# More like this word problem

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Hi All,

I am trying to get my kids to solve some math kangaroo questions. Here is one that was challenging for her:

Fido the Dog, Philemon the Cat and 4 monkeys together weigh 24 lbs. Fido and one monkey
together weigh 11 lbs. Philemon and 2 monkeys together weigh 1 lb less than Fido and one monkey
weigh together. Each of the monkeys weighs the same. How much does Philemon weigh?

She eventually solved it, but she wants to practice more these kind of questions. How do I look these up? What are these kind of questions called?

Thank you!

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I don't know specifically, but bar models are really helpful for this kind of problem.  Really, really helpful.

My kids had them in Math in Focus, but I know other programs have them or people can supplement with them.

But it is shocking how good bar models are!

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Well, I think Philemon is 4, but I had to guess numbers at the end.

I got it down to:  3 monkeys plus Philemon equals 13, and Fido plus one monkey equals 11, very easily with bar models.

After that I don't know what to do, without guessing.

Edited by Lecka

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She solved with writing the equations and variables, but there should be an easier way for a 2nd grader!

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7 minutes ago, dmmetler said:

wow... and this question showed up in math Kangaroo for Grade 1/2

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I think a 2nd grader could get as far as I did with bar models, lol.

They are surprisingly good.

And then when you have "M +M +M +P =13," it is easy to see M has to be less than 4, and then there are only a few numbers to try substituting.

I still think it is HARD for 2nd grade, but bar models are really possible for 2nd grade and kids can go a long way with them.

Edited by Lecka
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I don't know how to upload, but with bar model, it is very easy to make a bar model where:

The total is 24, F and M are 11, and then you draw a bracket under the rest of the bar, and it is easy to see you would subtract then.

It is shockingly easy, when with algebra, it would be harder.

I didn't learn this way, and I think it is amazing.

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Oh, I just remembered, we moved and where we live now they are called "tape diagrams" instead of "bar models."  As far as I can tell, they are the exact same thing.

We live in New York now and they are teaching tape diagrams in public school here.

So I do think it's realistic 2nd graders in a lot of places are learning to set up word problems this way, especially for addition and subtraction.

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Those sorts of problems are in HOE.

My 3rd grader could solve it now (not in 1st or 2nd).

Fido the Dog, Philemon the Cat and 4 monkeys together weigh 24 lbs. Fido and one monkey
together weigh 11 lbs. Philemon and 2 monkeys together weigh 1 lb less than Fido and one monkey
weigh together. Each of the monkeys weighs the same. How much does Philemon weigh﻿?﻿

She would write F+P+M+m+m+m=24

f+m=11

p+m+m=10

Then she would cross out the f and m and put in 11, cross out p and 2 m's and put in 10 and solve 21+m= 24, so the monkeys weigh 3 lbs.  So F weighs 8 and P weighs 4.

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I do have no idea how to do the last part without guessing numbers to substitute, using bar models, but I think maybe that is how they would expect a 2nd grader to do it?  I don't really know.

Helping my kids with homework, I have seen problems where, when I help them, at the end they guess numbers to substitute, so it's as good as I can do.

Edit:  also I think that they (the teachers, the math program) think it helps the kids' number sense to guess numbers to substitute sometimes.  I'm not sure why I think this, but it is my impression.  But I am a help-with-homework-at-home person on this.

Edited by Lecka

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2 minutes ago, 8FillTheHeart said:

Those sorts of problems are in HOE.

My 3rd grader could solve it now (not in 1st or 2nd).

Fido the Dog, Philemon the Cat and 4 monkeys together weigh 24 lbs. Fido and one monkey
together weigh 11 lbs. Philemon and 2 monkeys together weigh 1 lb less than Fido and one monkey
weigh together. Each of the monkeys weighs the same. How much does Philemon weigh﻿?﻿

She would write F+P+M+m+m+m=24

f+m=11

p+m+m=10

Then she would cross out the f and m and put in 11, cross out p and 2 m's and put in 10 and solve 21+m= 24, so the monkeys weigh 3 lbs.  So F weighs 8 and P weighs 4.

This is exactly how she solved it. She is just looking for more like this to practice. I could not find any questions like that. So I was wondering I could find more questions like this.

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My kids definitely could not have solved it that way.  I bet my son could have solved it with bar models, though.  Just to say -- how do they probably expect 2nd graders to be able to do it.

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Another question from the same paper:

Katie bought three identical pencils, two identical pens and two identical erasers, and paid
\$11.60. Hannah bought one pencil, two pens and two erasers, and she paid \$8.40. How much does
one pencil cost?
A) \$1.20 B) \$1.50 C) \$1.60 D) \$3.20

This one was also similar but it involved decimal division which my kid did not know how to, so had to skip

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I don't teach bar diagrams but I think they would simply write f m p m m m=24 and then write11 in a bar under f m and 10 in a bar under p m m and  see that m equals 3.

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There are problems like these in MEP primary.

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38 minutes ago, School Mom said:

Another question from the same paper:

Katie bought three identical pencils, two identical pens and two identical erasers, and paid
\$11.60. Hannah bought one pencil, two pens and two erasers, and she paid \$8.40. How much does
one pencil cost?
A) \$1.20 B) \$1.50 C) \$1.60 D) \$3.20

This﻿ one was also similar but it involved decimal division which my kid did not know how to, so had to skip

If you write out like the other example with each item right underneath the others, it is pretty easy to see the answer.

PPPppee=11.60

--Pppee=8.40

each pencil is 1/2 of 3.20

Whether or not that is something your avg 1st or 2nd grader can do is an entirely different question. My 3rd grader would find that problem simple but she has already completed math through 4th grade level and decimals, division, etc are not at all new ideas for her.

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1 hour ago, 8FillTheHeart said:

I don't teach bar diagrams but I think they would simply write f m p m m m=24 and then write11 in a bar under f m and 10 in a bar under p m m and  see that m equals 3.

This!!!!!!!!!!!  I was not seeing it.  This is how you would do it with a bar model.

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I think there are word problems like this.... with bar models.... they are about setting up the bar model, but they only use addition and subtraction.

It's hard to say, but they are big on setting up word problems with bar models or tape diagrams in a lot of schools now, and kids do them a lot.

From what I did, it would just be grouping a monkey with fido, which I just was not seeing.

But I think this is something where, now that I have seen an example, I would be able to do problems with this set up.  My older son is the same way, once he sees how to do it with a bar model, he can do it.

For my daughter she would need to have had practice with this kind of problem, she wouldn't be able to just see it once.

I think it is amazing, though, how a problem like this can be solved with a bar model.

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Definitely Singapore Math Intensive Practice.

I remember my daughter doing ones with much larger numbers in 2B IP-- something like if a papaya + orange + apple+ banana = 354 and then would give you like two other clues where you had to plug in and create similar substitutions to how you solve your example problem (sorry the book is in storage and I don't feel like making up my own 😊) but I remember her doing it the same way.

They also did similar problems with weights-- if 3 triangles weighs as much as 2 circles.... etc with substitutions

Anyway, since 2B had those types of problems, I imagine the level 1 intensive practices and the 2A intensive practices would also have them but with similar numbers to your example. We didn't discover IP books until 2B, though, so sorry, can't be more precise than that.

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On 2/14/2019 at 10:49 AM, School Mom said:

She solved with writing the equations and variables, but there should be an easier way for a 2nd grader!

ime they use a balance beam model or singapore bar model.

You can find a lot of these problems at the Thinking Blocks website or just pick up SM.  Well worth the time and effort.

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On 2/14/2019 at 10:30 AM, School Mom said:

Hi All,

I am trying to get my kids to solve some math kangaroo questions. Here is one that was challenging for her:

Fido the Dog, Philemon the Cat and 4 monkeys together weigh 24 lbs. Fido and one monkey
together weigh 11 lbs. Philemon and 2 monkeys together weigh 1 lb less than Fido and one monkey
weigh together. Each of the monkeys weighs the same. How much does Philemon weigh?

She eventually solved it, but she wants to practice more these kind of questions. How do I look these up? What are these kind of questions called?

Thank you!

using double pan balance model as they are looking at relationships; students often draw blocks on top of  pan balance to help visualize; the equals sign here seperates what is on each pan; keep in mind students in first grade have had hands on experience

F,  P , M, M, M, M = 24 given in question

F, M = 11 given in question

P, M, M, 1 = F, M = 11 given in question , then realize P, M, M = 10

substitute P, M, M = 10  back into first relationship to see  F,10, M,M =24    replace F, M with 11 to get 11, 10, M = 24 and realize   M is 3

if M is 3, and we know F, M is 11, then F is 8

if P, M, M is 10 and M is 3, we realize P is 4

check the work

F,P,M,M,M, M = 8,4,3,3,3,3,=? 24 yes

F, M = 8,3 =? 11 yes

P,M,M,1=F, M =11 ==> 4,3,3,1=8,3=?11 yes

Edited by HeighHo
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Thank you so much, everyone! the Singapore bar model definitely helps! I did not know about this, just checked.

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I will add the suggestion that if you would like explicit instruction on bar modeling and Singapore style word problems, you may want to consider Fan Math Process Skills in Problem Solving.

We were fine with CWP as I was comfortable with teaching bar modeling to my son without instruction. Other moms have found the Fan Math books more helpful as it explicitly demonstrates and teaches this.

Edited by calbear
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