up
At opposite sides of the playground draw out two boat shapes. Draw a compass half-way between them.
Pick a pirate captain and first mate.
Pick a Navy captain and first mate.
This is where any dressing up hats make it fun.
Split the rest of the class randomly into pirates or sailors – tokens can help here.
Compass Game
Each captain must stay in their ship.
The class spread out across the playground. The first mates are rescuing their crewmates based on their captains’ instructions.
Each captain shouts instructions eg 4 steps north, 2 steps west.
(The instructions can be varied depending on the level of difficulty eg 5 steps NW).
Once a crewmate is reached, they ‘swim’ back to their boat. Variation: If a sailor rescues a pirate (or vice-versa), they are held hostage for 10 seconds.
Winners
The first team to rescue their whole crew.
Variation:
When a person is rescued, the first-mate becomes the captain and the rescued person becomes first-mate. In this way lots of pupils get to practise using directions.
If you need a quieter version of this activity, the captains can hold up mini whiteboards with directions, rather than shouting.
Extension
Develop the concept of bearings with the first mate starting next to the captain and following a bearing.
