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I will be starting to teach my 9-year old daughter how to solve word problems using Singapore bar modeling. I purchased Challenging Word Problems 2 & 3. We have never used Singapore before, only Saxon and Kumon. She has difficulties with reading comprehension and word problems are hard for her.
To prepare myself I’m practicing doing problems in the book. I’m also going to practice with the problems on Thinking Blocks, a wonderful interactive website that enables users to practice with bar diagrams.
I’ve searched for help, and found this scripted prompt that appears useful:
STEP ONE: What do you know already? - Can you draw a bar (or two) to show what you already know?
STEP TWO: What do you need to find out? - How are you going to find that out? - Does the bar(s) you have set up/drawn give you any clues as to what kind of question (operation) this is and what you need to do with the numbers?
STEP THREE: Now DO it and find the answer(s)!
I have virtually no teaching skills, and I’m feeling challenged by the prospect of trying to explain how to solve word problems. Typically I have found myself tongue tied when helping with homework word problems.
Any advice for me? Any resources you would suggest?
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At the early levels (2 and 3) the problems usually contain parts and the whole. For example, there are 22 cookies. I gave away 7. How many cookies are left. In this problem we know the whole and 1 of the parts. I would have my child draw the top bar and label it 22. Then she would tell me there are 2 parts, the cookies I have and the cookies I gave away. She would then draw the second bar, divide it in two and label one side 7. Singapore teaches in level 2 when one is missing a part subtract. During level 2 our mantra was, "if all the parts are present add, if one is missing subtract!" Another example. I have 6 bags of cookies. Each bag contains 4 cookies. How many cookies altogether. In this example the whole is missing, but the parts are present. In this example I would have my child draw the bottom bar and divide it into 6 parts. She would write 4 in each part. Then, ahe would realize she is missing the top bar which represents the whole. She would then solve. At first we talk about how this problem lends itself to adding or multiplying. If a problem is too difficult I solve it for them so they can watch how it is done and drawn. I then rewrite a similar problem and have then try on their own. I keep rewriting problems, one per day, until they have that "style" mastered.
You may want to get the textbooks, if the challenging word problems are too difficult for you to teach. I found the textbook very user friendly and we would complete 1 lesson per day. The kids would complete the problems from the text on white boards with me supervising, and then they would complete the corresponding workbook page on their own. The next day we would check the workbook page and go over any difficulties and then proceed to the next lesson, etc. It has worked great for us and I cannot believe how strong my children are in math. They are just beginning 6A. Good Luck.
Bar models can get quite complicated and I could probably write a book about the variations that can occur. The best thing you can do is to go one grade level BACK and start with those word problems. Whenever I would get stuck I would ask Jenny in the Singaporemath.com forums and she was very helpful.
The mistake that I made with Singapore word problems was paying more attention to the bar model, which is a useful gimmick to be sure, but not emphasizing writing coherent mathematical statements and declaring the variable, etc. I had to go back and reteach that. My son was getting the correct answer to all sorts of hairy word problems but wasn't doing a good job of showing his work.
Here is a sample of how I ended up making him do his work (about fifth grade):
http://bp0.blogger.com/_6Bdjlk_XwVc/RblM10iqJeI/AAAAAAAAACQ/ZQUV8Ho-JJY/s1600-h/word+problems.JPG
It was easy to get to THAT point after he mastered the bar diagrams though. My advice is to emphasize "showing your work" more so than the bar models themselves. Bar models come and go but mathematical justification is here to stay.
Also, it will be easier and quicker for you to figure out the physical layout of the bars in the beginning than the kid. With my second kid in Singapore I have found that if I draw the blank bar models and have him label them and stick the numbers on them that things are going much smoother than having the kid learn it all at once. Choose only those word problems which can be represented by the same layout in the beginning so that the kid can see the pattern and save the others for last.
I agree about the textbooks (not the workbooks, although those are good for extra practice.) I'd get the corresponding textbooks for support.
The textbooks often have a page of very similar, simple word problems covering one topic. Getting a lot of practice with them on one type of word problem helps to "see" is much quicker down the road.
For instance, I've heard many teachers of the early grades speak of how kids get hung up with subraction. One teacher I know really likes to use the bar models to show that the language may change with subraction word problems, but the bar models tend to look the same.
You can use the charts as well, after you've done with bar models. See http://kitchentablemath.blogspot.com/2007/06/on-charts-and-word-problems-in-math-and.html
I am not a big fan of bar models. In some cases, they can work wonderfully and my son (end of fifth grade) can see how a complicated problem is easily solved. In other cases (I wrote about this before), they can get in the way. There are many ways to draw the bars and the key relationship may be difficult to find. And some problems (with not nice numbers) just don't work with bars. You can take a problem that works wonderfully with a bar model, change the numbers, and then it can't be done. This doesn't happen with algebra.
I am a very big proponent of making the transition to algebra as soon as possible. It's no more difficult than many bar models. In one post I made, I showed how much easier it is, and it works for all problems.
You can even start with very simple word problems, like:
If Greg has 4 bags of apples and there are 15 apples per bag, how many apples does Greg have?
A = the total number of apples.
A = 4 bags X 15 apples/bag
You can even start talking about units and how the "bag" units cancel out (bag/bag = 1) and you are left with apples for the units of the answer.
I have always disliked the idea that algebra (simple equations) is complicated. Most curricula wait to talk about algebra until the word problems get complicated. This is not the best time to introduce algebra.
OK, I'll get off my soap box.
I'm teaching bar modeling to my son. The problem is that he won't get algebra for a year or so, and bar models beat the crap out of guess and check. I am trying to teach him algebra now too but he thinks I'm trying to get him too far ahead of his class.
For practical advice, Myrtle's suggestion to draw the boxes and let the child fill in the values is a good one. I've done that with my son. The other is to do many of the bar models before sitting down with the child. Most of the bar models fall into just a few layouts. You can show these patterns to the child. For example, one favorite bar model talks about the percentage of a whole and then a percentage of the remainder. the key word is remainder.
Another useful skill is to relate a fraction to a whole. For example, if you have part of a bar that contains 45 objects and the problem states that this is 5/9ths of the whole, then the child has to realize that to find the total number of the whole, you would divide 45 by 5/9. I see this sort of thing in Singapore 5 all over the place. It's a good reason to know how to quickly divide fractions.
Someone previously suggested starting off with very simple word problems - eg "Pencils cost $1 each. Shona buys two pencils. How much did Shona spend?"
Maybe try several problems like that so she gets used to the idea that she can do word problems and gets used to extracting the key information before you move on to less obvious word problems.
Thank you, everyone!
I will continue to practice them myself so that I feel comfortable doing bar modeling.
I definitely think that starting out by drawing the bars myself will be a good idea. It will probably help to ease my daughter into the technique.
I did not purchase the textbook because the Challenging Word Problems book has three worked examples with step-by-step guidance for each type of problem, followed by 12 practice problems and then a few more challenging problems. If the textbook has more explanations about how to do the word problems that definitely would be helpful. Or maybe the teacher guide? I need to rethink this.
I noticed that the main difference between books 2 and 3 is that book 3 uses bigger numbers in its problems. For example, instead of 150 + 60 apples, it might have 473 + 897 apples. But, the same types of bar modeling techniques are used in both books.
I am not a big fan of bar models.
Steve, you’re scaring me!
I'm teaching bar modeling to my son.
Okay, now I feel better. Whew!
Bar models can get quite complicated and I could probably write a book about the variations that can occur.
They get insanely complicated.
I can't do them at that point (though I continue to think it would be a good thing if I could...)
Here's my advice, which you may already know: never, ever utter the words, "Do you understand?"
A kid will always say he understands.
Kids have to show you they understand by doing the problem or procedure.
Since I don't have a lot of math teaching experience - but maybe even if I did have a lot - I ask constant questions.
It focuses attention, because your child has to answer questions constantly, and it gives you continual information about whether your child is actually following the lesson.
Charts are great!
Basically bar models and charts both solve the working memory problem.
My friend's child supposedly has working memory problems. (I find that hard to believe, since everyone's working memory is tiny... but maybe it's so.)
Both approaches let you get all the information written down in a way that lets you see it all at once.
FYI: WORKING MEMORY ISN'T THE MAGICAL NUMBER 7
It turns out that working memory for most of us can only hold about 3 items at once.
Charts & bar models are a way of chunking information without having to memorize it.
I think the bar models do more than that, btw, but they are certainly a means of getting around the limitations of working memory.
Saxon kicks in with bar models at a later time(coinciding with fractions), only they make the bars verticle. There are several exercises where the student must draw and label the bar.
When teaching 3rd grade math (we have used the Singapore curriculum for 5 years), labels and number sentences are just as important as the bar modeling. Below is a redux of a posting I left on the Singaporemath Yahoo group (in case it looks familiar):
I tell my students that no one ever says to you "15" or "Hey Cassy, what is 6 x 7?" Numbers always relate to something else.
60 cookies in a box, yourself and 3 friends, how many do you get?
The ipod costs 366 dollars
10 guppies in a tank
6 goldfish
$7
83 kilograms
2 hours
We refer to these as "labels". Every word problem needs to be labeled correctly and that includes the number sentence.
Here's a 2-step word problem from the 3a textbook p. 48:
"Brian has 6 goldfish. He has 5 times as many guppies as goldfish. If he puts his guppies equally into 3 tanks, how many guppies are there in each tank?"
We know the problem is a "2-stepper" and divide our answer area in half.
Step 1 - How many guppies?
In third grade, we start with the bars:
gold [-6-]
gups [-6-][-6-][-6-][-6-][-6-]
Equation: 6 x 5=30
The number sentence would be:
He had 30 guppies altogether.
Step 2 - How many guppies in each tank?
I'm not sure how to do the bars with a keyboard, but you would make one bar with the "30" written above in a giant bracket and divide the bar into three. There would be a smaller bracket below a single unit with a question mark. That's the unknown.
Equation: 30/3=10
The number sentence:
There were 10 guppies in each tank.
The problems are easy, the students can do them in their heads. I simply tell them for now we're working on our bars and our labels. Mastering the labels and the bars makes measurement and conversions easier, and sets the foundation for more challenging problems. Here is a word problem from the 1995 4th grade TIMMS that my 3rd graders had no problem figuring out by drawing the bars:
There are 10 girls and 20 boys in Juanita’s class. Juanita
said that there is one girl for every two boys. Her friend
Amanda said that means 1/2 of all the students in the class
are girls.
How many students are there in Juanita’s class?
Answer: ________________
Is Juanita right?
Use words or pictures to explain why.
Is Amanda right?
Use words or pictures to explain why.
This book is a great resource:
a handbook for Mathematics teachers in primary schools
isbn: 9810159056
I picked mine up on ebay.
wow, thanks!
oh!
You know what --- I think I have that book!
I need to look up fractions.
I was stumped today.
My friend's son came over and - surprise, surprise - he has NO idea what's going on with equivalent fractions.
I didn't know how to teach it.
I got out my fraction manipulatives; I showed him that 3/3 equals one and that 1/3 multiplied by 3/3 is the same value.
He was seeing each piece separately (I believe), but the pieces were remaining separate.
He definitely couldn't make the leap from the visual representation, with the manipulatives, to the mathematical.
Saxon, of course, would say just keep doing it - at some point it will "feel natural" -- which is true.
I've experienced this several times.
But I'm wondering what I could have done within just this one session to make the connection begin to "take."
I did ask him tons of questions...and I had him do as much of the math & the moving of manipulatives as I had time to do.
I THINK I may be finding that boys are less interested in the bar models than girls.
This is based on an "n of 2," mind you (2 boys).
But now that I'm a full-time Bayesian, I don't necessarily think that an n of 2 is wrong.
And of course Steve is a guy, so there's my n of 3.
It turns out that working memory for most of us can only hold about 3 items at once.
Well, that explains a lot.
LABELS -- YES!
KEEP ASKING QUESTIONS -- YES!
I must remember these things. I do remember the labels were important when we were doing Saxon.
It turns out that working memory for most of us can only hold about 3 items at once.
Well, that explains a lot.
It does, doesn't it?
And it fits perfectly with Real Life Experience.
In college I could never remember all 4 courses I was taking at once.
I could just remember 3, not 4.
Of course when I got to Dartmouth, where we took 3 courses each quarter, I could only remember 2.
"Steve, you’re scaring me!
I'm teaching bar modeling to my son."
Steve's right. I've taught Singapore to 3 kids, right up to the NEM series (7th grade.)
Three issues:
1. The bar models are great for the early years, but by the time you hit 4th or 5th grade, the problems beg Algebra. I held off on those problems, and then taught Algebra early. Now my kids are all in Algebra, supplemented by Grade 5 Singapore Challenging word problems.
2. While bar models work great for some kids, other kids will NEVER use them. I have a kid like that. He'd rather figure it out with
words, in his head. My visual kid, on the other hand, tends to rely on them, which is fine.
3. Parker and Baldridge, author of the book for elementary school teachers based on the Singapore curriculum, say don't make kids use a bar diagram. Only use a bar diagram if it makes sense to your student. I view P&B to be the last word on how to properly use Singapore Math.
In other words, bar diagrams are not a must. They're just another useful tool.
All of that said, I think it's a great way to introduce word problems.
"The bar models are great for the early years, but by the time you hit 4th or 5th grade, the problems beg Algebra."
That's a perfect word. "beg"
"The bar models are great for the early years, but by the time you hit 4th or 5th grade, the problems beg Algebra."
"While bar models work great for some kids, other kids will NEVER use them."
These are good thoughts. I'm off to Singapore next week for a summer math program and will add these questions to my growing list. We'll get to observe and discuss at two primary schools, one secondary and the National Institute of Education
Are there any other questions about Singapore math curriculum and implementation you would like answered?
CassyT, thank you for that offer. I posted it up front.
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