Cogs and Gears!
Problem
Cogs and Gears
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Here are some of the cogs we can think about:
These are some different sized cogs that can click in together.
They rotate around the middle (where the number is). They can be joined in a variety of different ways. For example, we can think about the peach coloured 10 joined with the purple 15. If the 15 is turned around exactly once in a clockwise direction what will happen to the 10?
Then what if the 15 was joined to the orange 5 instead, if the 15 now turned round exactly once in a clockwise direction what will happen to the 5 cog?
Now you can explore other cogs joined together and say what happens when one of them is turned.
To explore further, these cogs and more can be downloaded here allcogs.doc
You are probably curious about what happens with joining cogs of different sizes and asking yourself some questions. Here are some starting ideas that you may lead you to be curious about what happens.
Three cogs together.
Try joining 3 cogs together what happens to the other two when you rotate one just once. You choose which 3 cogs you want to use.
In this picture, the black blob is the handle and I turn it around once clockwise.
The question then is what has happened to the 4 and 6 cogs, how much have they turned and in which direction?
Two cogs together
Join 2 together how many times will you have to turn the bigger one round for the smaller one to rotate exactly 4 or 5 times. In this picture, the black blob is the handle and as I turn it anticlockwise I keep note of both the 4 cog (to see when it has turned exactly 4 or 5 times) and the 12 cog to see how much it turns.
More Cogs
Try fitting 4 cogs together, and what happens when you rotate one of them once.
Try fitting 6 cogs together, and what happens when you rotate one of them once.
In this picture, I turn the 9 just once clockwise and try to see exactly what happens to the other three cogs
Or you might be curious about . . .
Student Solutions
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Teachers' Resources
Why do this problem?
This activity involves looking, exploring and thinking further, all in the process of being curious. The more pupils progress through the activity, the greater the opportunities for learners to open new doors to move further and further.
The activity also opens out the possibility of pupils asking “I wonder what would happen if . . .?”. Children's curiosity when working on this activity can take them to many different places. The children's perseverance can be witnessed by the teacher, the activity helping the pupils to persevere to search for more and more. While they are working on their explorations there is present the
catalyst for resilience being developed by each pupil.
Possible approach
Some pupils will receive enough imput by just being presented with the activity as shown on the site with the addition of the other size cogs being downloaded. If you have available some pupils will need to play with the cogs of different sizes from their construction kits. Because this activity is aimed at allowing pupils to be curious about "what happens when . . ." the only extra part of the teacher's approach is to make sure the pupils know that almost "anything goes" and to feel the freedom to explore. There are no required answers.
Key questions
What have you been doing with the cogs you've chosen?
Have you noticed anything that you can tell me about? Then tell me.
Possible extension
Give pupils the opportunity to develop and explore their noticings so that they have some "rules" that they develop about what happens.
Further extension
Here is a video,which you can view"full screen" and then return to this page.
The "46 teeth cog" is motorised, see what happens to the other cogs.
Possible support
There may be some who need to work one to one with the construction materials that have cogs in order to make a start.