A Little Common Core Math problem

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A Little Common Core Math problem
Ok, this math problem isn't too bad for Common Core. It came from my daughter's fourth grade math book. I'm not sure how the teacher is teaching the way to solve this type of problem, but I do know he's not a fan of Common Core in general. Anyway, let me share the problem first.
Jane has two pets, a dog and a cat. The dog weighs 8 times as much as the cat. Together, the dog and cat weigh 63 pounds. How much does the dog weigh?
Answer Options
a) 7
b) 48
c) 56
d) 58
Right. So, my approach to this was to simply write out the two equations and then solve them simulatenously. I admit, it dawned on me as I was doing it that it now made sense why my son (who is in 2nd grade) is spending so much time on learning transitive properties of addition and subtraction. Because that's the underlying theory that is used when solving simultaneous equations with common variables.
Ok, now enter my 9 year old daughter. She's a smart cookie. And I'm not just saying that, I've seen the COGAT results (141 composite) and the gifted test results that affirm my statement. She apparently solved it iteratively by testing each answer by dividing the choices by 8 and then...and then I didn't understand how she concluded that the correct answer was X (I left it as X in case people want to test themselves). She got irritated at me because I pressed her on how she solved it when she couldn't easily explain herself.
I then showed her the equations approach which thoroughly annoyed her (she says I take forever to explain stuff).
Ok, so what's my point here?
Our elementary school has an after school YMCA program that serves as an afternoon daycare. It's nice because it's right in the school and they spend the first hour doing homework or quiet play. After that they do games and stuff and they both have friends there as well. So by the time I pick them up a little later in the afternoon they've had time to complete homework. The three YMCA teachers (not the school's teachers) will assist with homework if they need help. I've told both my kids that if they need help, they are to WAIT until we get home and I will help them (or my wife).
Yesterday, my reasons for this were borne out.
None of the three YMCA teachers could solve the problem individually. My daughter said it took them a total of 15 minutes and working together (the three teachers) before they managed to confirm if my daughter had the right answer. And they needed a calculator.
Yikes.
Jane has two pets, a dog and a cat. The dog weighs 8 times as much as the cat. Together, the dog and cat weigh 63 pounds. How much does the dog weigh?
Answer Options
a) 7
b) 48
c) 56
d) 58
Right. So, my approach to this was to simply write out the two equations and then solve them simulatenously. I admit, it dawned on me as I was doing it that it now made sense why my son (who is in 2nd grade) is spending so much time on learning transitive properties of addition and subtraction. Because that's the underlying theory that is used when solving simultaneous equations with common variables.
Ok, now enter my 9 year old daughter. She's a smart cookie. And I'm not just saying that, I've seen the COGAT results (141 composite) and the gifted test results that affirm my statement. She apparently solved it iteratively by testing each answer by dividing the choices by 8 and then...and then I didn't understand how she concluded that the correct answer was X (I left it as X in case people want to test themselves). She got irritated at me because I pressed her on how she solved it when she couldn't easily explain herself.
I then showed her the equations approach which thoroughly annoyed her (she says I take forever to explain stuff).
Ok, so what's my point here?
Our elementary school has an after school YMCA program that serves as an afternoon daycare. It's nice because it's right in the school and they spend the first hour doing homework or quiet play. After that they do games and stuff and they both have friends there as well. So by the time I pick them up a little later in the afternoon they've had time to complete homework. The three YMCA teachers (not the school's teachers) will assist with homework if they need help. I've told both my kids that if they need help, they are to WAIT until we get home and I will help them (or my wife).
Yesterday, my reasons for this were borne out.
None of the three YMCA teachers could solve the problem individually. My daughter said it took them a total of 15 minutes and working together (the three teachers) before they managed to confirm if my daughter had the right answer. And they needed a calculator.
Yikes.
Last edited by investingdad on Thu Oct 30, 2014 1:59 pm, edited 1 time in total.
Re: A Little Common Core Math problem
investingdad wrote: She apparently solved it iteratively by testing each answer by dividing the choices by 8 and then..
I like your way (equations) better. In the real world, she will not be gifted with a small number of possible answers to test.
Re: A Little Common Core Math problem
Equations? Iterations? The answer just popped into my head.
Re: A Little Common Core Math problem
So, you're saying that your daughter would not have been able to solve the problem if it were not Multiple Choice?
If so, That's not a good plan.
If so, That's not a good plan.
Last edited by BahamaMan on Thu Oct 30, 2014 1:15 pm, edited 1 time in total.

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Re: A Little Common Core Math problem
Ran into a similar scenario with my 5th Grade son. He is able to identify the correct answer based on the multiple choice selections, but cannot perform the following calculation steps:
Spoiler alert!!
D = 8C
D + C = 63
1. 8C + C = 63
2. 9C = 63
3. C = 63/9 = 7
4. D + 7 = 63
5. D = 56
I help him with his math homework and it is frustrating for both of us.
Spoiler alert!!
D = 8C
D + C = 63
1. 8C + C = 63
2. 9C = 63
3. C = 63/9 = 7
4. D + 7 = 63
5. D = 56
I help him with his math homework and it is frustrating for both of us.
"The first principle is that you must not fool yourself and you are the easiest person to fool" Feynman.

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Re: A Little Common Core Math problem
BahamaMan wrote:So, your saying that your daughter would not have been able to solve the problem if it were not Multiple Choice?
If so, That's not a good plan.
Absolutely, I agree. Which is why I sat her down and showed her how to tackle this type of problem through the proper use of simple equations and variables. Fortunately, she'll tolerate my explanations. My son, on the other hand, is EXACTLY like I was in school...if the answer is right, move on already and don't bother me with the details. I already know what's in store for us because I put my dad through it.
What really caught me off guard, however, was when the three Y teachers had to spend 10 or 15 minutes debating with each other how to get the right answer.
Last edited by investingdad on Thu Oct 30, 2014 1:17 pm, edited 1 time in total.
Re: A Little Common Core Math problem
Could your daughter have solved this problem without the multiple choice answers available?
I like both methods for multiple choice testing. Being able to switch between your daughter's simplified elimination approach and algabraic problemsolving approach is how I've scored well on standardized testing for basically my entire life. The last real test I took was the CPA exam, and both approaches continued to be useful. In real life, though  only the algabraic method is useful for my job.
As for the YMCA  I don't know what to say. I once had a coworker who was having a problem with something, so I got a pad of paper and used algebra to solve it. He just stared dumbfounded and said, "Is that algebra?!"
I like both methods for multiple choice testing. Being able to switch between your daughter's simplified elimination approach and algabraic problemsolving approach is how I've scored well on standardized testing for basically my entire life. The last real test I took was the CPA exam, and both approaches continued to be useful. In real life, though  only the algabraic method is useful for my job.
As for the YMCA  I don't know what to say. I once had a coworker who was having a problem with something, so I got a pad of paper and used algebra to solve it. He just stared dumbfounded and said, "Is that algebra?!"

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Re: A Little Common Core Math problem
As usual, my recommendation for this particular problem is to just put a BLANK for the student to put his/her answer in.
That's how it's done in college, none of this silly multiple choice stuff...
That's how it's done in college, none of this silly multiple choice stuff...
Attempted new signature...
Re: A Little Common Core Math problem
[deleted] misread question
I did see the a blurb about Common Core on the news the other night. I was shocked when they showed how they are teaching kids to do subtraction these days.
I did see the a blurb about Common Core on the news the other night. I was shocked when they showed how they are teaching kids to do subtraction these days.
Last edited by 2retire on Thu Oct 30, 2014 1:21 pm, edited 1 time in total.
 SteelyEyed
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Re: A Little Common Core Math problem
Your daughter's solution:
A. Divide answers by eight to determine possible cat weights.
B. Add answers from steps A to to original weights.
C. The sum that equal 63 is from the choice that is correct.
I did things like that in school, but only as a backup if I couldn't figure it out the correct way first.
A. Divide answers by eight to determine possible cat weights.
B. Add answers from steps A to to original weights.
C. The sum that equal 63 is from the choice that is correct.
I did things like that in school, but only as a backup if I couldn't figure it out the correct way first.

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Re: A Little Common Core Math problem
Miakis wrote:Could your daughter have solved this problem without the multiple choice answers available?
Yes, she would have figured it out, though her methods would not have been the cleanest or most elegant.
 jimb_fromATL
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Re: A Little Common Core Math problem
Hmmm. it's been 60+ years since I was in the 4th grade, but I'd have thought an adult should be able to do that in their head in about 5 or 10 seconds. I don't know that I'd call it solving simultaneous equations. I'd call it addition, division, and multiplication.
jimb
jimb
Re: A Little Common Core Math problem
Are the YMCA teachers actually teachers or are they minders?

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Re: A Little Common Core Math problem
I might be wrong but are those qualified teachers at YMCA or more of child care teachers?
My root answer is that most of the common people that I interact with face to face are surprised that I can do a two digit by two digit multiplication in mind and tell answer in more or less time it takes them to do on calculator. When I go to stores and say give 5.07 for a 99c item that totals to 1.07 with tax, they dont understand why i am giving that extra 7 cents.
My root answer is that most of the common people that I interact with face to face are surprised that I can do a two digit by two digit multiplication in mind and tell answer in more or less time it takes them to do on calculator. When I go to stores and say give 5.07 for a 99c item that totals to 1.07 with tax, they dont understand why i am giving that extra 7 cents.

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Re: A Little Common Core Math problem
The use of multiple equations is usually taught starting somewhere between 6th and 8th grade depending on the advancement level of the student. Your daughter will be taught how to correctly solve this problem in school soon.
Here is my thought process for this answer: The cat has to weigh an odd amount that isn't 5 (obviously because the final answer would have to end in 5 or 0). 7 sounds about right. 7*8=56. 56 + 7 = 63. Dog weight 56. This process is much quicker in my mind than solving using equations. My teachers always hated my explanations for solving things... fortunately for them abstract solving kind of goes away once calculus and beyond starts up.
Here is my thought process for this answer: The cat has to weigh an odd amount that isn't 5 (obviously because the final answer would have to end in 5 or 0). 7 sounds about right. 7*8=56. 56 + 7 = 63. Dog weight 56. This process is much quicker in my mind than solving using equations. My teachers always hated my explanations for solving things... fortunately for them abstract solving kind of goes away once calculus and beyond starts up.
Re: A Little Common Core Math problem
Buddtholomew wrote:Ran into a similar scenario with my 5th Grade son. He is able to identify the correct answer based on the multiple choice selections, but cannot perform the following calculation steps:
Spoiler alert!!
D = 8C
D + C = 63
1. 8C + C = 63
2. 9C = 63
3. C = 63/9 = 7
4. D + 7 = 63
5. D = 56
I help him with his math homework and it is frustrating for both of us.
Has your son had algebra yet? It is sometimes hard to grasp the concept of substituting letters for numbers. Once you do, it becomes obvious. Sometimes we forget how difficult it was for us to learn things at first, especially if we are using it in our jobs every day.
My thought process was dog is 8 times cat, the two together are 9, 63/9=7, dog is 8*7 = 56.
Last edited by rkhusky on Thu Oct 30, 2014 1:28 pm, edited 2 times in total.

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Re: A Little Common Core Math problem
Buddtholomew wrote:Ran into a similar scenario with my 5th Grade son. He is able to identify the correct answer based on the multiple choice selections, but cannot perform the following calculation steps:
Spoiler alert!!
D = 8C
D + C = 63
1. 8C + C = 63
2. 9C = 63
3. C = 63/9 = 7
4. D + 7 = 63
5. D = 56
I help him with his math homework and it is frustrating for both of us.
My equations were a little different:
D = 8C
D + C = 63
1. C = 63  D
2. D = 8(63D)
3. D = 504  8D
4. 9D = 504
5. D = 56
6. C = 7
My preference was always to first solve the variable that was initially isolated. In this case, at the expense of an extra step.

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Re: A Little Common Core Math problem
jimb_fromATL wrote:Hmmm. it's been 60+ years since I was in the 4th grade, but I'd have thought an adult should be able to do that in their head in about 5 or 10 seconds. I don't know that I'd call it solving simultaneous equations. I'd call it addition, division, and multiplication.
jimb
As an engineer, my preference is to write out the equations and test the answers. So, yeah...
Besides, I need to show her the correct approach for when the problem isn't so simple.

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Re: A Little Common Core Math problem
I am impressed that they are teaching math at that high a level in 4th grade.
I don't remember solving algebra equations until much later in life.
I agree with The Wizard, multiple choice isn't a very good way to evaluate whether or not you learned something. It is a good way to evaluate if you are good at taking multiple choice tests though.
There is no reason to use multiple choice tests with today's recognition software.
I don't remember solving algebra equations until much later in life.
I agree with The Wizard, multiple choice isn't a very good way to evaluate whether or not you learned something. It is a good way to evaluate if you are good at taking multiple choice tests though.
There is no reason to use multiple choice tests with today's recognition software.
Re: A Little Common Core Math problem
investingdad wrote:Miakis wrote:Could your daughter have solved this problem without the multiple choice answers available?
Yes, she would have figured it out, though her methods would not have been the cleanest or most elegant.
When I was doing my Masters, I was a GTA for an intro accounting class. You would be surprised by how many students were incapable of doing what your daughter did:
1. Read and understand the question.
2. Check the data points to see if they make sense.
3. Avoid unnecessary, timeconsuming work.
Re: A Little Common Core Math problem
I think solving 2 simultaneous equations is above a fourth grade math level. Without knowing the fundamentals of algebra, testing the given possible solutions is a good way to solve it.
However, this is a simple problem and anyone with even some high school education should be able to solve in the proper manner.
However, this is a simple problem and anyone with even some high school education should be able to solve in the proper manner.
Re: A Little Common Core Math problem
First, using just plain number sense, you should be able to come up with a basic estimate almost immediately. You know that if the dog weighs 8 times as much as the cat, there's no way the dog weighs 7 pounds, and you can eliminate choice A.
I can't build equations in my head, and I operate in an environment where I don't have the luxury of writing down answers. Being able to solve problems like this in your head is important. Let's think logically though here.
I split up the 63 pounds into 9 equal sections, 8 of which are dog, 1 of which is cat. So each section is 63 / 9 or 7. Since the dog is 8 of those sections, I know the dog must weigh 8 x 7. I know my times tables, which brought be to answer choice C.
In the real world, you don't always have the luxury of a calculator, and you don't always have the luxury of a pen and paper either. Being able to solve this in your head is valuable. Writing out equations is not practical for solving in your head.
I can't build equations in my head, and I operate in an environment where I don't have the luxury of writing down answers. Being able to solve problems like this in your head is important. Let's think logically though here.
I split up the 63 pounds into 9 equal sections, 8 of which are dog, 1 of which is cat. So each section is 63 / 9 or 7. Since the dog is 8 of those sections, I know the dog must weigh 8 x 7. I know my times tables, which brought be to answer choice C.
In the real world, you don't always have the luxury of a calculator, and you don't always have the luxury of a pen and paper either. Being able to solve this in your head is valuable. Writing out equations is not practical for solving in your head.
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Re: A Little Common Core Math problem
It took me a whileI didn't use a stopwatchmaybe a minute... and the reasons are that a) I STILL am shaky on the quadrant of the multiplication table with the 6's and 7's and 8's in it, and b) I correctly got the weight of the cat and was mentally hovering my virtual pencilIBM Electrographic, "make sure your marks are heavy and black" before thinking to reread the problem and noticed they wanted the weight of the dog.livesoft wrote:Equations? Iterations? The answer just popped into my head.
Weeeeeellll... I don't know about that. It is quite a puzzle. I want the kids to learn mathematics, but with the insane overreliance on standardized testing that is the current educational fad, I think they had better be learning quizmanship, too.BahamaMan wrote:So, you're saying that your daughter would not have been able to solve the problem if it were not Multiple Choice? If so, That's not a good plan.
And of course... the whole idea of what things people need to know, and why, keeps shifting. I saw a circa1900 high school arithmetic book that had directions for extracting a cube root with pencil and paper. A cube root. The first step is easy: divide off the digits into threes. We learned how to do square roots in the 1960s. Is that important today now that we are never more than five feet away from a calculator?
Trigonometrynot the theory, but the actual calculations and suchwas pretty important to Virginia gentlemen farmers who were expected to do their own surveying (yes, with rods and chains, and, I suppose, calculating distances IN rods and chains... and degrees, minutes, and seconds...), or to Napoleonicera midshipmen learning navigation. Is it important today?
Is it necessary to have a table of integrals when we would, as a practical matter, work any realworld problem numerically?
Has a theorem really been "proved" if the proof is 13 gigabytes long and cannot be checked by a human being?
Is a closedbook test even appropriate any more, when all problems in the real world will be solved by people with Internet access?
Oh, by the way... 7 times 8 is 42, isn't it?
Last edited by nisiprius on Thu Oct 30, 2014 1:35 pm, edited 1 time in total.
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Re: A Little Common Core Math problem
I'm all for pragmatism  if it's a multiplechoice test, why not try the answer choices? It's a very effective approach.
That said, if I were going to do algebra, I'd say that the cat is x and the dog is 8x. 8x + x = 63, so 9x = 63, so x = 7. Dog is 8x, so (8)(7) = 56.
The longer conversation is that this is a ratio question. The ratio of cat to dog is 1:8. You can solve ratios by turning the numbers into algebraic quantities (1x and 8x), adding them together, setting them equal to the total, solving for the multiple (x), and then looking back to the question to see which quantity they want (the 1x or the 8x).
I have no idea why the YMCA teachers couldn't solve this question  that would give me pause.
NightOwl
That said, if I were going to do algebra, I'd say that the cat is x and the dog is 8x. 8x + x = 63, so 9x = 63, so x = 7. Dog is 8x, so (8)(7) = 56.
The longer conversation is that this is a ratio question. The ratio of cat to dog is 1:8. You can solve ratios by turning the numbers into algebraic quantities (1x and 8x), adding them together, setting them equal to the total, solving for the multiple (x), and then looking back to the question to see which quantity they want (the 1x or the 8x).
I have no idea why the YMCA teachers couldn't solve this question  that would give me pause.
NightOwl
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Re: A Little Common Core Math problem
Solving this problem with equations requires algebra. Since algebra is not being taught at that grade level the students must rely on critical thinking skills. She did solve the problem – and did it without algebra. Not elegant but sufficient. Good for her.

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Re: A Little Common Core Math problem
Buddtholomew wrote:Ran into a similar scenario with my 5th Grade son. He is able to identify the correct answer based on the multiple choice selections, but cannot perform the following calculation steps:
Spoiler alert!!
D = 8C
D + C = 63
1. 8C + C = 63
2. 9C = 63
3. C = 63/9 = 7
4. D + 7 = 63
5. D = 56
I help him with his math homework and it is frustrating for both of us.
Maybe I misunderstood but he is trying to find the right answer by testing all solution? Would it not be more efficient to teach them the correct way the first time?
Cat = X
Dog = 8x
Cat + Dog = 63
x + 8X = 63
9x = 63
x = 7
Cat = x = 7
Dog = 8x = 8*7
Dog = 56
C is the correct answer.
This is how I was taught algebra some twenty years ago so I am not sure if common core now frowns on my methods. Also, I did not take alegbra until the 7th grade (this was early for us as honor kids) so asking a fourth grader to do same type of reasoning may be unfair.
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Re: A Little Common Core Math problem
P.S. "Jane has two pets, a dog and a cat. The dog weighs 8 times as much as the cat. Together, the dog and cat weigh 63 pounds. How much does the dog weigh?"
The dog weighs eight cats. Together, they weigh nine cats. Therefore nine cats weigh 63 pounds. Therefore, a cat weighs um... um... um... 63 ÷ 9...
...hang on just a second... 9, 18, 27, 36, 45, 56, I mean 54, 63... OK.
Therefore a cat weighs 7 pounds. Therefore a dog weighs 8 cats which is...
uh... um... well, maybe another way, that would be 63  7, uh...hang on a second...
...62, 61, 60, 59, 58, 57, 56.
(I'm exaggerating. A bit).
The dog weighs eight cats. Together, they weigh nine cats. Therefore nine cats weigh 63 pounds. Therefore, a cat weighs um... um... um... 63 ÷ 9...
...hang on just a second... 9, 18, 27, 36, 45, 56, I mean 54, 63... OK.
Therefore a cat weighs 7 pounds. Therefore a dog weighs 8 cats which is...
uh... um... well, maybe another way, that would be 63  7, uh...hang on a second...
...62, 61, 60, 59, 58, 57, 56.
(I'm exaggerating. A bit).
Last edited by nisiprius on Thu Oct 30, 2014 1:43 pm, edited 2 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Re: A Little Common Core Math problem
lululu wrote:Are the YMCA teachers actually teachers or are they minders?
I don't know the backgrounds but they're clearly not certified teachers. Which is why I don't want my kids going to them for homework help. Nothing personal, they're nice enough...but if they cannot solve this sort of problem w/o working together for 10 minutes while my daughter arrived at the answer on her own, then I don't want them helping my kiddos with homework.
As I said, I don't know how the teacher is teaching the approach to this type of problem. I've met him (he's in his 50s) and he came off as the sort of person that I can trust to teach math, plus he's told the students that some moms and dads may show them different (better) ways to solve problems and they were welcome to use those methods.
So, it's a tricky line to tow...I KNOW how she can solve it and I WANT to show her, but I understand there is pacing here.
Re: A Little Common Core Math problem
I don't see anything wrong with her approach.
If you had said, something like "It's great that you solved it!...can you come up with a way to solve it without having the list of answers?", then you might have had better success at mentoring her. (I'm using 20/20 hindsight of course.)
She was resourceful, after all.
If you had said, something like "It's great that you solved it!...can you come up with a way to solve it without having the list of answers?", then you might have had better success at mentoring her. (I'm using 20/20 hindsight of course.)
She was resourceful, after all.
Re: A Little Common Core Math problem
Higman wrote:Solving this problem with equations requires algebra. Since algebra is not being taught at that grade level the students must rely on critical thinking skills. She did solve the problem – and did it without algebra. Not elegant but sufficient. Good for her.
+1. And I'm not quite sure I understand how common core is to blame for this or anything, for that matter, since most textbooks haven't yet incorporated the common core standards. http://www.edweek.org/ew/articles/2014/ ... m.h34.html. I suppose common core is just the latest bogeyman, blamed for everything from ebola to Miley Cyrus.

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Re: A Little Common Core Math problem
tadamsmar wrote:I don't see anything wrong with her approach.
If you had said, something like "It's great that you solved it!...can you come up with a way to solve it without having the list of answers?", then you might have had better success at mentoring her. (I'm using 20/20 hindsight of course.)
She was resourceful, after all.
Good pointer, thanks. That's why I'm an engineer and not a teacher, very different mindsets.
I agree that she was resourceful, and also proud of herself. She brought this to my attention on the ride home because she was amazed that the three Y teachers (or minders ) were struggling for so long to find the answer. I admit to wanting to brag on her a bit as well...it's what dads do.

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Re: A Little Common Core Math problem
This reminds me of my high school days. We were being taught this field of math called "analysis", which was really just precalculus. We learned how to do things such as finding areas under the curve or a slope of a point on a curve by drawing the tangent. My dad would get so frustrated at it when he would help me with my homework because, "I can solve this problem in 5 seconds with calculus! Why do you need to graph it out?" Good times. Wolframalpha has made my calculus ability go the way of the dodo.
This is the same thing. They are teaching her the hard way of doing things, so that when she learns algebra, there is an "aha!" moment.
This is the same thing. They are teaching her the hard way of doing things, so that when she learns algebra, there is an "aha!" moment.
Re: A Little Common Core Math problem
lol If you quized random people on the street i guarentee you far less than 50% of the people would give you the correct answer in under 23 min.
I wouldn't be too hard on the YMCA teachers. I think you may be overestimating the math skills of the general population.
Solving 2x2 linear equations is not 4th grade level work either. I'm sure it will come with time.
I wouldn't be too hard on the YMCA teachers. I think you may be overestimating the math skills of the general population.
Solving 2x2 linear equations is not 4th grade level work either. I'm sure it will come with time.

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Re: A Little Common Core Math problem
Rupert wrote:Higman wrote:Solving this problem with equations requires algebra. Since algebra is not being taught at that grade level the students must rely on critical thinking skills. She did solve the problem – and did it without algebra. Not elegant but sufficient. Good for her.
+1. And I'm not quite sure I understand how common core is to blame for this or anything, for that matter, since most textbooks haven't yet incorporated the common core standards. http://www.edweek.org/ew/articles/2014/ ... m.h34.html. I suppose common core is just the latest bogeyman, blamed for everything from ebola to Miley Cyrus.
People completely misunderstand the math portions of common core and the purpose of its techniques. It is trying to teach kids how to solve math problems in a more naturally intuitive way. People that don't like it have a case of That's Not How They Did It In My Day!
Re: A Little Common Core Math problem
tadamsmar wrote:I don't see anything wrong with her approach.
If you had said, something like "It's great that you solved it!...can you come up with a way to solve it without having the list of answers?", then you might have had better success at mentoring her. (I'm using 20/20 hindsight of course.)
She was resourceful, after all.
Yep I would totally use her approach on a multiple choice test. The right way won't be taught for another few years in school, so her resourcefulness is definitely impressive.
I am not surprised that many adults have forgotten how to do basic algebra. I find a lot of people freeze when faced with a question like that.
My wife told me many years ago that she is bad at math, but she could easily solve this problem (the proper way with simultaneous equations or by divide and add in her head) in a matter of seconds. I told her she is good at math compared to most adults these days in the US, who tend to freeze when they see numbers. And I was right. People at her work look to her to crunch numbers and do stuff in Excel (and she is in HR).
Re: A Little Common Core Math problem
This seems like a good problem to me  I enjoyed doing it, and it took me a minute or so. It also seems above a secondgrade level, and I'm impressed if your son is figuring it out, regardless of his methods.
Without discussing policy, my understanding of common core as it relates to math is that kids are SUPPOSED to be learning more about HOW to figure these things out than just getting the answer. There is room for a little bit of trial and error, and your daughter's approach seems pretty reasonable (I would have done that at her prealgebra age).
I can't explain the folks at the Y  that is a little upsetting  but I don't mind a vision of the world where our secondgraders are figuring out problems like these on their own.
Best of luck!
Without discussing policy, my understanding of common core as it relates to math is that kids are SUPPOSED to be learning more about HOW to figure these things out than just getting the answer. There is room for a little bit of trial and error, and your daughter's approach seems pretty reasonable (I would have done that at her prealgebra age).
I can't explain the folks at the Y  that is a little upsetting  but I don't mind a vision of the world where our secondgraders are figuring out problems like these on their own.
Best of luck!
Re: A Little Common Core Math problem
My child is in fifth grade and has similar problems in his math book (the school follows the common core). Based on standardized testing (NWEA) he is currently at the 99th percentile for 11th grade, but is struggling with the common core curriculum.
Why? Because the assessment tests insist that students provide an explanation for the answer; simply providing the solution is not good enough. Like livesoft, he'll come up with the answer, but then say "Equations? Iterations? The answer just popped into my head". Not good enough for the school. So while he can easily solve trigonometry and algebra problems from his sister's ninth grade books, he's considered "below proficiency" for his grade
Why? Because the assessment tests insist that students provide an explanation for the answer; simply providing the solution is not good enough. Like livesoft, he'll come up with the answer, but then say "Equations? Iterations? The answer just popped into my head". Not good enough for the school. So while he can easily solve trigonometry and algebra problems from his sister's ninth grade books, he's considered "below proficiency" for his grade
Last edited by mudfud on Thu Oct 30, 2014 1:57 pm, edited 1 time in total.

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Re: A Little Common Core Math problem
TSR wrote:This seems like a good problem to me  I enjoyed doing it, and it took me a minute or so. It also seems above a secondgrade level, and I'm impressed if your son is figuring it out, regardless of his methods.
Without discussing policy, my understanding of common core as it relates to math is that kids are SUPPOSED to be learning more about HOW to figure these things out than just getting the answer. There is room for a little bit of trial and error, and your daughter's approach seems pretty reasonable (I would have done that at her prealgebra age).
I can't explain the folks at the Y  that is a little upsetting  but I don't mind a vision of the world where our secondgraders are figuring out problems like these on their own.
Best of luck!
This was actually a fourth grade problem. I probably confused things just a bit when I mentioned my son who is a 2nd grader.
Re: A Little Common Core Math problem
When I was in 5th grade, we were taught the "new math" by an incompetent teacher. I clearly recall that we learned nothing the first 10 weeks and we were pretty good at letting the teacher or perhaps our parents know it. We then got a substitute teacher and were told the first teacher had a nervous breakdown. Math has been easy ever since.
The lesson I learned is that some teachers should not be teaching. Full disclosure: I am a teacher myself.
The lesson I learned is that some teachers should not be teaching. Full disclosure: I am a teacher myself.
Re: A Little Common Core Math problem
Higman wrote:Solving this problem with equations requires algebra. Since algebra is not being taught at that grade level the students must rely on critical thinking skills. She did solve the problem – and did it without algebra. Not elegant but sufficient. Good for her.
Re livesoft: The answer was self evident to me as well. But . . . it is a valid point that there is a lot of groundwork behind use of simultaneous equations and that is certainly not something done in forth grade or understood by almost any forth grader. That the second grader got some kind of insight from being shown simultaneous equations seems dubious, but I wasn't there. Therefore the question is what the curriculum was actually trying to teach or exercise in that problem. Maybe the point of the homework was to identify the answer by testing each possibility in turn, and there is still the question what the test might have been. It would be interesting to hear the explanation for how the answer would be found by dividing the choices by eight. The chain of logic would be to divide each possible answer by eight and then add the result back to the number being tested and see if the sum is 63. That means that you are adding together the weights of the dog and cat and trying to get 63 lbs. That works for 56 + 56/8 = 56 + 7 = 63. It is credible that a fourth grader could devise this approach. The point of this would be use of logical reasoning to solve a puzzle, an admirable mathematical skill at any level, but is this a typical activity in Common Core? You do get a lot of this sort of thing in Math Olympiad and Continental Math League.
My guess is that 90% of the adult population would struggle with this question and than fewer than 5% or even 1% would actually sit down and write equations. People who are going to be hired for after school daycare are no way going to have capabilities to do this sort of thing. It is actually somewhat commendable that they did indeed confirm the right answer.
So here is a question. What fraction of the workforce has a requirement in their daily work to be able to answer a question such as this using algebra? What fraction has a requirement to answer a question like this by using puzzle solving skills?
Re: A Little Common Core Math problem
investingdad wrote:TSR wrote:This seems like a good problem to me  I enjoyed doing it, and it took me a minute or so. It also seems above a secondgrade level, and I'm impressed if your son is figuring it out, regardless of his methods.
Without discussing policy, my understanding of common core as it relates to math is that kids are SUPPOSED to be learning more about HOW to figure these things out than just getting the answer. There is room for a little bit of trial and error, and your daughter's approach seems pretty reasonable (I would have done that at her prealgebra age).
I can't explain the folks at the Y  that is a little upsetting  but I don't mind a vision of the world where our secondgraders are figuring out problems like these on their own.
Best of luck!
This was actually a fourth grade problem. I probably confused things just a bit when I mentioned my son who is a 2nd grader.
Ah, sorry, and thanks for the clarification. Regardless, it's clearly a quasialgebraic question and thus would sit more comfortably in a middleschool classroom.

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Re: A Little Common Core Math problem
dbr wrote:Higman wrote:Solving this problem with equations requires algebra. Since algebra is not being taught at that grade level the students must rely on critical thinking skills. She did solve the problem – and did it without algebra. Not elegant but sufficient. Good for her.
Re livesoft: The answer was self evident to me as well. But . . . it is a valid point that there is a lot of groundwork behind use of simultaneous equations and that is certainly not something done in forth grade or understood by almost any forth grader. That the second grader got some kind of insight from being shown simultaneous equations seems dubious, but I wasn't there. Therefore the question is what the curriculum was actually trying to teach or exercise in that problem. Maybe the point of the homework was to identify the answer by testing each possibility in turn, and there is still the question what the test might have been. It would be interesting to hear the explanation for how the answer would be found by dividing the choices by eight. The chain of logic would be to divide each possible answer by eight and then add the result back to the number being tested and see if the sum is 63. That means that you are adding together the weights of the dog and cat and trying to get 63 lbs. That works for 56 + 56/8 = 56 + 7 = 63. It is credible that a fourth grader could devise this approach. The point of this would be use of logical reasoning to solve a puzzle, an admirable mathematical skill at any level, but is this a typical activity in Common Core? You do get a lot of this sort of thing in Math Olympiad and Continental Math League.
My guess is that 90% of the adult population would struggle with this question and than fewer than 5% or even 1% would actually sit down and write equations. People who are going to be hired for after school daycare are no way going to have capabilities to do this sort of thing. It is actually somewhat commendable that they did indeed confirm the right answer.
So here is a question. What fraction of the workforce has a requirement in their daily work to be able to answer a question such as this using algebra? What fraction has a requirement to answer a question like this by using puzzle solving skills?
No, no...my 2nd grader isn't in the picture here at all. I simply mentioned that as I was solving the equations for my 4th grader, it dawned on ME why my 2nd grader was being focused so hard in his own math books on transitive properties of addition and subtraction. Because you need to understand that 12=84 is related to 4=128 in order to tackle those simultaneous equations correctly.
My guess is that 90% of the adult population would struggle with this question
Do you really think 90% would struggle with this? It is certainly possible that I have a severly skewed expectation of what the average person should be able to figure out with math. I'm surprised to hear somebody thinking the bar should be so low for the general population.
Last edited by investingdad on Thu Oct 30, 2014 2:10 pm, edited 2 times in total.

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Re: A Little Common Core Math problem
mudfud wrote:My child is in fifth grade and has similar problems in his math book (the school follows the common core). Based on standardized testing (NWEA) he is currently at the 99th percentile for 11th grade, but is struggling with the common core curriculum.
Why? Because the assessment tests insist that students provide an explanation for the answer; simply providing the solution is not good enough. Like livesoft, he'll come up with the answer, but then say "Equations? Iterations? The answer just popped into my head". Not good enough for the school. So while he can easily solve trigonometry and algebra problems from his sister's ninth grade books, he's considered "below proficiency" for his grade
You just gave me some bad grade school flashbacks. I was basically your child at that age. I was a very abstract thinker. I always solved problems on the fly but would have trouble explaining how I solved problems like I did. Anways, my parents were insistent that I was getting extremely bored in the atlevel classes but my teachers didn't think I should advance. My parents and the school came to an agreement that I would take some sort of supervised performance test to decide if I was at the right level. Well I didn't actually get to see my grade on that test, but the school offered my parents to have me skip a grade
We compromised and I took some classes with the older kids (math,science) and some with my normal class (language arts, history, etc.).
Re: A Little Common Core Math problem
mudfud wrote:My child is in fifth grade and has similar problems in his math book (the school follows the common core). Based on standardized testing (NWEA) he is currently at the 99th percentile for 11th grade, but is struggling with the common core curriculum.
Why? Because the assessment tests insist that students provide an explanation for the answer; simply providing the solution is not good enough. Like livesoft, he'll come up with the answer, but then say "Equations? Iterations? The answer just popped into my head". Not good enough for the school. So while he can easily solve trigonometry and algebra problems from his sister's ninth grade books, he's considered "below proficiency" for his grade
This makes me sad and makes me worried about my daughter's education.
I was around the same age as your child when they almost did not let me into the advanced math path (basically starting algebra and geometry a year earlier) for some reasons despite believing (rightfully) that I had a better grasp of the material than anyone in my class. They gave me a chance reluctantly. I ended up shooting to the top of my class in every math class, got a perfect score in math on the SAT's and got straight A's in math at an Ivy League college.
 dodecahedron
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Re: A Little Common Core Math problem
Your daughter is very resourceful. And her technique can easily be generalized to nonmultiple choice situations. If she hadn't been given multiple choices, she could have just guessed a plausible number for the weight of the cat (or the dog), tried it to see if worked, and then intelligently modified her next guess based on what she learned from her first attempt. Advanced problem solvers (including Bogleheadssee below) often do that kind of thing in real world situations (which are generally messier than anything you find on a test or homework, multiple choice or not.)
An ideal problem for learning has lots of valid approaches to it, and children can learn a lot if they are encouraged to play with the problem, to take ownership of the process, finding multiple approaches to solving it, and reflecting on what strategies work well and not so well for them in different types of problem solving situations.
As a wonderful mathematician and problem solver, George Polya, a professor at Stanford famously said, "It is better to solve one problem five ways than five problems one way."
Polya wrote a classic book on problem solving (How to Solve It, published by Princeton University Press) that was aimed at older students, but the essential advice boils down to principles simple enough for young children like your daughter to appreciate. Here is some of that distilled into simple terms to share with her.
http://math.berkeley.edu/~gmelvin/polya.pdf
You will notice the very first technique on the list is "Guess and check," which is a venerable problem solving strategy used by world class mathematicians. It is also one I see Bogleheads use all the time (e.g., let's try this SWR and see what happens when we model it. Hmm, not so good, let's try this...)
It is not the only weapon in our arsenal of problem solving tools, but it is a worthy one not to be sneezed at or dismissed.
An ideal problem for learning has lots of valid approaches to it, and children can learn a lot if they are encouraged to play with the problem, to take ownership of the process, finding multiple approaches to solving it, and reflecting on what strategies work well and not so well for them in different types of problem solving situations.
As a wonderful mathematician and problem solver, George Polya, a professor at Stanford famously said, "It is better to solve one problem five ways than five problems one way."
Polya wrote a classic book on problem solving (How to Solve It, published by Princeton University Press) that was aimed at older students, but the essential advice boils down to principles simple enough for young children like your daughter to appreciate. Here is some of that distilled into simple terms to share with her.
http://math.berkeley.edu/~gmelvin/polya.pdf
You will notice the very first technique on the list is "Guess and check," which is a venerable problem solving strategy used by world class mathematicians. It is also one I see Bogleheads use all the time (e.g., let's try this SWR and see what happens when we model it. Hmm, not so good, let's try this...)
It is not the only weapon in our arsenal of problem solving tools, but it is a worthy one not to be sneezed at or dismissed.
Re: A Little Common Core Math problem
The principle being taught here is probably algebra, but it doesn't really matter.
The challenge is for the child to recognize that the X is 9. (8 +1). Then the method to arrive at the answer is simple division and multiplication, or can be arrived at by division and subtraction. As with all problems, the answer can be correctly arrived at via several paths. The loop left out is purposeful, to help the child noodle through to a logical path. Many children become adapt at doing this intuitively, which is not discouraged as higher math makes use of intuitive skills.
If you teach a child the path, you've removed the creative element of the homework. We don't really want kids memorizing formulae, we want them developing their neural pathways to develop solutions. The struggle should be allowed. Children don't have these neural pathways yet, and math problems is a good way to develop them. IMHO the first born child is often hobbled in math skills. This may be because they are getting too much help at home, and the later children get less attention and have the chance to struggle a little until they have created the neural pathways for these logical sequences.
Once they have the pathways, the educator gives them the vocabulary to describe the methods used. But that comes after developing the skill.
Nope, I'm not a teacher, but I am pretty well versed in brain development. Maybe you guys shouldn't be helping the kids with math homework.
The challenge is for the child to recognize that the X is 9. (8 +1). Then the method to arrive at the answer is simple division and multiplication, or can be arrived at by division and subtraction. As with all problems, the answer can be correctly arrived at via several paths. The loop left out is purposeful, to help the child noodle through to a logical path. Many children become adapt at doing this intuitively, which is not discouraged as higher math makes use of intuitive skills.
If you teach a child the path, you've removed the creative element of the homework. We don't really want kids memorizing formulae, we want them developing their neural pathways to develop solutions. The struggle should be allowed. Children don't have these neural pathways yet, and math problems is a good way to develop them. IMHO the first born child is often hobbled in math skills. This may be because they are getting too much help at home, and the later children get less attention and have the chance to struggle a little until they have created the neural pathways for these logical sequences.
Once they have the pathways, the educator gives them the vocabulary to describe the methods used. But that comes after developing the skill.
Nope, I'm not a teacher, but I am pretty well versed in brain development. Maybe you guys shouldn't be helping the kids with math homework.
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Re: A Little Common Core Math problem
I think resourcefulness counts, I think looking for multiple approaches counts, I think figuring out a way to check the answer counts.
An interesting question, to which I don't know the answer, is this.
Suppose you answered the problem by saying:
"The answer 56 popped into my head. So, I checked it by dividing it by 8 to get the weight of the cat, 7 pounds, then adding that to 56 to get the weight of both, and got 63, which is what the question says. Therefore, 56 is the correct answer."
How would that answer be assessed?
That seems pretty sound to me.the assessment tests insist that students provide an explanation for the answer; simply providing the solution is not good enough.
An interesting question, to which I don't know the answer, is this.
Suppose you answered the problem by saying:
"The answer 56 popped into my head. So, I checked it by dividing it by 8 to get the weight of the cat, 7 pounds, then adding that to 56 to get the weight of both, and got 63, which is what the question says. Therefore, 56 is the correct answer."
How would that answer be assessed?
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
Re: A Little Common Core Math problem
dodecahedron wrote:Your daughter is very resourceful. And her technique can easily be generalized to nonmultiple choice situations. If she hadn't been given multiple choices, she could have just guessed a plausible number for the weight of the cat (or the dog), tried it to see if worked, and then intelligently modified her next guess based on what she learned from her first attempt. Advanced problem solvers (including Bogleheadssee below) often do that kind of thing in real world situations (which are generally messier than anything you find on a test or homework, multiple choice or not.)
An ideal problem for learning has lots of valid approaches to it, and children can learn a lot if they are encouraged to play with the problem, to take ownership of the process, finding multiple approaches to solving it, and reflecting on what strategies work well and not so well for them in different types of problem solving situations.
As a wonderful mathematician and problem solver, George Polya, a professor at Stanford famously said, "It is better to solve one problem five ways than five problems one way."
Polya wrote a classic book on problem solving (How to Solve It, published by Princeton University Press) that was aimed at older students, but the essential advice boils down to principles simple enough for young children like your daughter to appreciate. Here is some of that distilled into simple terms to share with her.
http://math.berkeley.edu/~gmelvin/polya.pdf
You will notice the very first technique on the list is "Guess and check," which is a venerable problem solving strategy used by world class mathematicians. It is also one I see Bogleheads use all the time (e.g., let's try this SWR and see what happens when we model it. Hmm, not so good, let's try this...)
It is not the only weapon in our arsenal of problem solving tools, but it is a worthy one not to be sneezed at or dismissed.
Great post and I agree with everything. The guess and check method is extraordinarily useful and a great way for kids to solve problems where advanced methods are not available to them yet. Newton's Method for determining the square root is a great example of how it is a great way to teach your brain this way of thinking. And we use these types of concepts in advanced programming all the time. And the beauty is that it comes natural to kids.
 dodecahedron
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Re: A Little Common Core Math problem
investingdad wrote:As an engineer, my preference is to write out the equations and test the answers. So, yeah...
Besides, I need to show her the correct approach for when the problem isn't so simple.
It is rare that a problem (simple or not) has a single "the correct approach." Since you are an engineer, I'd suggest checking out the resources at mathcounts.org. MATHCOUNTS is a national problem solving competition program for middle schoolers. (One of the big three "bees" along with spelling and geography.) The National Society of Professional Engineers is one of the lead founding sponsors of the program. Although your daughter isn't in middle school yet, there are lots of fun and free problem solving materials on their website which she might enjoy playfully exploring. And you will see that MATHCOUNTS really encourages students to be resourceful in inventing their own approaches, which are sometimes better than anything a grownup could come up with.
Another great site is the Art of Problem Solving. http://www.artofproblemsolving.com/ it is primarily aimed at older students, but they do have some resources for younger problem solvers.
Also check this out:
http://www.amazon.com/HardElementaryS ... 1489507175
Last edited by dodecahedron on Thu Oct 30, 2014 2:29 pm, edited 2 times in total.
Re: A Little Common Core Math problem
investingdad wrote:My guess is that 90% of the adult population would struggle with this question
Do you really think 90% would struggle with this? It is certainly possible that I have a severly skewed expectation of what the average person should be able to figure out with math. I'm surprised to hear somebody thinking the bar should be so low for the general population.
I actually think more than 90% of the population would struggle with this, but I tempered my statement a little. The issue is that being presented with a problem like that and actually needing to get the answer doesn't happen to people more than about 0.00001% of their time and activities, if even that. Even I, a retired research scientist and product development engineer, would leap to the answer mostly due to getting involved in helping in local schools than from any repeated exercise in my real job. Well, ok, the other place is in putting numbers to some of the little arithmetic puzzles we run into right here on this forum.
As far as what the bar should be, the use of learning this kind of math is not that we formulate and solve simultaneous equations in everyday life but rather that this is a piece of the mathematical content that has to be known to advance to more advanced levels in math which in turn need to be understood so that we can comprehend various formulations that might be needed to do new math, and science and engineering. One statistic I found is that scientists and engineers account for about 5% of the total labor force. That might be perhaps 2% of the population or 3%4% of the adult population. Elementary and secondary teachers are about 1% of the population, but more than half of those would struggle with that problem. Where are there other occupations or pasttimes where such skills would be assumed to be present?