# 264. Distance-Time Drama

*HEALTH WARNING*
You may require nerves of steel to complete this dramatic construction of a distance-time graph. A mental swear box may also be handy for everytime you resist the urge to say what you are thinking. Strong coffee is not advisable as you want to be the image of serenity, not a jittery wreck.

Aim
To construct distance-time graphs from collected data and interpret the speed from a graph.

Equipment
Metre sticks or tape measure
Open area outside
Pencils
Paper (squared/graph etc)
Ruler
Calculator
Stopwatch (or mobile phone app)
Chalk (optional)

Activity – in theory

1. Group your students in threes. They will rotate roles between runner, timer and recorder.
2. Pick four points in your school yard that are a reasonable distance apart. Chalk X’s and A to D next to them. Your graph will start at A and end at D. If you have the space you can create more than just four points.
3. Students are responsible for measuring the distance between A & B, B & C and C & D. These are the three activity stations.
4. Students take it in turns in their groups to run (walk, hop, dance etc) between two points. The time for each student at each station is recorded.
5. Once the data is collected, students gather the information in a table – cumulative time & distance columns will be helpful for plotting a distance time graph.
6. Each student draws three graphs, on the same axes, to represent the speeds of their group.
7. Each student then calculates their speed for each station. They can compare their calculations with their group and what is going on in the graph. Hopefully they will deduce that the gradient of the graph represents the speed.

Activity – in practice

Where to start?

Please … don’t be disheartened if your activity starts like mine did! We got organised and went outside. I designated groups to stations and they started measuring, moving onto the next station when they were done.

One group came up to me and complained that the distances were all the same. Rather than hold onto the end of the tape measure at the start, then measure, this group put the end on the ground, spooled out the tape measure and walked to the next station – trailing the end of the tape along the floor.

A second group complained that the other groups were spending too long on measuring when they were waiting for a tape measure. I’d counted them out one per group – where was it?

‘Oh, we left that in the classroom’.
Mental gnashing of teeth.
‘Would that be the locked classroom?’ I ask
‘Yeah … we’ll get it’ off run two students
They come back complaining the classroom is locked!

Okay … we get the measuring done. Then they start running and timing. I check on one group and notice they are merrily taking all of their times away from ten minutes. They explain the mobile phone is counting down from ten minutes. Although I was impressed by their ingenuity, maybe changing the phone mode would have been more appropriate.

And let’s not mention the student who, on the final station, accidentally wiped all the results off the mini-whiteboard …

Then a miracle happened!

I collected their data together on a spreadsheet and projected it on the board. We discussed any anomalies and how we would progress. We decided neat printouts would help. They drew their graphs, colour coded their data and observed the gradient link to speed. I was very impressed by the speed at which they grasped this concept and proud of their (eventual) independent work.

Here is a sample of their work:

Example 2:

Example 3:

# 229. Speed Camera Maths

Speed Cameras are so last century: discerning law enforcement agencies favour the Average Speed Camera!

These motorway delights timestamp when you go through certain checkpoints and calculate your speed between them. No complicated laser guns required, just number plate recognition and a little distance/time calculation. This already sounds like a KS3/4 class activity or a Mechanics A-Level starter.

Equipment
Squared paper
Pencil
Ruler
Coloured pens
Calculator (optional)

Question
Can you find three different (safe) strategies for staying on the right side of the law through extended roadworks? You must average 40mph over 12 miles (original speed limit 60mph).

Visual Prompt
To start off with just draw out blank axes and discuss how you could visually represent this problem.

Idea 1
A distance-time graph

Idea 2
A speed-distance graph

Idea 3
A speed-time graph

The straightforward option
How long should it take you to get through the roadworks if you stick to exactly 40mph? What does this look like on a graph? Which type of graph shows this information best?

The boy racer wants to go fast, but avoid a ticket – what could he do?

Hint
What does ‘Average Speed’ actually mean?
Can you instantly jump between speeds?
Is acceleration going to effect your calculations?
What assumptions should you make about acceleration?
Do you need to work out the area under the graph or the gradient at all? How will you do this?
Can you describe what is going on?
Is it safe/legal?

Outcome
Your students should be able to produce many different graphs of how to stay on the right side of an average speed zone. They should be able discuss their findings with each other. However the morality or safety of their driving ideas may be a topic of discussion for a later PSE lesson …

# 188. Ducks, chalk and gravity

So how did TeachMeet result in me standing in a supermarket one evening doing a price comparison of duct tape?

Let us go back in time to #mathsmeetnorthwest. Dave Usher did a brilliant presentation on ‘Big Maths’, including the use of gaffer (duct) tape in lessons. I thought this was a genius idea – sticky, sturdy and temporary. I didn’t get a chance to buy any at the weekend, so I ended up in the supermarket on a weeknight.

Cheap own brand duct tape at £2.95 for 15m or branded ‘Duck’ tape at £3.95 for 25m?

I started school the next day with one idea on how to use it, which quickly developed into three..

Lesson 1: Averages

Equipment: Duct tape, liquid chalk marker

I did averages and range indoors. This meant I couldn’t chalk the walls or floor. However I could mark out key features with tape. I used the activity Averages and marked out the median, the highest and lowest values on the floor. It was at this point I figured out I could write on black duct tape with liquid chalk marker – brilliant! We labelled the wall with the highest and lowest heights of the class so we could see the actual range of heights.

Lesson 2: GCSE Revision

Equipment: Exam papers, scissors, glue, wall paper, duct tape

I have been using the Foundation GCSE Review with my Higher GCSE resit group. Reviewing ten Higher GCSE papers involves over 200 questions – that’s a big wall display! Both of the TeachMeets I have attended have used the idea of learning wallpaper. So that’s what we used – I’m grateful that some of my students are over 6ft tall or the wall display wouldn’t have gone up.

Now the duct tape was used to secure the top of the wall display and to ‘passer-by’ proof the bottom. It should last longer now that the lower end is reinforced.

Lesson 3: A-Level Mechanics

Equipment: Duct tape, liquid chalk, mobile phones, calculators, soft ball (I used a ball of wool)

It’s all very well drawing diagrams for A-Level Mechanics questions, but how about a life size diagram? We were looking at vertical motion under freefall/gravity. I gave the students pieces of duct tape chalk labelled with a, s, u, v, t. We went to the staircase and labelled the wall with the tape – so u (initial velocity) was taped to the top of the bannister and v (final velocity) went on the floor at the bottom of the stairs, etc.

The students then labelled what they knew: a=g, u=0, v=?, t=?, s=?

The students used mobile phones to time the drop from the bannister to the floor and calculated the distance and final velocity. The physical activity allowed us to think about how to draw these kinds of diagram.

And finally …
Just some pictures of an alternative whiteboard: