Subtraction math question

Discussion in 'General Education' started by Loveslabs, Dec 6, 2013.

  1. Loveslabs

    Loveslabs Companion

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    Dec 6, 2013

    I don't seem to have the words to help my second grade class understand why this method of subtraction works, so I would appreciate it if someone could help me. My biggest fear is confusing some of the students. Some of my students figured out yesterday the following.

    76-28=_____

    70-20=50
    8-6=2
    50-2=48

    I am ok with this strategy, but I am not sure how to help them understand why it works. I don't even think they have the words to explain it, but yet they are convinced it works. I challenged them to see if it always works, and they did prove it always works.
    Also, I don't want to come right out and tell them why it works, but rather I want to guide them as they figure it out.
    Thanks!!!
     
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  3. czacza

    czacza Multitudinous

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    Dec 6, 2013

    There are some YouTube videos on partial differences subtraction. I'm not a fan of this strategy as it DOES confuse many...especially at lower grades hen kids don't have full ownership of basic 'math facts' and place value.:2cents:
     
  4. monsieurteacher

    monsieurteacher Aficionado

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    Dec 6, 2013

    I agree... if the kids have figured it out on their own as a strategy that works for them, great... but I don't know I would focus on having it as a whole class strategy in grade two.

    Technically, what you are doing with that question is as follows:

    76-28
    70 - 20 = 50
    6 - 8 = -2
    50 + (-2) = 48

    As you can see, it's a little complex for second graders.

    I would try an open number line with them instead.
     
  5. ajr

    ajr Rookie

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    Dec 6, 2013

    This is a more formal way to write that process down, albeit with proof steps omitted.

    76 - 28
    (70 + 6) - (20 + 8)
    70 + 6 - 20 - 8
    (70 - 20) + (6 - 8)
    (70 - 20) - (8 - 6) (why is this step here)

    I can't see why this particular process is useful, but the idea behind it - that numbers are made up of other numbers - could be effectively conveyed.

    The step that confused me was

    8 - 6 = 2
    Is this being done just to avoid negative numbers? If so, this is terrible, since it adds unnecessary mental gymnastics that don't serve a purpose other than avoiding negative numbers. I'd just wait for negative numbers to exist before explaining this.

    I'd personally move to

    (70 - 20) + (6 - 8)
    and then leave it, because that's enough to do mental math. But, I don't know anything about teaching second graders and what abstractions they're comfortable with.
     
  6. Jerseygirlteach

    Jerseygirlteach Groupie

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    Dec 6, 2013

    Are you using everyday math? One of the many reasons I dislike this program is that it uses partial sums in lieu of regrouping. I have tried teaching both ways (since I think it's important for kids to learn how to regroup), but they only seem to grasp regrouping - never partial sums. So, that's what I stick with. I'd teach both methods and let them work with the one that makes the most sense to them.
     
  7. Loveslabs

    Loveslabs Companion

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    Dec 6, 2013

    I want to clarify a couple of things.
    1. I didn't teach this strategy. We haven't dealt with subtraction this year except for the basic facts. I gave the students a big piece of paper and asked them to find as many strategies as they could to solve the problem. I wanted to see what they knew and where they were at with the concept.
    Side note- They dug in and worked for 20 minutes. They were absolutely silent. (No, I didn't tell them they had to be quiet.) Nobody gave up even when they were stumped. I was so proud of them!
    2. The part about 6-8=2 was what they were saying when they explained their strategy. Those are not my words.
    3. We don't teach math with any particular series. We spend a lot of time allowing the children to explore numbers and solve problems their own way. We lead them to where we want them to be through questions and challenges.
    4. Surprisingly, four of my students came to me already understanding the concept of negative numbers. About 5 others have a small understanding of the concept and are really trying to grasp it.
    Side note- One child said, "Think of a number line as a tree. The ground is zero. The trunk is above ground and has all of the positive numbers. The roots are below the ground growing straight down and those are the negative numbers. They are in a hole like you are if you owe someone money." (Yes, I almost fell over when he said that!)
    5. I never learned to subtract this way, so it isn't natural to me. I will check out YouTube to see what they have to say. I really don't want to ignore these children and their strategy. I want to validate their strategy without confusing them.
    Thank you to those who responded.
     
  8. Aliceacc

    Aliceacc Multitudinous

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    Dec 6, 2013

    AAAACCCCKKKKKK!!!!!!
     
  9. ecteach

    ecteach Devotee

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    Dec 6, 2013

    YAY! I am so glad someone posted something like this. My son, who is in third grade, brought a problem like this home the other day. It was a bit more complicated. He just DIDN'T get it. I am a developmental specialist at heart. Adults do this, so we just assume that kids can do this. No one taught us to do this, we just learned to do it over the years by generalizing. We use money; we have simply been exposed to these numbers over and over again. These children haven't. They can't do this yet. Their little brains aren't ready for it. I wish the people who developed Common Core understood the way the brain develops.
     
  10. monsieurteacher

    monsieurteacher Aficionado

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    Dec 6, 2013

    Loveslabs, I don't see anything wrong with what you did. I would encourage the students who did discover that, but I don't know that I would try to have them show the rest of the class. You may want to show those kids that what they are doing is adding negative numbers. I would validate the strategy without trying to get the whole class to the same point.
     

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