A Great Student Question!

I had a great lesson come as a result of the Flipped Class with my year 8s the other day. We were working on solving linear equations, and during our WSQ conversations at the start of the lesson a few students in one group asked "How do you solve an equation with 2 variables? Is it possible?" Great question, I thought! With that small group I briefly explained that you need to have 2 equations to solve for 2 variables and went through a quick and simple example. Originally I thought I'd give some of the students that as extension work the next lesson, but instead I decided to start the next lesson with the whole class working on this problem:

There are some rabbits and chickens in a field. Altogether there are 62 heads and 190 feet. How many rabbits and how many chickens are there?

I didn't give them any strategies or hints to solve this, and most did trial and improvement to try to work it out, which, in my opinion, at this stage is a valid strategy for this type of problem. 

Once they had had a few minutes trying to work this out (and after clarifying that chickens had 2 feet each and rabbits had 4!) and about half the class had worked out the solution we discussed some students' strategies together on the board. 

After some giving explanations of their trial and improvement I moved them on to creating equations to represent the word problem, which some had attempted to do on their own. They had no problem understanding that the "heads" part of the problem could be written as:

r + c = 62

and that the "feet" part of the problem could be written as:

4r + 2c = 190

I discussed with the that if we only knew the total amount of "heads" in the field that it would be impossible to know how many of each animal we had, and that we needed the second bit of information about the amount of feet to solve the problem. So we agreed that with equations, if we have 2 unknowns then we need at least 2 equations to solve them. 

The next bit was more challenging, as I showed them how to use substitution to solve. It helped that the problem was in context so rearranging the first equation to give:

c = 62 - r

was easy to understand - simply the amount of chickens was 62 minus the number of rabbits. The substitution bit took longer for some to get than others to get and I'm not convinced they would all be able to solve a problem like this on their own, but the fact that they have all now been introduced to simultaneous equations at year 8 (normally we teach it in the last half of the year in year 9) was good enough for me. The students were then given the choice to work on solving "regular" linear equations or simultaneous equations problems for the rest of the lesson.

I thought this was a great example of how, because of the WSQ structure that goes along with the video tutorials, the students asked a questions that led to a lesson that I would not have normally taught them at their age. The questions actually changed what I had planned to teach and moved them beyond the curriculum, and the whole class had some sort of challenge presented to them. What an awesome "teaching moment!"