Stumped by Singapore 2A problem. Help please.

[Alice]

Ok, not really. I can do the problem but I can't figure out how to explain it to ds without algebra and other math concepts he doesn't know.

 

If A + B = 20 and A-B = 8 than A=___ and B= ___.

 

I kept trying to explain it to him but couldn't figure out how to other than to tell him just to plug in different numbers and see if they worked. In the middle of me doing it with algebra, he figured it out and said the right answers (A= 14 and B= 6) but he doesn't know how he did it.

 

We moved on but I'm still wondering if I'm missing something in how I could explain this to him.

[KrissiK]

Does the IG give you any help? I hope so. We're starting 2a after Christmas and I wouldn't be able to explain that one at all.

[Dinsfamily]

What page? I pulled out ds's 2A materials to see it in context.

[Penelope]

Is that an IP problem? I seem to remember a couple like that.

 

I think those are actually trial and error. I show him how to set up the picture like a number bond. Then we could write out the equations on the side and figure out which numbers would work. I can't see how one would solve that with a bar diagram.

[Alice]

This is in the Intensive Practice book so is extra. It's on page 90 of the IP book for 2A in the mid-year review. I know the problems in this book are harder so realize he probably isn't expected to know how to do it easily. It may be the only way to tell him without algebra is to plug in the numbers, but I was just wondering if I'm missing something.

 

Ds is pretty mathy so a lot of times he just sees the answers or does it in his own way without a lot of explaining on my part. I can do math and got pretty far in school in it. But I'm just a good student and not someone who really "gets" math. So sometimes I second guess myself about whether or not I'm doing the best job of teaching it.

[Old Dominion Heather]

I'd show it with bar diagrams (which never works well when you try to type it out, but I will try).

 

[....A......][...B...] =20

 

[....A......] (these are equal)

[...B...][8]

 

If we took the 8 off, then A would equal B

 

so that

[.....a.....][....b..] =20

[...b...][...b...][8]= 20

 

so

 

B=6 and A is 14.

[8filltheheart]

I don't use SM, but if I were going to explain this problem to a young child, I would go about it something like this:

 

If you know that If A + B = 20 and A-B = 8 than A=___ and B= ___, then you know that A is bigger than B. How much bigger? (8 b/c when you take B away from A you still have 8)

 

If there is a difference of 8 between the 2 numbers, what would happen if subtract 8 from 20? (that would get rid of the difference that exists between the 2 numbers b/c 8 was the difference between them)

 

How much does that leave you with? (12) if you now have 2 groups that are equal, how much are in each group? (6) So, if A is 8 more than that, how much is A? (6+8=14)

 

FWIW....I would do all of that with something hands on and concrete.

 

HTH

[FlockOfSillies]

One of the cool things about SM is how they teach bar models. Once they master them, kids can solve complex problems that would normally require algebra.

 

Here's how I did it:

 

Draw two bars, one longer than the other. (You know that one is larger because they told you A-B=8.) to the left, label the longer bar A and the shorter bar B. (My apologies for the poor ASCII pix.)

..______________

A|.....................|

..|_____________|

...________

B|............|

..|_______|

 

Now you're going to label them with the rest of the information they gave you. The sum of the two numbers is 20, so you put a bracket or a V-shape to the right with a 20 next to it, to show that the two numbers together make 20. Like this:

 

..______________

A|.....................|

..|_____________|..\

...________.............\

B|............|............./.20

..|_______|............/

 

 

 

Now for the second part, A-B=8. You will want to draw a vertical dotted line through Bar A that is even with the end of Bar B, and then label it with another tent and the number 8, to show that A is as big as B, PLUS 8.

 

..................8

................/... \

.............../..... \

..______________

A|............|.......|

..|_______|_____|..\

...________.............\

B|............|............./.20

..|_______|............/

 

 

Now, hopefully, at this point your student will realize that the left portion of A is the same size as B. So you have 2 B's. In other words, A=B+8. (You can even write "B" inside that left portion of A to help emphasize the point.) So, you can plug this new information into your number sentence.

 

A+B=20 is now B+8+B=20, or B+B+8=20.

 

From there, your student will hopefully have enough experience to know that he can subtract 8 from 20 to get 12 (I don't use the term "both sides of the equation" for this age student).

 

If not, you can show him what to do. You can put parentheses around the B+B to help the student think of it as one number, point to it and say, "Something plus 8 equals 20. How do we find the missing number?"

 

If he doesn't see that he needs to subtract, then go over the parts-whole rule with him -- when we want to find the whole (or the all-together number), we add. When we want to find a part, we subtract. In this case, you have the whole and one part, and the other part is missing. So you subtract.

 

So then you have B+B=12. Then you can ask, "What number added to itself makes 12?" and your student will say, "6." He's just found the value of B, so he can go back and find the value of A, since it's based on the value of B.

 

I have a book on my shelf that I haven't used yet, called Step-by-Step Model Drawing: Solving Word Problems the Singapore Way, by Char Forsten. You may want to look into it if you want focused teacher training on using bar models to teach SM.

 

HTH.

Edited December 3, 2010 by FlockOfSillies
ASCII. 'nuf said.

[JuliaM]

Hi

This is my first post and I am from England so forgive me if I do not use familiar terminology. I saw your query as felt I should reply as I encountered a similar problem. I was stuck with what approach to use until I looked in the Singapore i-excel Heuristic and Model approach Primary 1 book, where a worked example was given. It involved systematic listing:

19+1=20

18+2=20

17+3=20 and so on

Then look at the list for the two numbers that subtract each other to give the number required. The example given was for numbers within 10 but I assume the same idea applies. It's quite simple if a little drawn out.

Hope this helps

Kind regards

Julia

[Alice]

Thanks everyone. I like the bar models. We haven't really gotten to that in the regular texts, so that might be part of the issue. I know SM uses them a lot but hadn't really gotten used to using them with him for problems. Thanks Brenda for the book rec.

 

Thanks also 8FilltheHeart, that's a good explanation. And a good suggestion to do it with something concrete.

[wapiti]

This problem also shows up in EPGY quite a bit, around the second grade level and just gets harder from there. I didn't know how to explain it without resorting to all sorts of higher math LOL, but my DH showed them to add the equations (which is still not so easy to understand at that age!)

 

A + B = 20

A - B = 8

___________

2A + 0 = 28

 

therefore A = 14 (though of course that involves division, which some kids might not know how to do at that age, let alone seeing that the process you need to do is 28/2)

 

I'd still LOVE to hear an easier way of explaining this. I must be missing something. :bigear: :bigear: :bigear:

[Pata]

Hi

This is my first post and I am from England so forgive me if I do not use familiar terminology. I saw your query as felt I should reply as I encountered a similar problem. I was stuck with what approach to use until I looked in the Singapore i-excel Heuristic and Model approach Primary 1 book, where a worked example was given. It involved systematic listing:

19+1=20

18+2=20

17+3=20 and so on

Then look at the list for the two numbers that subtract each other to give the number required. The example given was for numbers within 10 but I assume the same idea applies. It's quite simple if a little drawn out.

Hope this helps

Kind regards

Julia

 

:iagree: A friend of mine who used to teach math in the Singapore school system gave me a book that taught their teacher's strategies to solve problems and the above post was one of them. The IP may have been expecting your ds to think it through, just like he did. It seems strange, but Singapore tries to teach the student to think in the language of math, so the let's see if this number works approach is totally valid :).

[JuliaM]

It is also the only approach that made sense to my son.

Julia

[lisamarie]

I just taught my son to do algebra. If A+B=20 and A-B=6, then 20-6=your answer. There are similar problems in SM2b which we have encountered. DS figures it out just fine using algebra. They pretty much are teaching simple algebra in the teacher's manual. The bar models are using algebra when they give the whole and 1 of the parts and ask you to find the other part.