Third grade math homework

[Anonymous]

DD brought home this problem. They have not been taught how to solve it in class, and I can't remember how.
Dustin and Michael together have 96 baseball cards.
Michael and Kevin to together have 93 cards.
Dustin and Kevin together have 81.
How many cards does each boy have?
There is a bonus question too, but I can't recall what it is.
Any ideas how to figure this out?

[Anonymous]

Anonymous wrote:DD brought home this problem. They have not been taught how to solve it in class, and I can't remember how.
Dustin and Michael together have 96 baseball cards.
Michael and Kevin to together have 93 cards.
Dustin and Kevin together have 81.
How many cards does each boy have?
There is a bonus question too, but I can't recall what it is.
Any ideas how to figure this out?

D + M = 96
M + K = 93
D + K = 81

You can multiply the last line by -1 on both sides, so:

D + M = 96
M + K = 93
-D - K = -81

Add all of them together and you get:

-D + D = 0
M + M = 2M
K + -K = 0
96 + 93 - 81 = 108

So, 2M = 108, M = 54.

Substitute back and you get D = 42 and K = 39.

This is how I would do it. I have NO idea of the process that they would teach to a 3rd grader. These are problems similar to the ones my daughter got in an HGC last year in 4th.

[Anonymous]

Anonymous wrote:

Anonymous wrote:DD brought home this problem. They have not been taught how to solve it in class, and I can't remember how.
Dustin and Michael together have 96 baseball cards.
Michael and Kevin to together have 93 cards.
Dustin and Kevin together have 81.
How many cards does each boy have?
There is a bonus question too, but I can't recall what it is.
Any ideas how to figure this out?

D + M = 96
M + K = 93
D + K = 81

You can multiply the last line by -1 on both sides, so:

D + M = 96
M + K = 93
-D - K = -81

Add all of them together and you get:

-D + D = 0
M + M = 2M
K + -K = 0
96 + 93 - 81 = 108

So, 2M = 108, M = 54.

Substitute back and you get D = 42 and K = 39.

This is how I would do it. I have NO idea of the process that they would teach to a 3rd grader. These are problems similar to the ones my daughter got in an HGC last year in 4th.

Wow! Not the OP, but I would never have figured that out.

[Anonymous]

At that age, I expect they want the kids to do something by trial and error.

[Anonymous]

Anonymous wrote:

Anonymous wrote:DD brought home this problem. They have not been taught how to solve it in class, and I can't remember how.
Dustin and Michael together have 96 baseball cards.
Michael and Kevin to together have 93 cards.
Dustin and Kevin together have 81.
How many cards does each boy have?
There is a bonus question too, but I can't recall what it is.
Any ideas how to figure this out?

D + M = 96
M + K = 93
D + K = 81

You can multiply the last line by -1 on both sides, so:

D + M = 96
M + K = 93
-D - K = -81

Add all of them together and you get:

-D + D = 0
M + M = 2M
K + -K = 0
96 + 93 - 81 = 108

So, 2M = 108, M = 54.

Substitute back and you get D = 42 and K = 39.

This is how I would do it. I have NO idea of the process that they would teach to a 3rd grader. These are problems similar to the ones my daughter got in an HGC last year in 4th.

OP here. Thanks. we got a bunch of equations like D+ M=96, so M=96-D, (96-D) +K =93, etc. but i couldn't solve anything. They have not been taught negative numbers yet, although DD kind of understands the concept.
I am not sue they were meant to really figure this out or if they are supposed to be demonstrating how they would try to figure it out. DD is sure she is supposed to get an answer because there is also the bonus question that I forgotten.

[Anonymous]

I don't think they want trial and error There is an easier way to solve this problem -

Solve two equations simultaneously:
M+K = 93
D+K = 81

You want to get rid of the Ks so you multiply the last equation by - 1
then have:

M+K = 93
-D-K = -81
then add together the two equations (the Ks are eliminated)

M-D = 93-81
M-D = 12
D = M-12

Plug this in to the first equation (D+M = 96):

M-12 + M = 96
2M = 108
M = 54

Then plug this figure in to get the other numbers. I'm an engineer and this is how it should be explained.

[Anonymous]

Thank you 10:19!

[Anonymous]

Anonymous wrote:I don't think they want trial and error There is an easier way to solve this problem -

Solve two equations simultaneously:
M+K = 93
D+K = 81

You want to get rid of the Ks so you multiply the last equation by - 1
then have:

M+K = 93
-D-K = -81
then add together the two equations (the Ks are eliminated)

M-D = 93-81
M-D = 12
D = M-12

Plug this in to the first equation (D+M = 96):

M-12 + M = 96
2M = 108
M = 54

Then plug this figure in to get the other numbers. I'm an engineer and this is how it should be explained.

This is why DCUM rocks! Thank you (from a non- engineer).

[Anonymous]

Anonymous wrote:

Then plug this figure in to get the other numbers. I'm an engineer and this is how it should be explained.

This is how it should be explained, using formal algebra. But third-graders haven't had formal algebra yet. They don't know about (for example) multiplying both sides of an equation by -1. And I don't know if most third-graders are ready for the kind of abstract thinking this requires.

There should also be a concrete, representational way to solve the problem. Unfortunately I haven't thought of one yet!

[Anonymous]

Anonymous wrote:At that age, I expect they want the kids to do something by trial and error.

I gave this quote and I am a math teacher.

[Anonymous]

OP,

This is a big issue many parents have with MCPS right now. They pretend to give "enrichment" by giving 3rd graders these challenging problems. I cut and pasted one of DS's math problems in Google and came up with a complete PDF of the question, possible answers and methodology commentary, where the author explained that this problem was given to 5th and 6th graders.

My concern is that the rest of the math curriculum is very simple (ie, not as advanced as I would want). The math problems are too complex compared to the rest. There is nothing in the middle to "train" the kids to stretch to these complex multistep problems. Everyone wants their children to learn how to formulate and strategize in math. But here the burden is placed on the parent to support their child, not the school, which is ALL WRONG.

So why does MCPS give out these problems?
Either MCPS genuinely believes the effort to think things through is worth it even if students don't fully grasp the strategy involved. This I strongly disagree with: my kid could learn this so much better with a different approach, ie step-by-step instruction in class to solve simple to complex word problems;
Or MCPS is just fobbing off parents with talk of "enrichment" (one problem a week!) so that no one can accuse them of lack of differentiation/acceleration. I believe the latter.

Either way, it's quite disheartening. Parents have had their children cry because they cannot understand these problems, which undermines the whole premise of encouraging the students to stretch their minds. We have alerted the principal and 3rd and 4th grade teachers, but she probably cannot do anything about it, since it is mandated by the curriculum 2.0.

[Anonymous]

Anonymous wrote:
Either way, it's quite disheartening. Parents have had their children cry because they cannot understand these problems, which undermines the whole premise of encouraging the students to stretch their minds. We have alerted the principal and 3rd and 4th grade teachers, but she probably cannot do anything about it, since it is mandated by the curriculum 2.0.

Curriculum 2.0 mandates giving students problems they can't understand?

It's odd that this hasn't happened in my kid's classes, then.

[Anonymous]

Anonymous wrote:OP,

This is a big issue many parents have with MCPS right now. They pretend to give "enrichment" by giving 3rd graders these challenging problems. I cut and pasted one of DS's math problems in Google and came up with a complete PDF of the question, possible answers and methodology commentary, where the author explained that this problem was given to 5th and 6th graders.

My concern is that the rest of the math curriculum is very simple (ie, not as advanced as I would want). The math problems are too complex compared to the rest. There is nothing in the middle to "train" the kids to stretch to these complex multistep problems. Everyone wants their children to learn how to formulate and strategize in math. But here the burden is placed on the parent to support their child, not the school, which is ALL WRONG.

So why does MCPS give out these problems?
Either MCPS genuinely believes the effort to think things through is worth it even if students don't fully grasp the strategy involved. This I strongly disagree with: my kid could learn this so much better with a different approach, ie step-by-step instruction in class to solve simple to complex word problems;
Or MCPS is just fobbing off parents with talk of "enrichment" (one problem a week!) so that no one can accuse them of lack of differentiation/acceleration. I believe the latter.

Either way, it's quite disheartening. Parents have had their children cry because they cannot understand these problems, which undermines the whole premise of encouraging the students to stretch their minds. We have alerted the principal and 3rd and 4th grade teachers, but she probably cannot do anything about it, since it is mandated by the curriculum 2.0.

OP here. These were my thoughts exactly. I feel like DD is being almost mocked for qualifying for enrichment. You want enrichment? Here figure out this problem that is years ahead of anything you have been taught. If they want her to do this work, they should actually take the time to teach it to her in class.

[Anonymous]

They should start by teaching kids to set up equations and then teaching kids to solve equations with two variables only.

Mark and Kevin have a total of 25 marbles.
(M + K = 25)

Mark has 5 more marbles than Kevin
(M = K + 5)

and then teach them to figure it out by substituting Kevin for Mark.

( (K+5) + K = 25 ) and solve for K

All I can say is that unless they have this concept down well - the kids will flounder. I see that many kids do not even have a basic understanding of how to "isolate the variable" (solve for K in this example).

[Anonymous]

I'm the math teacher PP (actually, ex-math teacher). I haven't taught in this country, though (but in other English-speaking countries). I want to add that I would never have given that problem to 3rd graders - apart from the level of it, it has absolutely no context and is a million miles from a real life problem that someone might come across - and not even interesting to boot.

It's such a shame that US math has lost its way in recent years. When I was training as a math educator, the US had some of the best resources. Now I'd look elsewhere for inspiration.