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26 Sep 2005 - 19:45 Mathsurf, the Pearson Scott Foreman & Pearson Prentice Hall web site that supports Middle School Mathematics, a constructivist curriculum. I didn't get around to working the problem myself, but I posted it because the problem felt wrong.....it felt like the opposite of a challenging problem in Mathematics 6 by Enn R. Nurk and Aksel E. Telgmaa. All of the challenging word problems in RUSSIAN MATH can be solved with effort. Story problems in Russian Math have only one possible answer. Doug & Steve don't seem to be too impressed with the Mathsurf problem.
After competing in the high jump at a high school track and field meet, Mike, Ben Josh, Sam, and Chad compared their results. It turned out that:
a) Mike jumped higher than Ben but not as high as Josh;
b) two boys jumped the same height;
c) Sam, who jumped 1.3 m, did not jump as high as Ben;
d) Mike jumped 20 cm higher than Sam;
e) Chad jumped 5 cm less than Josh but 10 cm higher than Ben.
Question: How high did each boy jump?
page 205, #811
For me, this was quite a challenging problem....but it was clearly solveable, and I did solve it. (Thank God for bar models.) Working on it was fun, challenging, exciting, taxing (I hope I'm not sounding incredibly....delayed), and I learned from doing it. One thing this problem teaches is to keep your eyes open. I've done enough of the book now that I instantly knew that 'two boys jumped the same height' was going to be the Deciding Clue. But if I hadn't known that, the fact that this 'condition' (is that the right word?) was so different from the others would have helped direct my attention to it. I also sharpened up my visual modeling skills. I think there's some disagreement on ktm about the value of visual modeling, but for me it's important. And I 'deepened' my abilty to 'form a unit' (Caroline & I will both be writing posts about that shortly....) My sense is that the Mathsurf target problem probably wouldn't do any of this for me, or for any student.....what do you think?
(I'll post my answer to the Russian problem after I find out from you guys whether I got the answer right!)
bar model solution
key words: bar model solution Russian math problem scan of bar model solution
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Does the Russian book not have the answers in the back? I remember reading somewhere (maybe it was the "Gambill method") that the kids should always have the answers available... Anyway, here's what I got: Sam = 1.3m
Ben = 1.4m
Chad = Mike = 1.5m
Josh = 1.55m Are these the same as your answers? I would like to see what your bar model approach was like. I did this problem by laying out the kids' relative positions on a number line. That Mathsurf problem is awful. -- CarolynJohnston - 27 Sep 2005
I'll go find them-- NO! The RUSSIAN MATH book does NOT have the answers in the back! I think the translator is working on compiling all the answers (I estimate about 10,000 problems in the book altogether). It definitely needs the answers. -- CatherineJohnson - 27 Sep 2005
I used a number line, in essence. (I think--I'll have to show you what I did). -- CatherineJohnson - 27 Sep 2005
Let's see.... I left everything in cm. Sam: 130 cm
Mike 150 cm
Ben: 140 cm
Josh: 155 cm
Chad: 150 cm
Yup, same answers. I'm going for a run; will scan in the bar models later. Interesting that you used a visual.....I assume you can do this problem by setting up algebraic expressions with unknowns, but is it harder that way? -- CatherineJohnson - 27 Sep 2005
Much harder. I wouldn't do it algebraically. -- CarolynJohnston - 27 Sep 2005
OH, interesting. It seemed harder to me; that's for sure. -- CatherineJohnson - 27 Sep 2005