The expressions were:

1) -10 + (-5) + 3

2) -12 + (-6)

3) 20 + (-20) + 10

4) 8 + 3 + (-1)

5) 9 + (-8) + (-1)

Yes, these are simple expressions but the purpose was to have them justify their answers using visual models and to understand how positive and negative numbers are combined. I also wanted them to use the vocabulary: zero pairs, combine, opposites, and additive inverse.

Once I put the expressions on index cards, the next step was how to effectively 'hand out' the cards:

a) Did I want to do it by asking for volunteers?

b) Did I want to use a systematic method - every sixth person that enters class gets a card?

c) Create a unique method for delivering the cards so students weren't aware of what was going on?

a) Asking for volunteers always gives me the same four to five people and is not an effective way to assess my students. I wanted to get students off guard. I didn't care if they had done the homework or not but I wanted to see if they understood the concepts.

b) Systematic method would be nice if my students showed up at the same time. However, that's been another issue in the morning is not all homeroom release their students at the same time because not everyone gets released from morning formation at the same time.

c) The above two questions led me to thinking about the 'snowball' activity. Instead of having the students write down an expression and throw it, I would create paper airplanes with the index cards. I would throw the paper airplanes towards the middle of the classroom and who ever picks it up has to come to the board and explain it. Sounded great! So how did it go....

__Positives:__1) The students were caught off guard. I didn't tell them what was on the cards in advance. Out of the five students that picked them up, two of them had not done the homework and are not active participants in daily discussion. This gave me an opportunity to assess their understanding. I allowed other students to come up and present a different visual aid if they wanted. The students got into it and I didn't have to say much.

2) A great way to begin looking at the mathematical 'rules' for adding integers. A few students were not into the visual aids and were able to explain to the group about when you add a negative and a positive that's really just subtraction and the sign for the sum will be determined by the whichever addend has the higher absolute value.

3) As students were leaving class, a few came up to me and said they had enjoyed the class for the first time all year. They want to do more activities like this. :)

__Negatives:__1) My paper airplane skills are not great. Need to work on that - the airplanes didn't fly as far as I wanted.

2) One student refused to come to the board to work out his problem. He handed it off the card and his homework paper to another student to present to the class. I was okay with this - I was the shy kid in math class when I was in middle school and I understand why some students don't like to get up in front of others. However, a few very vocal students did not like it and thought it wasn't fair. So that issue needs to be address before we do another activity of this type.

**NEXT UP:**Today we will be reading a few pages from Alex Bellos's "

*The Grapes of Math*" (pages 169 - 175; Chapter 7: The Positive Power of Negative Thinking). Will be using the Jigsaw collaboration method. Each group will read a couple paragraphs, summarize, then read/present to class. I'm going to try to get some pics to post for this one.

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