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Thread: Two COTR questions

  1. #1
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    Default Two COTR questions

    Is it recommended that my child still work out all division problems by hand, or, she wants to know, can she start using a calculator?

    And, here is a goofy one, that I should know the answer to but don't: In the book, the way division is presented at the beginning, from what I can understand, anyway, is opposite to the way I taught it. Now I am worried that this confusion I caused will come back to hurt my kids later. (I taught them that the quotient is the number of things that end up in each group, not realizing that it is the other way round like the COTR book seems to have it, and now I'm all discombobulated, but this issue always discombobulates me anyway, so nothing new there!)

    TIA for anyone who can help!

    Maria
    DD 12, using 6M core with 7th Grade COTR
    DS 10, using 5M core

  2. #2
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    Default Re: Two COTR questions

    Quote Originally Posted by Maria2 View Post
    Is it recommended that my child still work out all division problems by hand, or, she wants to know, can she start using a calculator?

    And, here is a goofy one, that I should know the answer to but don't: In the book, the way division is presented at the beginning, from what I can understand, anyway, is opposite to the way I taught it. Now I am worried that this confusion I caused will come back to hurt my kids later. (I taught them that the quotient is the number of things that end up in each group, not realizing that it is the other way round like the COTR book seems to have it, and now I'm all discombobulated, but this issue always discombobulates me anyway, so nothing new there!)

    TIA for anyone who can help!

    Maria
    I don't have COTR so take my answer with a grain of salt...

    Calculators...I don't usually let my kids start using them until algebra unless a textbook specifically says that a calculator is to be used. I would use your best judgement as to what the section is trying to accomplish. If it is section on division, then no calculator for the division.

    A quotient is defined as the answer to a division problem. if you think of a long division problem as a house, the quotient is on the roof, the dividend (the number you are dividing up) is inside, and the divisor is out front at the door. You might be asked to find the number of groups or the number in a group, but the answer is the quotient.

    Hope that helps a bit.
    Dorinda

    DD 14 - 9M with Geometry, MPOA(Henle 2, Comp3), Lukeion Greek2
    DS 12 - core 7M with Henle 1
    DS 8 - core 3A/4A
    DS 4 - loving life with AAR1

  3. #3
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    Default Re: Two COTR questions

    Quote Originally Posted by Mom2mthj View Post
    I don't have COTR so take my answer with a grain of salt...

    Calculators...I don't usually let my kids start using them until algebra unless a textbook specifically says that a calculator is to be used. I would use your best judgement as to what the section is trying to accomplish. If it is section on division, then no calculator for the division.

    A quotient is defined as the answer to a division problem. if you think of a long division problem as a house, the quotient is on the roof, the dividend (the number you are dividing up) is inside, and the divisor is out front at the door. You might be asked to find the number of groups or the number in a group, but the answer is the quotient.

    Hope that helps a bit.
    Thank you so much for your reply. I actually get really shaky and even tearful about about Math which does not help my kids. arg. I know the quotient is the answer, but when my dd was learning division, she would skip-count to get the answer, finding the "missing number." How many twos are in ten, kind of thing. I always told her that was ok, as long as she understood that for example, 10 divided by 2 is of course 5, and that the 5 meant that there were actually two groups with 5 things "inside" each group. The book seems to explain it as 5 groups with two things inside each group, the quotient being the "number of twos" instead of the "two groups of five." This relieves me, because it is easier for my jumble brain, but I feel so bad for having taught it wrong. So I have realized that I completely mis-explained this to the kids, and I'm not surprised since I always get flipped around on this one no matter how much I think about it. sigh. Now I'm more confused than ever. time to throw in the towel and find a tutor?
    DD 12, using 6M core with 7th Grade COTR
    DS 10, using 5M core

  4. #4
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    Default Re: Two COTR questions

    Honestly, you are stressing over English not math. Some programs teach very specific ways of naming the parts of a problem. Maybe MP thinks it's important (Cindy?), but I don't. I want my kids to understand the math. 10 can be divided into 2 and 5. If 10 is divided by 2 the quotient is 5. If 10 is divided by 5 the quotient is 2. I really don't care if my kids think of two plates full of five things or five plates full of two things. It's the same thing to me. In my mind if I have 10 and divide by 2, I am dividing it into 2 parts and each part will have 5 pieces. That's what the fraction equivalent shows. 10/2 means to divide 10 in half. Each half is 5.
    But really it shouldn't matter which way you think of it because 2 and 5 are factors of 10 which means you can have 2 plates of 5 or 5 plates of 2 and both give you 10 items.
    As far as calculators- if the lesson is teaching long division then of course no calculators. If you feel they need to practice long division then no calculators. If you feel they know division just fine and a calculator allows them to do the lesson faster then let them use it. If I'm teaching percents I let them use calculators. If I want to know 24 is what percent of 57, I'm just fine with them typing 24/57 into a calculator rather than doing the long division.
    Debbie- mom of 7, civil engineering grad, married to mechanical engineer
    DD, 23, graphic design and illustration major
    DS, 21, mechanical engineering major
    DS, 19, Dual chemistry and Philosophy major, considering Catholic seminary
    DS, 16, Kolbe 11th grade
    DD, 13, dyslexic, MP 8M
    DS, 10, super squirmy, possible dysgraphia, MP 5A
    DD, 4 (in Aug 2017), cutest little interrupter of school ever, some MP Jr K if we fit it in.

  5. #5
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    Default Re: Two COTR questions

    Quote Originally Posted by momgineer View Post
    Honestly, you are stressing over English not math. Some programs teach very specific ways of naming the parts of a problem. Maybe MP thinks it's important (Cindy?), but I don't. I want my kids to understand the math. 10 can be divided into 2 and 5. If 10 is divided by 2 the quotient is 5. If 10 is divided by 5 the quotient is 2. I really don't care if my kids think of two plates full of five things or five plates full of two things. It's the same thing to me. In my mind if I have 10 and divide by 2, I am dividing it into 2 parts and each part will have 5 pieces. That's what the fraction equivalent shows. 10/2 means to divide 10 in half. Each half is 5.
    But really it shouldn't matter which way you think of it because 2 and 5 are factors of 10 which means you can have 2 plates of 5 or 5 plates of 2 and both give you 10 items.
    As far as calculators- if the lesson is teaching long division then of course no calculators. If you feel they need to practice long division then no calculators. If you feel they know division just fine and a calculator allows them to do the lesson faster then let them use it. If I'm teaching percents I let them use calculators. If I want to know 24 is what percent of 57, I'm just fine with them typing 24/57 into a calculator rather than doing the long division.

    Thank you so much, Momgineer- it is really a huge relief to me. I am learning math slightly ahead of/alongside my kids as far as I can go, because through a series of unfortunate events I never actually learned it. This means I can't see the road in front of me, leading to a bit of stress about what will be important and what won't matter.. Today I realized that I wasn't sure how to explain it again to my younger one- or if I should even try-
    Anyway- I appreciate your help more than you know, you prevented a serious MMM. (mommy math meltdown.)
    DD 12, using 6M core with 7th Grade COTR
    DS 10, using 5M core

  6. #6
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    Default Re: Two COTR questions

    Quote Originally Posted by Maria2 View Post
    Thank you so much, Momgineer- it is really a huge relief to me. I am learning math slightly ahead of/alongside my kids as far as I can go, because through a series of unfortunate events I never actually learned it. This means I can't see the road in front of me, leading to a bit of stress about what will be important and what won't matter.. Today I realized that I wasn't sure how to explain it again to my younger one- or if I should even try-
    Anyway- I appreciate your help more than you know, you prevented a serious MMM. (mommy math meltdown.)
    I just want to encourage you that you did not teach your daughter incorrectly. I also want to draw an analogy that you are to math like I am to swimming. I don't feel comfortable with swimming, I don't really like putting my face in the water, I panic at the thought of diving into the deep end, I don't have good technique, and never had any endurance to speak of. It has a lot of social and emotional baggage attached to it from being forced to swim in gym class. Some of the fear was from my mom who passed on the fear to me, some of it was I just didn't have the opportunity to learn when all my friends were probably learning. When my kids came along I knew that I didn't want to pass on my fear. I got in the pool and got comfortable enough that I could float down the lazy river and fake that I liked it. I took my kids to swim lessons and I know enough now that I can help them out and tell them what they are doing right or wrong without being able to do it myself. They are not all fast swimmers, but they are confident and they get the job done with good technique and they love it. I say this because math sounds similar for you. You have some baggage, but you are doing a great job and setting a great example of learning alongside them. Your kids will do well in math and someday you might actually like math. Swimming and I still haven't found the love, but we do coexist.

    Good luck and never hesitate to ask questions here. We are all learning something and are here to help each other.
    Dorinda

    DD 14 - 9M with Geometry, MPOA(Henle 2, Comp3), Lukeion Greek2
    DS 12 - core 7M with Henle 1
    DS 8 - core 3A/4A
    DS 4 - loving life with AAR1

  7. #7
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    Default Re: Two COTR questions

    Thank you Dorinda! I've been asking so many questions lately and felt a bit guilty. Thanks for the kindness.
    DD 12, using 6M core with 7th Grade COTR
    DS 10, using 5M core

  8. #8
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    Default Re: Two COTR questions

    Quote Originally Posted by Maria2 View Post
    Thank you Dorinda! I've been asking so many questions lately and felt a bit guilty. Thanks for the kindness.
    Maria, have you ever watched the math videos on Khan Academy? Completely free (they recommend creating a free account to track your learning, but you don't have to do that). It covers everything from Early Math to Calculus and Trigonometry. Each concept is broken down into bite-size pieces so each video is only a few minutes long. It might give you more confidence. I've also used it to show concepts to my middle-schoolers when we ran into trouble.
    Last edited by jen1134; 10-12-2017 at 07:22 PM.
    Jennifer

    2016-2017
    DS-13 & DS-12 (mix of MP5 & MP7), DS-10 (4th for New Users), DS-8 (MP K), DD-6 (MP K), DD-4 (FSR), DD-2

    2017-2018
    DS-14 & 13 (mix of 6M & 8M)
    DS-11 (5M),
    DS-9 (?)
    DD-7 (MP1)
    DD-5 (SC2)
    DD-2-1/2

  9. #9
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    Default Re: Two COTR questions

    Quote Originally Posted by jen1134 View Post
    Maria, have you ever watched the math videos on Khan Academy? Completely free (they recommend creating a free account to track your learning, but you don't have to do that). It covers everything from Early Math to Calculus and Trigonometry. Each concept is broken down into bite-size pieces so each video is only a few minutes long. It might give you more confidence. I've also used it to show concepts to my middle-schoolers when we ran into trouble.
    Thank you! I love Khan academy! Only drawback is the format seems to kind of skip around topics for me, I think, but I can't really tell because I don't know the sequence. But it is great! The explanations are so good. I'm kind of looking for something really systematic, gentle, really step-by-step that holds my hand, since I'm so phobic. But yes I have an account, and have been working my way slowly through the math videos I find starting at *blush* I think the 5th/6th grade level. I'm onto prealgebra now, but stopped because I'm trying to understand how my dd's book is presenting it and to be at the same lesson she is doing so I can help if needs be. Score for me I was able to help her with the very basic understanding of equations, doing the same thing to the same side and why! That made me feel soooooo good, usually she is the one explaining stuff to me, haha!
    Last edited by Maria2; 10-12-2017 at 08:59 PM.
    DD 12, using 6M core with 7th Grade COTR
    DS 10, using 5M core

  10. #10
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    Default Re: Two COTR questions

    Momgineer and Dorinda already gave you great answers, and I agree with them.
    When talking through a division problem I use the correct vocabulary: dividend (number being divided) and divisor (number dividing by), especially useful when teaching fraction division ("Which one do you "flip"? The divisor!)
    Similarly, I like using minuend and subtrahend when teaching subtraction. Knowing the name of the *thing* is quite useful for communicating.
    The answer to an addition problem is a "sum"
    The answer to a subtraction problem is the "difference"
    The answer to a multiplication problem is the "product"
    The answer to a division problem is the "quotient"

    A mother of 3 sons who all earned perfect scores on the SAT was interviewed on the Today show not long ago. Their secret? She made them start on Khan Academy arithmetic and work *every* lesson to be sure there were no gaps. So by starting in 5th/6th grade, and working steadily through, you will learn it *all* correctly. Good for you! Khan will keep you moving through in sequence, so you don't need to worry about "jumping around". You are setting a great example - keep it up!
    Cindy Davis
    Science and Math teacher at Highlands Latin School - Indianapolis
    ds-23 college graduate: working, reading, writing
    ds-21 college senior: German/Biology/Chemistry/Secondary Education
    dd-19 college sophomore: Nursing

  11. #11
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    Default Re: Two COTR questions

    Quote Originally Posted by Cindy in Indy View Post
    Momgineer and Dorinda already gave you great answers, and I agree with them.
    When talking through a division problem I use the correct vocabulary: dividend (number being divided) and divisor (number dividing by), especially useful when teaching fraction division ("Which one do you "flip"? The divisor!)
    Similarly, I like using minuend and subtrahend when teaching subtraction. Knowing the name of the *thing* is quite useful for communicating.
    The answer to an addition problem is a "sum"
    The answer to a subtraction problem is the "difference"
    The answer to a multiplication problem is the "product"
    The answer to a division problem is the "quotient"

    A mother of 3 sons who all earned perfect scores on the SAT was interviewed on the Today show not long ago. Their secret? She made them start on Khan Academy arithmetic and work *every* lesson to be sure there were no gaps. So by starting in 5th/6th grade, and working steadily through, you will learn it *all* correctly. Good for you! Khan will keep you moving through in sequence, so you don't need to worry about "jumping around". You are setting a great example - keep it up!
    Thanks Cindy for the definitions. I agree they are important to use. Still, I have never been very graceful at working subtrahend and minuend to my conversation with my children. Not exactly sure why. The 4 names for the answers I meant to add to my post because they are so important for trying to decipher what is being asked for in word problems. Alas, I ran out of time because I was on my way out the door to take my 4yo to his swim lesson.

    I wish I had seen the interview. My kids have used khan academy for fun/filler, but I never really thought about just using it all the way through. Did they go through calculus on khan? Not that I am going to, but could you ever just ditch the textbook and do khan instead? What would you sacrifice?
    Dorinda

    DD 14 - 9M with Geometry, MPOA(Henle 2, Comp3), Lukeion Greek2
    DS 12 - core 7M with Henle 1
    DS 8 - core 3A/4A
    DS 4 - loving life with AAR1

  12. #12
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    Default Re: Two COTR questions

    I like Cindy's precision in terms and I just can't resist relating them to Latin. Many math terms are from Latin and, at a certain point not very far down the road in studying Latin grammar, the meanings just click and become very apparent and easy for Latin students to remember.

    The divisor, a derivative of divido, is the actor, the doer, the number that divides, the divider.
    The dividend, from the gerundive of divido, follows the formula for translating gerundives and is the number to be divided.
    And the quotient, from the Latin words quot and quotiens, answers the question, how many?
    Minuend, from the Latin gerundive of minuo, is the number to be diminished, to be made smaller.
    Subtrahend, from the gerundive of subtraho, is the number to be subtracted, to be withdrawn, to be removed.

    I would never be able to keep minuend and subtrahend straight without Latin.
    Bonnie
    Last edited by Bonnie; 10-13-2017 at 08:29 AM.

  13. #13
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    Default Re: Two COTR questions

    Thank you Cindy! I did notice that when I was trying to explain things to the kids over the years, it seemed absolutely crucial to know those terms. I just found I couldn't make sense of explaining it without knowing exactly what we were referring to, especially with division when it is presented in different ways. God can use weakness for good because I was pretty picky about making sure the kids learned that stuff so that we would understand each other. It amazingly seems to work out pretty well, so far! I am so relieved about Khan, and I will continue on with those lessons then, knowing it will prep me for helping dd and ds. I'm even starting to feel a teensy bit excited now that the math is getting to the point I just never thought I would be able to understand, but I am! Thank you for sharing that information, and for the kindness.

    Thank you Bonnie for that information- that is truly fascinating! I love it. I am going to show that to the kids, especially dd will think that is so cool. She loves Latin, it's her favorite subject.

    There is so much healing and love in this place. My heart is full this morning.
    DD 12, using 6M core with 7th Grade COTR
    DS 10, using 5M core

  14. #14
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    Default Re: Two COTR questions

    Quote Originally Posted by Mom2mthj View Post
    I wish I had seen the interview. My kids have used khan academy for fun/filler, but I never really thought about just using it all the way through. Did they go through calculus on khan? Not that I am going to, but could you ever just ditch the textbook and do khan instead? What would you sacrifice?
    This mom used Khan Academy as a supplement (her sons were public-schooled). I would not want to give up a textbook, because you can actually move quicker through many topics with a textbook. (I find Sal's explanations a bit laborious, but he is thorough.) Khan is a great supplemental resource, and in their case, it filled in some gaps and ensured mastery of every skill. Here is a link to an article about the family. (It looks like they earned perfect scores on ACT, rather than SAT.)
    Cindy Davis
    Science and Math teacher at Highlands Latin School - Indianapolis
    ds-23 college graduate: working, reading, writing
    ds-21 college senior: German/Biology/Chemistry/Secondary Education
    dd-19 college sophomore: Nursing

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