Modeling Integer Computation

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My third grade class explored integers this week.  Over the past few days students have started to become more comfortable in being able to compare and locate integers on vertical/horizontal numbers lines.  The next sequence is integer computation.  I find this to be more of a challenge for students.  Specifically, some students find the concept of subtracting a negative integer to be confusing.  Most students have encountered computation at this stage as either addition, subtraction, multiplication, or division.  The idea of subtracting a negative isn’t something that they’ve experienced and can cause students to question their own understanding.

This topic was discussed at #msmathchat last Monday night.  The consensus was that students need to experience different models to gain a better understanding of how to put together and take apart integers.

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Manipulatives, such as counters and the such are always important.  I believe most teachers use some type of manipulative to showcase integer computation.  Sometimes they’re taken away too early.

The problem that sometimes comes up with this, is that students want to move towards only following a rule/process to find the solution.   This “answer getting” mentality can lead to a lack of understanding and isn’t beneficial long-term.  Wording also plays a role with integers.  Getting caught up with “add” and “subtract” can limit what students perceive.  How about find the “difference” between x and y?

Changing the wording and using a number line can make a huge difference and can empower students to rely on their own understanding of computation and integers.

I kept this chat in mind as my third grade crew finished up a lesson on integer computation.  Near the end of one lessons I gave each student a blank number line and asked them to find the difference between two integers.  The instructions are below.

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Students were given dice and headed to work.  Students ended up rolling the dice and then created their number lines.  They were required to show a number model, the number line and any type of work that was used to find the solution.  The number line was initially blank and they had to fill it in with the numbers related to their problem. There were initial questions, but it seemed as though the multiple models/strategies were beneficial.

I believe students are making progress in better understanding how to put together and take apart integers.  There’s more work ahead of us, but I’m excited about the growth so far.  Next week, the third grade class is scheduled to use a number line to show multiplication and division.  I’m thinking of using a similar model for those lessons.