**UPDATED
Today was the first time I HAD to grab my teacher's manual because I couldn't figure out this math word problem (without using algebra). This is from Isabelle's 4th grade Singapore math book!! My 4th grade math book would never have had this problem!! LOL!
Ready? See if you can figure this out WITHOUT using algebra. I wanted to use algebra but Singapore has the students use bars and graph pictures to help solve their word problem.
OKAY. Here it is:
3000 exercise books are arranged into 3 piles.
The first pile has 10 more books than the second pile.
The number of books in the second pile is twice the number of books in the third pile.
How many books are there in the third pile?
Can you figure it out? I'm sure engineers and scientists can do this in their head. But I couldn't. Please show your work! Remember, no algebra allowed!!!
**Craig just got home from a trip and Isabelle showed him her problem. While Craig was scratching his head (because he was trying not to use algebra), Isabelle was beaming .
She showed him her way and he was impressed!
Belle went to bed (way too late because she was waiting for him to come home) all smiles.
Craig and I are having a good discussion on why weren't we allowed to draw pictures for word problems in grade school? Were any of you discouraged from drawing pictures for word problems? I remember feeling dumb whenever I just NEEDED to draw a picture. Obviously, drawing a picture for 2345/3 wouldn't make sense. LOL! But the idea that there is a systematic way to teach word problems with bar graphs excites me (and makes me wonder how much higher my SAT scores could have been!!) Obviously, I did not get perfect scores! LOL! Have any of you ever thought about retaking tests just for the sake of it? I have! LOL!
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Lets see.
3000-10=2990
Now the first and second piles are the same size, so they are both twice as big as the third. Divide by five, two parts for each of the big piles, one for the small pile.
2990/5=598
Third pile is 598.
Second pile 598*2=1196
First pile is 1196+10=1206
1206
+1196
+ 598
------
3000
Does that count? Do I get a good job sticker? :-)
You get an excellent sticker!!!
Isabelle's diagram looked something like this:
pile 1: I------I------I--10--I
pile 2: I------I------I
pile 3: I------I
Imagine bar diagrams for the above.
Great job Jennie!! I was stumped and my brain just froze. LOL! It sounded so much like an algebra problem that I just couldn't get past it. Luckily, Isabelle did since she drew her bar diagrams! LOL!
I would argue that it is still an algebra problem. I would use little "X"'s instead of bars, but it would look the same...2x + 10, 2x, and x! I guess I have a lot to learn. ;-)
Kristen,
It is an algebra problem, but it can be solved without using algebra. Belle's in the 4th grade and has word problems everyday that would normally be solved w/ algebra by older math students, but with bar graphs these same problems can be solved without the use of algebra and by younger math students. Cool huh!
The bar graphs make it more concrete for them. And actually, its sometimes quicker. Singapore students are taught to solve word problems with bar graphs starting in the second half of third grade. They can solve complex problems much quicker than their American counterparts because they can make the abstract more concrete with the use of picture graphs. They can do this for SAT or GRE tests.
Its kinda like bringing your cuisinaire rods or base ten blocks with you into the test center! I was discouraged from drawing pictures when I was in school.
Singapore teaches to draw a picture graph(s) and then start with math sentences.
Funny how they are #1 in math in the world and they teach to draw picture graphs!! I mean I'm actually teaching Belle specific graphs to draw and she is starting to think this way.
I could go on and on about Singapore math!!
Wow... I may have to get Nathan on Singapore. I'm impressed. I don't think we were allowed to use pictures... always had to show our "figurings" with numbers.
I was afraid to post on here last night for fear of looking dumb (I'm going on my second cup of coffee and the need to chat is overcoming my fears.... LOL!). I can't solve the problem without using algebra. Period. I don't even know what you gals are talking about up there in your comments. Seriously.
I am definitely going to be checking Singapore out.
Explain how you decided to use 5 to divide by. I follow what you are doing but I just can't put the five into it!
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