Experimenting with Strategies to Measure Elapsed Years......

 Lead In:

We began by brainstorming some    

of the key inventions we have learnt about that have helped shape our measuring of time system we have today. (see pic)

We then jumped onto our laptops and found out when 5 or 6 of these time measuring devices were invented and to challenge our thinking by including a few that were invented in B.C.

We then used placed these on a time line and thought about how they need to be spaced out.  A few of us continue to wonder about how B.C works on a number line and another offered a wonderful memory hook:  Think of B.C and A.D like a mirror reflection! 

Another helped by explaining how our measurement of years time line is symmetrical- the numbers on for infinity in both directions! Indeed they do. :)

Student-Created Investigations:

When we were satisfied that our time lines were well spaced out (quite a few us decided they wanted to redo them at home), we then did the following:

1. Choose any event on your timeline.

2. Create a number line and show a mental strategy you can use to find out how many years ago it was.

3. With the same year, repeat but use a different strategy.  can you find a different friendly number to experiment with?  Moving back from 2015 or moving forward from the given year?

4. Look at the two strategies and then evaluate which you find easier to do in your mind by circling it.

5. Repeat for other events on your timeline.

By doing this, I was hoping they would explore how we can create different strategies and that for some, perhaps they might discover a more effective mental strategy than what they usually use.  It was also hopeful that they would take risks by experimenting with different friendly numbers. A lot of the kids did try this and would sometimes remark how they had made a great discovery with a particular friendly number such as 1950, or how silly their strategy had become by trialling a particular year as a friendly number.  When that happened, we discussed how when we try something and deem it to fail, it is actually a success because we then see even more benefits in the other more effective strategy we could use.

Most of the children created timelines that showed many different events such as the invention of sundials, when the Mayan calendar was first used, the introduction of the pendulum clock in Europe, the first known water clock in Ancient China etc

This student (pic) decided to find out key events only in the history of the Ancient Egyptian calendar. Such an interesting approach! She explained that she is fascinated by Ancient Egypt and was happy she could link that personal passion in with her maths learning. :)

After investigating these strategies for how many years ago their events occurred, we then measured the distance in time between events on our timelines.  

Eg, How much time had passed between when the lunar calendar was invented in Scotland till when the candle clock was invented? etc

We repeated using number lines to show how we could mentally measure the difference in time and again explored two strategies for each question and then circled the strategy we found the easiest to do in our minds. 

Reflection:

We paired up and shared our thinking, explaining why we felt the strategies we circled were easiest for us to do mentally and also explained some of our experiments with trying to identify friendly numbers that might have turned out unexpectedly unfriendly and why that was so.

Assessment Feedback Using Learner Profile Attributes:

Measuring Elapsed Time Investigation                                  Mathematician: Patrick

	Emerging	Developing	Consolidating	Expanding
Thinker: Able to identify multiple strategies for measuring elapsed time in years, decades, centuries and millenniums
Communicator: Ability to visually show mathematical thinking in a clear, neat and well-spaced out manner

Patrick, you showed some good thought in spacing out your timeline, though you should have rethought how close the year 1656 is to year 1 compared to how close you had placed 600 BC.  However, your decision to spend extra time redoing your timeline so it was better spaced out shows your wonderful attitude in wanting to achieve your best in your learning. It’s a great attitude you have! You show you have a strength in determining how to use different mental strategies and analysing which you personally find more effective.  It was interesting to see you taking risks by experimenting with different 'friendly' numbers like you did with 1850 and 340 B.C even though, like you said they sometimes became 'unfriendly' in your mind, it is important to experiment and it is helping you strengthen your ability to measure elapsed years more confidently. A very good investigation and an excellent effort in presenting your thinking neatly. J