Third grade math homework

[Anonymous]

Anonymous wrote:OP, does the problem sheet say "Continental Math League" on it?

I don't see that on the sheet.

[Anonymous]

Anonymous wrote:This is the engineer who solved the problem using algebra. My husband solved it differently; he feels the problem is more "logic" than math.

Add the totals up:
D + K = 81
D + M = 96
K + M = 93
----------------
= 270

Since each kid is double counted above, divide by 2 to find the total number of cards. Once you have the total, subtract out the known amounts above to find the missing amount:
D + K + M = 135

We already know that D + K = 81
So subtract 135 - 81 = 54
Mike = 54

You can do the rest....

We have wicked smart kids

Op here. I e-mailed the teacher who said she primarily wanted to see the thought process. When DD got home, I asked her what if she added up all the sums to try to find the total number of cards. She said, "but each boy is double counted, so I would have to divide by 2," and then it all seemed to click. She followed the process you describe here, and got the answers.

[Anonymous]

Anonymous wrote:What school?

A small school in Silver Spring. For some reason, I don't like naming our school on DCUM.

[Anonymous]

OP, my now fourth-grader had these kinds of problems all of last year and it drove me nuts. She had no idea of how to begin to solve them and half the time I didn't either. I can't tell you how many nights I was on the phone or emailing with other parents in the class, all of us trying to figure it out. The teachers kept saying that they are learning strategies to figure out these problems, but my kid had no idea. Now she's in fourth grade and can barely do addition, subtraction or multiplication. I am really frustrated by it.

[Anonymous]

Anonymous wrote:At the 3rd grade, students are not yet exposed to algebra. However, many answers provided here are algebra based. What is going on?

The problems can be solved using formal algebra -- and if you know formal algebra, that's probably how you'd do it. But they don't have to be solved using formal algebra, as other PPs have demonstrated.

[Anonymous]

Anonymous wrote:

Anonymous wrote:At the 3rd grade, students are not yet exposed to algebra. However, many answers provided here are algebra based. What is going on?

The problems can be solved using formal algebra -- and if you know formal algebra, that's probably how you'd do it. But they don't have to be solved using formal algebra, as other PPs have demonstrated.

That's true, but it seems to be the case that they're not teaching any method to solve it. I think 3rd graders that could solve this without having some method explained would be few and far between.

[Anonymous]

Here's my effort to solve without using algebra processes.

D + M = 96
K + M = 93
So logic says D must be 3 more than K.

D + K = 81
If D is 3 more thank K, then split 81 in half, with a little extra to D. K is 39, and D is 42. Easy to figure out M after that.

It's hard to "forget" the algebra processes we all learned. It seems the biggest benefit from a teaching perspective would be to use this to show kids how to set up the equations and compare them.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:At the 3rd grade, students are not yet exposed to algebra. However, many answers provided here are algebra based. What is going on?

The problems can be solved using formal algebra -- and if you know formal algebra, that's probably how you'd do it. But they don't have to be solved using formal algebra, as other PPs have demonstrated.

That's true, but it seems to be the case that they're not teaching any method to solve it. I think 3rd graders that could solve this without having some method explained would be few and far between.

I agree. It would have been a good Problem of the Week for my kid in fourth grade at the HGC last year, though.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:At the 3rd grade, students are not yet exposed to algebra. However, many answers provided here are algebra based. What is going on?

The problems can be solved using formal algebra -- and if you know formal algebra, that's probably how you'd do it. But they don't have to be solved using formal algebra, as other PPs have demonstrated.

That's true, but it seems to be the case that they're not teaching any method to solve it. I think 3rd graders that could solve this without having some method explained would be few and far between.

I agree. It would have been a good Problem of the Week for my kid in fourth grade at the HGC last year, though.

Yes, my daughter had a set of Math Olympiad questions very similar to this in her 4th grade HGC class each week, but the teacher would go over the answer and talk about strategies etc. She also made it clear that she didn't expect kids to get every problem right and that they were learning a process of thinking and analyzing. Just throwing it out there for 3rd graders doesn't seem like it would accomplish much unless it's tied into a larger lesson.

[Anonymous]

Anonymous wrote:(Not the PP.)

Draw a bar. Give it a value of 96. Divide it somewhere. Label one part M and one part D. Stick another bar onto the end of it. Give it a value of 93. Divide it somewhere. Label one part M and one part K. Now you have a long bar, divided in four parts, labeled M, D, M, K, with a value of 96+93=189.

Now you know what D+K is, namely 81. So shuffle the pieces around in the bar so that you have four parts, labeled M, M, D, K. The two parts labeled D and K, combined, have a value of 81. So the two remaining parts, labeled M and M, have a value of 189-81=108.

If M+M=108, then M=54.

And then you can figure out the other ones.

(I'm the PP who's a fan of bar models, not the PP who came up with the bar-model solution.)

This is a great explanation and something I could use. Thank you.

[Anonymous]

Like this^^^