MATH: Teaching Integer Subtraction

Discussion in 'Middle School / Junior High' started by Chicken_Soup, Feb 28, 2008.

  1. Chicken_Soup

    Chicken_Soup New Member

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    Feb 28, 2008

    Hi,

    I need some help with a teaching techique. We're doing integer addition. Now, the standard process for subtracting integers is:

    1. Change it to an addition problem: a - b = a + (-b)
    2. Compare the signs
    . a. If the signs are the same
    . . i. Take the absolute value of both numbers
    . . ii. Add them
    . . iii. Take the sign of the bigger number
    b. If the signs are different
    . i. Take the absolute value of both numbers
    . . ii. Subtract the smaller from the larger
    . . iii. Use the sign of the bigger number

    This works, but here's the problem. Let's take 7 - 5 for example. According to this definition, here's what we have to do:

    7 - 5 [Given]
    7 + (-5) [Step 1]
    |7| - |-5| [Step 2.b]
    7 - 5 [Step 2.b.i]
    2 [Step 2.b.ii]
    2 [Step 2.b.iii]

    I taught a bunch of these examples in class, but it seems rather cumbersome. Any suggestions on technique? They take one look and tell me that the answer is 2, and they're also using calculators, so it seems a bit overkill.

    Sincerely,
    Soup
     
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  3. TeacherGroupie

    TeacherGroupie Moderator

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    Feb 28, 2008

    It is cumbersome - for 7 - 5. Are the kids going to be tested on solving 7 - 5 this way? If not, I'd recommend giving 'em credit somehow for recognizing when going through this procedure is overkill. (Knowing all the steps is good. Knowing when they're not all needed is maybe even better.)

    As to selling the procedure, you may need to walk them through a hairier example - something with variables, even? - in which this procedure is what saves one's bacon, then point out that you're starting them with the simpler examples so they'll really be confident that the procedure works and that they can make it work - and then they'll be able to depend on it when things get more complicated.
     
  4. mmswm

    mmswm Moderator

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    Feb 28, 2008

    Money, Money, Money. It always works. Say you have 5 bucks but you want to buy something that costs 20. Your friend lends you the money. Now how much do you have? They always say I don't have any, but I owe my friend 15 bucks. That's when you say EXCATLY!!! You have -15 bucks. Then you go on and say that when you saw your friend next, you only had 10 bucks and you need to give it to him. Now how much do you have? They say something like I owed him 15 and I gave him 10 so now I only owe 5. Right again, you have -5 bucks. The next day you give him another ten. What do you have? They say that now he owes them 5 bucks and once again, you say right, he gives you the change and now you have +5.

    Once they have a solid real life example that makes sense, they can generally absorb the rules fairly easily. And, as TG pointed out, when to use the whole procedure vs when to use the "shortcuts" is a valuable skill.
     
  5. Chicken_Soup

    Chicken_Soup New Member

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    Feb 28, 2008

    Thank you both for your responses.

    From reading your responses, I realized what happened in my class today. By walking them through a dozen examples of this method, they started seeing the shortcuts themselves. There was a little unplanned discovery learning in my class today! By grinding through the strict mathematical definition, they grasped the concept, and were able to see the answers without using the definition. This is where they need to be to solve more advanced problems with variables, etc..

    Sincerely,
    Soup
     
  6. kburen

    kburen Cohort

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    Feb 29, 2008

    I find that it works best to teach this with 2 sided counters (Yes, I teach K but I tutor kids in 7th and 8th grade math). You designate one side for positive and one side for negative and "do" the math with the counters. For example: yellow is positive and red is negative. 4 + (-3) put out 4 yellows then add to it 3 reds. 1 yellow and 1 red cancel each other out so you take them away and see what you have left.

    My college professor taught us this way and it was sooooo much easier to me. The girls that I tutor were appreciative of my showing them, and they draw the pictures on their tests and things if they need to.
     
  7. MrsC

    MrsC Multitudinous

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    Feb 29, 2008

    When I taught grade 7 and 8 math I introduced adding and subtracting integers using this method. It worked well for some of the students because it gave them a clear visual. I also encouraged them to draw/use a number line and show the "jumps" on there.
     
  8. Carmen13

    Carmen13 Groupie

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    Feb 29, 2008

    I have used "money", counters and also the real line. The counters method is a good one to introduce the process (and make the kids realize that -1+1=0), but when you have big numbers it's not practical anymore. So using the "money" method afterwards is the best thing to do, and the kids love it. I even use it with high schoolers, when solving equations. It works!
     
  9. Upsadaisy

    Upsadaisy Moderator

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    Feb 29, 2008

    I teach integers using the number line (visual method) and the rules. I must repeat the rules for subtraction a million times each year.

    Subtracting Integers
    1. DON'T
    2. Change to addition
    3. Reverse the sign of the next number
    4. Subtract the two numbers regardless of sign
    5. Choose the sign of the addend with the greatest absolute value
     
  10. Carmen13

    Carmen13 Groupie

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    Feb 29, 2008

    oops..number line, not real line!
    Thanks Upsadaisy!
     
  11. Upsadaisy

    Upsadaisy Moderator

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    Oh, I just thought it was a Portugal thing!
     
  12. Carmen13

    Carmen13 Groupie

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    Mar 1, 2008

    I did a literal translation (we say recta real=real line, real being from the real numbers)
     
  13. TeacherGroupie

    TeacherGroupie Moderator

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    Mar 1, 2008

    Ah: recta has to have originally been linea recta (literally 'line straight'), and I'm not able to reconstruct 'number' in Portuguese off the top of my head, but real would be shortened from something like numero real. It's staggering how many nouns in European languages started life as adjectives.

    Aliceacc, who is greatly missed, had a funny story about the math term latus rectum more or less here: http://forums.atozteacherstuff.com/showthread.php?t=34369.
     

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