I highly recommend everyone should watch them.
New Zealand Education Counts Website Link
Being inspired from this, I thought we'd try some of their ideas.
We began by discussing what we would need to do to be a successful group of mathematicians when we try to solve the ratio/rates word problems.
Here were our ideas we discussed:
Adding to these, I suggested that each group should also focus on the following:
° Everyone in the group has an equal amount of talking time.
° Be open-minded to different ideas and strategies before evaluating which is better to use.
° Everyone in the group should understand how and why the strategy works.
As I presented each, I asked why we thought these would be important. We discussed how talking helps us to learn as we formulate and share theories we might have. We also discussed how even strategies that aren't effective or don't work help us deepen our learning when we evaluate why they aren't so great.
Each person in the group allocated themselves a number from 1 to 4.
I explained that when it was time to share our ideas and strategies to the class, a number would be pulled out and the student with that number would be representing the group by sharing with us. This, I hoped, would ensure that everyone in the group would participate actively and that the group would ensure that everyone understands what they were doing. Being random, mixed ability groups this was important to ensure that everyone was learning and that some would not opt out and allow others to do the thinking.
We began with our first word problem:
The Crayola crayon company makes 2 400 crayons in 4 minutes.
- How many crayons does it make in 15 minutes?
- How long would it take to make 18 000 crayons?
After some time, numbers were pulled out and those group members shared with us the strategies they used and equally importantly they explained strategies they tried but weren't successful. In our class discussion, it was those 'unsuccessful' strategies that we focused upon more because, as we often discuss, it is those moments that can often give us deep mathematical understanding when we dissect why they don't work or aren't as effective.
I had found this question from a really useful website Math Village Website Link
I wanted to reintroduce the use of creating ratio tables as a useful strategy. So after, we discussed all our strategies, I showed them the video link on the page that showed a different approach. We discussed what we thought of that strategy- both its pros and cons.
Before beginning the second word problem, we referred back to our brainstormed list and reflected on which we felt we were being successful at and which we felt we should focus upon more for the next word problem.
The second word problem was really challenging.
A typist can type 120 words in 100 seconds.
- At that rate, how many seconds would it take to type 258 words?
- In 180 seconds, how many words could be typed?
There was a lot of head-scratching and deep thinking taking place as the groups trialled different strategies. Some groups felt they had eventually created a strategy that worked, but felt it wasn't very logical so they tried to find a more efficient strategy. I think this is a useful barometer of knowing how where one's class is at mathematically. All year long, our resounding message in discussions is that maths is not about getting a correct answer- it's about creating strategies and evaluating their effectiveness. Hearing children apply this even after they have got an answer and without prompting are great moments.
Again, numbers were pulled and those students shared with us the processes their groups went through. We thought it was interesting how when a group felt they had got an answer, what they did to test whether it was plausible or not.
And again, we watched the video link on the Math Village website to see their strategy and we discussed its pros and cons.
Finally, groups shared what elements they thought they had done well and needed to focus upon more to be a successful group. We liked this approach to maths learning a lot and we all thought it was a really useful way to think mathematically so we will definitely do this again- am thinking of doing this once a week to develop both mathematical understanding and the collaboration skills being developed.