Reflection: Student Led Inquiry Is it Postive or Negative? - Section 2: Warm up

 

After teaching this lesson again in another class I made a couple of small shifts that changed the whole lesson!

Shift 1: Rather than model each number line for them while going over their warm up I asked for volunteers to show me what the number line looked like and we had a disagreement on the very first problem!

The first student started at zero and showed two jumps on the number line, the first to -20 and the second showing adding 10 to -20. A second student said it could look different, so I asked him up and he started at -20 and showed a single jump of 10. This was a valuable discussion that returned to the context of hot and cold cubes. I was so happy this idea of multiple methods and collegial dissagreement surfaced so early, because what happened next was even better!

On the first problem my students all agreed on the right answer and were disagreeing only on the number line model. The next three problems generated dissagreement over the answers. The first problem created a safe opportunity to disagree, when the answer was not in question, which allowed us to surface and address misconceptions in these later problems.

Shift 2: After each number line presented I asked "who has a number line that looks different?"

Three different number line models were proposed for -10 - (-5), two correct and one incorrect. It was the incorrect model that sparked examination of the big mathematical idea of the equivalence of adding positives and subtracting negatives. Similar dissagreements surfaced for the last two problems as well.

Shift 3: I asked questions to facilitate the student discussion:

  • "can they all be correct?"
  • "who will explain what's going on in (this) number line?"
  • "does anyone want to respond/add to that?"
  • "what is confusing about this problem?"
  • "what is the same/different about all the number line models?"
  • "how can you use hot and cold cubes to help you convince your math brothers and sisters?"
  • "why does it make sense that an operation with a negative number would move us in the positive direction?"
  • "is there another problem that would look exactly the same on the number line?"
  • "why does it make sense that the two problems would look the same?"

Some of these questions were content specific, some were to elicit more thinking, and some were just to keep my students responding to each others ideas.

By the last problem, -3 x (-10), one of my students said, "I know my model is wrong, I know I should get positive 30, but my model gives me negative 30 [and] I can't figure out how to make it right," and asked if she could share it with the class. The subsequent discussion returned to hot and cold cubes. Several students pointed out that her 'jumps' on the number line were going in the wrong direction, because the -3 tells us to 'remove 3 groups (of 10 cold cubes)' which would increase the temperature, like adding hot cubes (positive direction). 

This lesson took a lot more time that ate into the remaining sections, but it was a much more valuable use of that time since the students were doing most of the thinking and talking about the tricky parts of the big idea. Taking this time provided a great opportunity for argumentation, intervention, and concept development at the same time. 

  Student Led Inquiry: Facilitating student discourse
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Is it Postive or Negative?

Unit 4: Operations with Integers
Lesson 18 of 24

Objective: SWBAT determine if a sum or difference will be positive or negative using various models.

Big Idea: Students will internalize the rules for integer addition by discovering patterns.

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Subject(s):
Math, adding integers, sorting, cooperative learning activity, subtracting integer, Number lines, facilitating student discourse
  54 minutes
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