Hands-On Integer Operations (Part 1: Adding Integers)

Integer operations are truly a make or break middle school math concept.  Students who “get” integers will be much better off than students who don’t, in terms of their future math success.  That’s why I really take my time when teaching integers each year.  I’m breaking up my blog post on teaching integer operations into 3 separate posts so that it’s not too ridiculously long. 🙂

There are a variety of ways to teach integer operations, but my absolute favorite strategy is using two-color counters.  I have found that some students struggle with using number lines and rules for integer addition, but if I give them two-color counters, every student is able to successfully add two integers.

I always start my lesson on integer addition with a discussion of zero pairs.  I usually do this by asking students what happens if I take one step forward (+1) and then take one step backwards (-1).  They tell me that I haven’t moved at all (or that I have moved zero spaces), so that’s how we form a conceptual understanding that 1 + (-1) = 0.

Once they get this, I pull out the two-color counters and tell them red is negative and yellow is positive.  I hold up one red and one yellow and ask what that equals, and they (usually) answer zero, which tells me they actually do get zero pairs (hooray!)   I then show them a handful of counters (some red and some yellow) and ask the class how many I have.  We discuss how all the zero pairs cancel each other out and whatever isn’t part of a zero pair is the answer. I like using virtual 2-color counters on my Board instead of trying to hold up actual counters since it’s easier for the class to see.  This free website is perfect for that purpose.

counters

Once we’re done with the introduction, I have the students work on some addition problems individually.  I put a bunch of problems on the board for the students to solve independently using the two color counters:

  1. -4 + 3
  2. -2 + (-6)
  3. 8 + (-12)
  4. -7 + (-2)
  5. 4 + (-1)
  6. -6 + 9
  7. -8 + (-1)
  8. 5 + -4
  9. -7 + 3

After the students finish showing each problem with the counters and writing down their answers, we go over the answers as a class.  I then ask the class to come up with integer addition rules based on the answers we got.  I start by having them come up with 3 rules (one for negative + negative, one for positive + negative, and one for negative + positive).

The students are typically able to come up with the rules using the examples from the board (which are color-coded):

  • Negative + Negative:  add the numbers & the answer is negative
  • Positive + Negative:  subtract the numbers & the answer is the sign of whichever number is bigger
  • Negative + Positive:  subtract the numbers & the answer is the sign of whichever number is bigger

We then have a discussion about why the 2nd and 3rd rules are the same. It usually takes awhile to get the answer I’m looking for… students tell me that it’s because it doesn’t matter what order you add numbers in and I ask them how they know that.  Eventually someone is able to come up with the answer of the commutative property of addition. 🙂

Then the students write down the two “official” rules in their notebooks:
adding integers notes

That takes me to the end of the class.  I give the students homework on adding integers (all with small numbers so that they can use 2-color counters if they want/need to).

The next day I don’t teach a new lesson.  I just have the students practice adding integers using the rules.  We do a few problems together after the do now and checking homework.  I then break them into pairs based on how well they seem to be doing with the lesson.  I have them do partner matching worksheets where one person does the 20 problems in the left column and their partner does the 20 problems in the right column and they have to find the matching answers.  If some of their answers don’t match, I have them redo those problems and work together to identify their mistakes.  I made 3 different levels of the worksheets so that each pair is challenged appropriately.  I love partner matching activities because they keep the kids engaged and the students are able to check their own work and help each other out, freeing me up to focus my attention on struggling students.

(For students who really struggle without the two-color counters,  I tell them to draw little + and – signs to illustrate the problem the same way they would have with the counters.  This helps remind them whether they should add or subtract and what sign their answer will be.)

For homework on day 2 of integer addition, I tell the students to study for a quiz tomorrow and I assign self-checking worksheets for written homework.  Then the next day I can ask if anyone has any questions before the quiz because with the self-checking sheets, they already know if they were successful with the homework or if they need help, without me having to check each answer with them.

For the integer addition quiz I give the class 10 problems on Socrative so that I can see the results instantly.  If the majority of the class did well, I move on to subtraction (I will write about how I teach integer subtraction in my next post).  If they struggled with the quiz I spend the rest of the period reviewing addition again.

While I usually teach a lesson a day in my math classes, I really drag out integers because they are so crucial to future lessons.  There is absolutely no point in moving on to subtraction until students have mastered addition.  Most of my classes have been good with it after just the two days, but I have taken the third day (after the quiz) with some classes who needed more practice.  I then requiz them the following day.

(If you are interested in purchasing the integer addition partner matching or self-checking worksheets I use, click the images below.  Each set of 3 differentiated worksheets is $1.75.)

integer addition partner matching pic1Integer addition self checking sheets pic1

Thanks for reading,
Christina

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