Integer Hell

Discussion in 'Secondary Education' started by JMUteacher, Oct 8, 2008.

  1. JMUteacher

    JMUteacher Rookie

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    So I'm a new teacher and I've started a unit about integers (well I'm about a week and half into it). Right now we're working on Adding and Subtracting Integers and I'm at my boiling point. My kids seemed to really get the whole adding integer rules (we sang a song to row row row your boat) but now that I've added subtraction some of them are in total chaos. They are confusing the rules and I just don't know what to do. I also need to start moving on to the rules with multiplication and division but I'm dreading next Monday when I plan to start. Anyone have any advice on how I can help them keep the rules straight? (I've also given them about four different types of notes to help them see it, ie plain notes and also a flow chart etc).
    Thanks!
     
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  3. Charger

    Charger Companion

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    I've been there. Every year I have kids who get it and several that never seem to understand. The problem is, even if they know how to do it, they don't want to take the time to work it through, so they make careless mistakes. I don't know how to solve the problem, even though this is my fifth year.

    :confused:
     
  4. mandagap06

    mandagap06 Devotee

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    I do not know. I do know that we just got done doing that in college math. We were doing it with something like 6x + (-10x)=80 or 6x+5=12+(-45x) but its the same process as far as the subtracting or adding part goes.
     
  5. robinsky

    robinsky Rookie

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    This is my first year also, and I'm also having problems getting this concept across. I think next year I'll teach it this way: teach the rules for addition first. If the signs are the same, add the absolute values and take the sign of the integers you're adding. If they're different signs, subtract the absolute values and take the sign of the larger absolute value. And for subtracting, change it to adding the opposite and follow the addition rules. This boils it down to just a few rules.

    I did a lot of stuff like having them walk number lines, deal with red and black chips, etc. That really works for some kids. But some kids just need the rules spelled out for them!
     
  6. Sarge

    Sarge Enthusiast

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    Draw a number line vertically so that you go up when you add and down when you subtract.

    Or have the kids imagine a super machine that is a boat, a submarine, and an airplane. Say "You're six feet under water. You go up four feet. How many feet are you under water now?" or "You are three feet under water, and you go up six feet. Now how high in the air are you?"
     
  7. Upsadaisy

    Upsadaisy Moderator

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    Wow, I really expect my students to master the rules for integers in 6th grade. By 7th grade, I want them to use those rules in solving equations.

    Anyway, I always tell them the rule for subtraction is the easiest - DON'T. We don't subtract, we change to addition and reverse the sign of the next number. Then follow the rules for addition. What can confuse them is that after they change to addition, they have to subtract when the signs of the addends are different.

    What curriculum are you using?
     
  8. mmswm

    mmswm Moderator

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    Why are you teaching addtion and subtraction seperately? There's no such thing as subtraction...it's the addition of a negative quantity :D...but barring that, trying to teach two seperate sets of rules when there is really only one set of rules is setting them up to crash and burn. Here's how I do it, and I rarely have students at either the middle school or the college fail to get the concept.

    There are two senarios...the numbers can have the same sign or the numbers can have different signs. (If it's something like 5- (-3), they have to simplify first.)

    So, lets decide what two numbers with the "same" sign look like. Here are some examples

    a + b
    -a -b
    -a + -b
    a - (-b)....(simplify first).

    Once we know what they look like we can just follow the "same sign" rule, which is to add the two numbers and keep the sign.

    Then we look at what "different" signs look like. Examples are:

    a -b
    a + -b
    -a + b
    -a - (-b)...(simplify)

    If two numbers have different signs, then we follow that rule...which is to subract the two numbers and keep the sign of the "larger" (the number who's absolute value is greater).


    If you want a real world application, use a checking account analogy, or borrowing money. The checking accoung analogy would go something like this:

    You have $15 in your account and you write a $20 check. What does you balance say? (15-20 = -5). Now, since you've overdrawn your account, your bank charges you a $30 overdraft fee, Now how much do you have? (-5 + -30 =-35). You make a $25 deposit, now how much do you have? ( -35 + 25 = -10). You're broke, so you go beg and plead with your bank to have mercy on you. They decide to be nice and reverse the fee, this means that they're subtracting a fee (a negative number), so you have -10 - (-30), which simplifies into -10 + 30 = 20.

    Hope that helps.
     
  9. Aliceacc

    Aliceacc Multitudinous

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    For starters, go on to mult and division, even if they're still shaky on addition and subtraction. Mult and division are by far the easier set of operations!!!

    And, like Upsadaisy, my kids don't learn subtraction rules-- they add the opposite.

    For addition, I always talk about money: postitive numbers are finding money, negative numbers are owing money.

    so -5+7 becomes: you owe $5 but you find $7. How much money do you end up with? Answer: $2.

    Hang in there-- they'll get it eventually. Once you've taught it and reviewed it, keep going but include a bit of review every day. Don't let this become a two month chapter!!!
     
  10. Upsadaisy

    Upsadaisy Moderator

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    Pretty soon you will get to be amazingly good at reciting the pertinent rule at any provocation, and the kids will hear each rule at least a million times by the end of the year. When reviewing problems, "What, you all didn't get -5? Oh, you got positive 5? Let's see, add two negatives, the sum is negative."

    Pretty soon they will be using the signs with rational numbers and will get lots more practice.
     
  11. mmswm

    mmswm Moderator

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    Or immediately, and without a consious thought, rattling off the borrowing money example....you owe your friend 10 bucks buy you only gave him 5...do you still owe him money? How much?
     
  12. Upsadaisy

    Upsadaisy Moderator

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    I always present two options for add/sub - memorizing the rules and visualizing a number line. Some kids really do better with one or the other and are aware of it. And, yeah, the rules for mult/div are simple, so I don't suggest they visualize.

    It is amazing how many opportunities you get to point out that the reason you can do something is stated in one of the properties. "Oh, so you just added these two integers first because they are easy to add - and because the associative property says you can group any way you want when adding...."
     
  13. Aliceacc

    Aliceacc Multitudinous

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    'Daisy, I think we're twins separated at birth!!

    Anything my kids miss the first time around is sure to be drilled into their heads in the subsequent weeks and months. So I'm pretty careful not to get bogged down by any one topic.
     
  14. Upsadaisy

    Upsadaisy Moderator

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    I know. It is so funny when I read your posts about math and find my own words!

    It's usually a thin line to tread, though, when you decide how long to review. Most years, I know there are some kids who will probably not catch up later on. Sigh. This year, I have only 5 kids (hahahaha) in my 7th grade class and they are all well-prepared. A couple will take honors algebra next year, so I have to keep things moving for them. (In our area, they need credit in algebra before applying to any of the decent magnet high schools.)
     
  15. mmswm

    mmswm Moderator

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    I've got the "keeping it real" theme in my classroom, so I'm constantly spouting off real life analogies. Integers are the easiest topic to come up with the analogies for. My kids may have other issues, but integers is on thing they all get :D

    Ya know...I didn't even stop to think about the mult/div. with the original post. I teach multiplication and division first. I think it gives them a little confidence boost when they get a new topic so fast, and then they're not scared when we start adding and more willing to try. It seems to work pretty well.
     
  16. Aliceacc

    Aliceacc Multitudinous

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    Me too. It means skipping around in the book a bit, but I always do mult and division first.
     
  17. Upsadaisy

    Upsadaisy Moderator

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    I had a 3rd grader last year who was able to use the rules for integers. He was fun.
     
  18. mmswm

    mmswm Moderator

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    5 Kids????? Wow.

    I'm with you on the magnet school thing. There's only a handful of decent high schools in this county and you either have to be a math/science wiz, or an artist to get into them.
     
  19. Upsadaisy

    Upsadaisy Moderator

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    My kids don't even have textbooks. They haven't come in yet. I never use them anyway. They have workbooks, I don't have a copy of one, nor is there a teacher's edition of the workbook. It is ridiculous. I have one student textbook. That's it. No problem.
     
  20. Aliceacc

    Aliceacc Multitudinous

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    Wow!!!

    I have 3 Honors Algebra classes, and one slightly below average Algebra class.

    They should have covered integers soon after I began my leave. I'm confident that the Honors kids will get it; we'll see on Tuesday how the slower kids fared.
     
  21. Upsadaisy

    Upsadaisy Moderator

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    Yes, mmswm, it is a crazy small K-8 school. We will be moving to a new location in 2 years and that should help us to expand. I teach 5th the rest of the day and only have 13 kids. One of them is leaving in January, too. My classroom is commensurately small...... (sorry, I know that's not a word).
     
  22. mmswm

    mmswm Moderator

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    Oh, good Alice, so I'm not crazy. My middle school admin wasn't real happy about me skipping around (none of the other teachers do it that way...whatever), till I pointed out that's how I've always taught it at the college (college prep courses). I was starting to think I was crazy for doing mult/div first, but I can't get past the fact that it's easier and addition, and who couldn't use a confidence boost when learning something new?
     
  23. Upsadaisy

    Upsadaisy Moderator

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    When I teach algebra, I cover the rules for integers in one lesson, then move on.
     
  24. Upsadaisy

    Upsadaisy Moderator

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    I like them to get the difficult rules over with. Then they are absolutely ecstatic when they learn about the rules for mult/div.
     
  25. Aliceacc

    Aliceacc Multitudinous

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    I agree on the mult/division thing.

    And, from a practical point of view, it gives them a couple of easy quiz/test questions. So you don't have kids getting NOTHING right on a test or a quiz, since you can throw some mult/division questions in there.

    And I skip around all the time!!!
     
  26. mmswm

    mmswm Moderator

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    I only have three classes now (I dropped to part time to be with my kids in the morning, since I work for the college at night). I have 8th honors algebra I, 7th regular and 7th honors.
     
  27. mmswm

    mmswm Moderator

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    I never thought of it that way, alice, but you're totally right.

    Kids need to experience success or thier confidence plummets.
     
  28. Aliceacc

    Aliceacc Multitudinous

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    As of Tuesday, I'm dropping my SAT prep classes. Instead, I'm working with the 22 year old sub covering the Calculus classes (the teacher had emergency surgery on Labor Day, and again last weekend. And I was out. And one of the teachers went into Labor 2 days after my surgery.)

    The poor girl is getting a bit of a hard time from the Seniors. So I'm going to observe her classes, help her prep, that sort of stuff.

    It should help her classes go a lot more smoothly, and makes my day a lot easier. Did I mention that I love our AP???
     
  29. mmswm

    mmswm Moderator

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    I read about that yesterday. Your P sounds really great. That sounds like a good solution for all of the various issues that cropped up.

    I taught Calc 1 over the summer...UGH...sometimes I wonder.
     
  30. TeacherGroupie

    TeacherGroupie Moderator

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    It is too a word!
     
  31. TeacherGroupie

    TeacherGroupie Moderator

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    Only kids? Is that ever news to me...
     
  32. mmswm

    mmswm Moderator

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    Not ONLY kids...but we were talking about kids at the time.....
     
  33. Upsadaisy

    Upsadaisy Moderator

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    Oh, thanks, TG.
     
  34. Lives4Math

    Lives4Math Comrade

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    Check out Pete's Power Point Station for an awesome power point on integers (it's called Interesting Integers!) I edited it for myself, only including basic info. and adding and it worked really well for my students!
     
  35. JMUteacher

    JMUteacher Rookie

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    Thanks so much. We did a whole role playing scenario where they learned about checks and losing money and owing money to the bank, and some of my kids are drawing on the experiences from that. I will definitely use the whole adding the opposites. Hopefully this will get the kids to move on to it!
    ps. On a side note I'm so glad that I found this site. Thank you all so much!
     
  36. mandagap06

    mandagap06 Devotee

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  37. Luv2Learn

    Luv2Learn Companion

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    This has been a very interesting read for me. Although I am in the process of only starting my education major, I'm leaning very much towards having math as a center focus.

    Thank you and please continue!

    Kris
     
  38. Upsadaisy

    Upsadaisy Moderator

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  39. tally

    tally New Member

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    Make it real for them. Try some examples like temperature. It's 6 degrees out and the temperature drops 10 degrees. How cold is it? Or how about cards - your score is 5 'in the hole' and you get 7 points. What is your score now? Or try money - you owe someone $10 and you borrow $7 more. What is the end result? Once they understand addition, then introduce subtraction as 'adding the opposite' integer. It's just one extra step added to what they do for addition. Bring as many real world examples that they can relate to into your lessons. Try to make it real to them on their level rather than a set of rules to be memorized may help.
     
  40. Upsadaisy

    Upsadaisy Moderator

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    If they have 30 problems to do and have to stop and think about temperature or bank accounts every time, that just won't work. They have to move beyond that.
     

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