TeacherGuideEverydayMath

Posted on May 30, 2005 @ 19:36 by CatherineJohnson

Wow.

Speaking of sneaking a peak at the teacher's guide, it just so happens that I have open, on my desktop, a bunch of pdf files from the Everyday Mathematics Teacher's Reference Manual, Grades 4-6, The University of Chicago School Mathematics Project, Everyday Learning Corporation, Chicago, IL, 1999, ISBN 1-57039-515-2, pages 127-139, courtesy of one Tsewei Wang, Ph.D., Associate Professor, Department of Chemical Engineering, University of Tennessee and Concerned Parent.

Have I mentioned how much I love the internet?

Interesting to see that Everyday Math teaches the same Guess-and-Check algorithm for long division that's in Trailblazers.

Only, Trailblazers calls it 'Forgiving Division' (pdf file; search for 'forgiving division'):

Forgiving Division Method
(URG Unit 4 pp. 5, 6, 53; SG p. 113)

A paper-and-pencil method for division in which successive partial quotients are chosen and subtracted from the dividend, until the remainder is less than the divisor. The sum of the partial quotients is the quotient.

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So say you're dividing 239 by 3.

Instead of using math facts to know that 3 goes into 23 seven times, you start by guessing how many times 3 goes into 239.


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OK, let's divide 239 by 3 using forgiving division!


'I'm ready!'



I'm going to start by guessing the number . . . 7!

I guess 7!

3 x 7 is . . . 21!

I write down 21 underneath 239, then I subtract, and I get . . . 218.

Whoa.

That's a lot.

OK, I'm going to use a strategy.

I'm going to guess . . . 10, because 10 is a friendly number.

10 x 3 is . . . 30!

I write 30 underneath 218, then I subtract----188.

Wow.

188 is big.

OK. 188. I'm down to 188.

. . . I'm going to try 10 again.

10 x 3 is 30, subtract 30 from 188, get . . . 158.

158?

Wait.

Wait.

I'm lost.

What number am I down to?

Oh. 158. I'm at 158.

OK, I'm going to try 20.

20 x 3 is 60, subtract from 158, get . . . 98.

Oh good! 98! That's really good! 98 is below 100!

Maybe I could try 30 this time.

30 x 3 is 90, subtract from 98, get 8!

Fantastic!

8!

8 is a really friendly number!

Now I can use my math facts and find that 8 divided by 3 is 2.

2 x 3 is 6, subtract from 8, get 2; 2 is less than 3, I'm done!

Yay!

Finally!

Now I add up all my partial quotients and the answer is------

7 + 10 + 10 + 20 + 30 + 2 = 79 remainder 2.

79 remainder 2!

That's the answer!

That's it!

All done!

Bye Bye!

The end!

Forgiving Division

see:
The Many Faces of the Bitter Single Guy

and:

BlameTheTeacher
ProfoundUnderstandingFundamentalMathematics
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
ILoveTheWorldWideWeb
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
WhoSaysLongDivisionIsHard
Everyday Math alternate division algorithm

keywords: Sponge Bob Bitter Single Guy

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Comments

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Catherine, this is a hoot. You are a nut. :)

-- CarolynJohnston - 31 May 2005

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I invented forgiving dimension for myself when we were tackling problems with multi-digit divisors. I'd find I'd have problems guessing things like, if the divisor was 56 and the first three digits 338, should I use 5 or 6, so rather than doing lots of multiplications at the side, I'd just pick the lower number, subtract it, and then add another one if the remainder was still greater than 56.

But as you say, it's ridiculous to always start that way.

-- TracyW - 14 May 2006

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oh my god, you are SUCH A MATH BRAIN!!!!!

see, the rest of us can't come up with this stuff on our own

we have to have gazillion-dollar NSF-funded crappy math curricula to bring it to our attention

-- CatherineJohnson - 15 May 2006

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spongebob

-- CatherineJohnson - 03 Oct 2006

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When SingMath^? does multiplication of fractions, there are easy multiplications and divisions. Kids don't want to even do these. And if you never MAKE kids do tough multiplication and long division, then there is no reason to learn how to simplify before you multiply (fractions).

-- EvilMathTeacher - 04 Oct 2006

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Wait!

I don't follow -

?

You're saying that Singapore Math doesn't do the complicated ones?

I haven't read/done the entire curriculum, though I've gone through some of the fractions lessons (but I think that may have been either Book 4 or 5....)

-- CatherineJohnson - 06 Oct 2006

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No, I wasn't clear...

At the beginning the multiplication is not difficult. So the kids don't think it's necessary to simplify.

Then they get just a little bit harder and they don't want to multiply. But simplifying first before multiply is such a foreign concept. SO...they'll buckle down and mulitply anyway. A lot of them are using lattice or repeated addition. It's time consuming, but it's doable. So they multiply the hard way.

The BEST way to motivate them to simplify first is to hand them the TOUGH questions. THEN, the lightbulb goes on and they say OH I GET IT NOW!!

Sorry, it's been a tough few weeks at school. Lots of meetings and no downtime.

-- EvilMathTeacher - 07 Oct 2006

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TopicType:	WebLog
SubjectArea:	AboutCurricula, ConstructivistTeaching, EverydayMath, IrvingtonMath, LongDivision, TrailBlazers
LogDate:	200505301936