Where’s the Third Wheel? or Introduction to Positive and Negative Integers

This week one of our learning objectives has been to perform operations using positive and negative integers. To introduce the concept with my 7th Grade Math students, I used @mathequalslove’s Integer Operations Work Mat. I knew from the first time I saw this and read all about it that I wanted to find a way to use it because I was so excited about the Sea of Zeroes and being able to model zero pairs. I decided that each of my students needed a mini mat of their own to go in their notebook and then counters of their own to work with. I punched out 10 red and 10 yellow 1” circles for each of my students. {Yep, crazy!} As I was passing out the counters to the students and they were assembling their INB page for today, we talked about what each counter could stand for in relationship to integers. We then talked about different ways that we use integers. Basically reviewing what we had already learned in the prior weeks to engage them and ease them into today’s lesson. Now it was time to pose a problem to them. I asked each of my students to model -3 + 2 on the left side of their mat. Once I saw everyone was attempting (and most finished) with the problem, I talked about how we can combine opposite signs to “cancel out”. I demonstrated this by sliding a common positive and negative together and moving them to the “Sea of Zeroes”. Next up was to call this a zero pair and then ask them if I could do the same thing again and of course they saw we could. What to do with that pesky -1 that we were left with? I worked through them understanding that was our solution to our problem to begin with. I turned it into a simple problem, “If your friend borrows three dollars on Monday and pays you back two dollars on Wednesday, how much would you still be owed?” This is where it confused them a bit because they knew that the answer was NEGATIVE 1 and not one so I had to review the vocabulary I used in the problem and that was quickly solved. To practice with my students, I continued to pose problems and walk around as the students were manipulating counters on their mats. As I was chatting with students and letting them tell me what they did, one student piped up and said, “It’s like the zero pairs are going on a date and the leftover counters are the third wheel.” I seriously stopped dead in my tracks and had to replay what he said in my head as I was laughing along. Because of this I asked the other students what they could relate it to so that they would have a way to remember how to work with zero pairs to simplify expressions and equations. After that, our short 45 minute class period was up. Yes, I get in a Bellringer, Good Things, mini review and a mini lesson on my 3 short days each week. That one day with my students when I get a 90 minute block is when we go further in depth on some topics that just need more, review prior concepts to develop understanding further and are able to do more group activities to strengthen their skills. Overall, I was pleased as punch with this lesson and can’t wait to review it with my students on Thursday as we go over Positive and Negative Integer Operation Rules and create a Four Flap Flippable with rules and examples. Speaking of, I have my flippable ready for you that goes along with the Operations Word Sort I am doing next Monday in my Resource Math class. Before we head into this activity to review keywords, we are going to do a short mini-lesson on prior knowledge to create an anchor chart of key words. I know that my sort doesn’t have all the possible words and I want to get some examples up for them as well that they have created. Oh, I almost forgot. I am currently participating in a giveaway over on the Learning4Keeps blog. She has several awesome collaborations put together and you can enter to win all of them just simply by signing up! How easy is that?   As an added bonus, the first three people who leave a comment today and state that they went over to Learning4Keeps and entered will receive my Order of Operations Word Sort Flippable emailed directly to them for use in your classroom!


  1. […] When I saw the Glittered Table Scatter I immediately thought of using it to keep track of score on some games. If you are playing a game a game and get a point then you get a heart. Students could then redeem their hearts for certain rewards. You could also use them as a counter manipulative for an activity like Zero Pairs. […]

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