Dialogue in a Thinking Classroom v2

Following up from my previous post, here is another brief set of notes on the action and dialogue in my grade 8 math class.  We start the day out with some voting questions where we use Plickers and Peer Instruction.  My general instructions for all classes when doing voting questions are as follows:

  1. No talking allowed while voting.  No sharing of answers or ideas. I want to see what your thinking and if you take your idea from someone else, I won’t know if you get it or not.
  2. After you vote, we’ll see if there is an overwhelming consensus.
  3. If there is a mix of answers, I will give you a couple of minutes to discuss your answer with your peers.  Try to convince someone that you’re correct and make them change their vote.  There’s a good chance that you will have to get out of your seat to find someone with a different answer.
  4. 2nd vote, and hopefully a) the number of correct votes has increased and b) there is a strong consensus for the correct answer

Voting question: Which statement is true?

  1. Adding a negative number makes the sum negative;
  2. adding a negative number makes the sum smaller;
  3. adding a negative number makes the sum bigger;
  4. adding a negative number makes the sum more negative.

Voting question: find the sum of (-4) + (-9)

  1. 5
  2. -5
  3. 13
  4. -13

<the students overwhelmingly answer both questions correct, which is a good sign>

Whiteboards, try these questions. It won’t take long. Use a number line if you need to. 5 + (-2) 5 – (-2) -4 – (-10) How did you know that 5 – (-2) was 7?

- Because 5 + (-2) made jumps to the left on the number line so this time we jumped to the right.

<-4 - (-10) has a lot of different answers so we take some time to distill this one. Below is brief overview on what the discussion looks like. For every sentence below there were probably 10 more in the actual class.>

I see three answers to -4 – (-10). Which one are you confident in?

- Hmm, “two negatives make a positive”.

I think I agree with your idea but I think some of the words can be confusing.

- “Adding a negative makes jumps to the left, so this one must be jumping to the right.”

- “On the number line instead of starting at 5 we start at -4.  But then we make jumps just like the one before it.”

Ok, I’m convinced. Normally I would let you write down what you just learned but I want this to be very clear to everyone because this is an important rule we will use a lot. Subtracting a number is the same as adding it’s opposite. Let’s think of some examples…

Ok there is 15 min left.  I have some practice questions for you.