Book Review: Math Doesn’t Suck

March 18, 2008 at 1:15 am (Algebra, Books, Mathography, Methods, Problem Solving)

mathdoesntsuck.jpgI first heard about Danica McKellar’s book in an NPR Podcast interview with her. I was very impressed and moved by Ms. McKellar’s dedication to promoting math education for young women. Too bad I didn’t have such a role model when I was a child.

I like this book.

There are a few flowery and girly things in the book that I have a little difficulty with, but I believe that it really does capture the main math concepts needed by students before they dive into Algebra: factors, primes, rational numbers/fractions, decimal representation of fractions, word problems, and solving for variables. More, importantly she tackles problems and examples of these concepts from subjects that girls can relate to. Some how, she successfully ties in beading, pizza, shoe shopping, espresso, the schoolgirl’s crush, etc. into the examples and problem sets in the book. More importantly, the book doesn’t talk down to girls.

Also, throughout the book Danica features the stories of several successful women who used math in their careers. I think these sections of the book are key for young women. This may date me, but I was told by a teacher that I didn’t need to know math because “I was a girl.” Infuriating as this was, I had to realize that this woman was still stuck in the Dark Ages. Ms. McKellar aptly states in her book, “… we have to be careful that we don’t fall victim to other people’s low expectations.” Kudos to Ms. McKellar for developing a wonderful book that reaches out to young women who are just starting to engage in the wonderfully empowering subject of Math.

P.S. I think the examples throughout this book can be used by Middle School teachers in addition to any examples they come up with in class.

You can read more about Danica McKellar and her book at her website: http://www.danicamckellar.com/

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More knitting and some algebra

January 25, 2008 at 10:52 pm (Algebra, Problem Solving)

I didn’t have a great deal of time to hash this out, but I thought I would create a few images that describe a knitting project I started. I’m knitting a seamless yoke sweater. It’s seamless because the body and sleeves are attached and then knit together to form the yoke. Other than the sewing in of ends to make things neat there’s absolutely no sewing involved with this project.

Here’s an example of what a yoke sweater looks like click on the link to enlarge:

yoke1.jpg

Here are the slides where I thought out the math for starting my yoke pattern:

yoke2.jpg yoke3.jpg

BTW: I may seem like I spent a lot of time creating the images, but not really. It was easy to reproduce those little dots. I just selected a whole row of them and then copied them over to the next section of the grid. I’m finding that by using shortcuts and pasting repeats of patterns makes creating illustrations much more easy.

I forgot to post my finished sweater:

My finished yoke sweater

My finished yoke sweater

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Mastering word problems

January 7, 2008 at 9:25 am (Number Properties, Problem Solving)

I don’t think I had any elementary school teachers who knew how to teach word problems effectively. I was just reading that mastering certain rules such as the properties of numbers (Associative, Commutative, etc.) actually help people understand how to solve word problems.

If you think about it many of use know how to do the mechanics of math in every day applications (figuring out your bill at a restaurant, estimating how many bags of lawn fertilizer or grass seeds to buy to cover your lawn, etc.). But how many of us really realize when we’re actually applying the properties of numbers to solve these problems?  I’m going to try to come up with as many examples of everyday applications of all of the properties below.

Off the top of my head I can think of a number of situations:

  • Figuring out the bill at the tapas restaurant
  • Adding needed yardage of different colors of yarn
  • Determining our grocery budget

Commutative

A + B = B + A and A*B = B*A

Associative

(A + B) + C = A + (B + C) and (A * B) * C = A * (B * C)

Inverse

A + -A = 0, A * (1/A) = 1

Identity

A + 0 = A, A * 1 = A

Distributive

A*(B + C) = (A*B) + (A*C)

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Rational Numbers and Yarn

January 3, 2008 at 10:09 am (Problem Solving, Rational Numbers)

I have a few little problems I’d like to work out. Remember my muffler problem from a previous post? I probably should finish it before winter is over so I need to figure out if I have enough yarn, and what type of striping design or pattern I can create.

About the amounts noted above, I basically eye-balled these amounts, so there isn’t 100% accuracy. That would entail unwinding all the yarn and then measuring it by the yard, which is of course, something I’m not willing to do.

I do know that according to the label there is 108 yards in every skein. So to get my approximate yardage for each skein I simply have to multiply the numbers and fractions above. I’ll give a visual representation of solving for the moss green amount first. By the way I got lazy and wrote out the problem on paper and scanned it as an image rather than using PowerPoint or a graphics program.

Of course, I could have just divided 108 by 4. That would have been easiest, but for the sake of reinforcing knowledge I regained last week, I wanted to solve using fractions.

Now I want to make a muffler which is shorter than a scarf so I’m going to make it 5 feet in length. I want the wearer to be able to tie the scarf at least once. FYI – a normal length for a scarf is the height of the person who is going to wear it. From my estimation below it will take 40 inches of yarn to make a foot. Therefore, it will take 200 inches or 5.555 yards per row (actually 5.5555 with the decimal repeating).

I suddenly realized that .1111 with decimal repeating equals the fraction 1/9. (Mr. Grant’s, my sixth grade teacher, efforts to drill the fraction decimal amounts into us didn’t fail me). So this number is actually 5 5/9 yards or in fraction form 50/9.

Back to my calculations, as I noted in the graphic each row of striping in a Garter stitch pattern takes 4 rows of knitting. So I’m going to take my 5 5/9 or 50/9 yard number and multiply that by 4. I get 200/9 or 22 2/9 yards. So considering that I only have 27 yards of yarn I now know that I can only make 1 stripe of moss green on my muffler. Maybe it’s enough for just the edging.

Gosh this is a lot more work that I thought, and of course, I’m an experienced enough knitter to be able to visually estimate what I can do, but now I can the problem thinking I employed here in the future to analyze more complicated problems when it comes to yarn estimation for patterns. I’m pretty stoked!

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Yarn Problem

January 2, 2008 at 6:04 pm (Problem Solving, Rational Numbers)

I have several left over skeins of wool yarn from Christmas gift projects and I’d like to use them. I decided that I would make a muffler for my husband. I’m a visual learner and problem solver so I made a quick little illustration. By the way, it’s really easy to make simple-simple graphics by simply using Powerpoint and the set of rough drawing tools. This is how I made the image below.

I knit fairly evenly and regularly, so I think my numbers of stitches per inch will work okay. So now my next steps are to calculate how much yarn I need and then make sure my stripe color design will work out. Note, I tested how much yarn it takes to make and 8 inch row. I was lazy and didn’t feel like doing the entire foot. I could easily solve this and determine how much it takes to make a foot by dividing the amount it takes to knit the 8 inches (40 inches of yarn/2=20 inches) and multiplying it by 3. So it takes 60 inches to knit a one foot row. Accordingly:

  • It would take 180 inches (or 5 yards) to make make a one yard row
  • It would take 360 inches (or 10 yards) to make a six foot row. Your average scarf is about 5-6 feet long.

Larger version of image:

Maybe I’ll just make a 4 foot long scarf… after all it’s just a muffler…I’ll spend some time doing more calculations on the amount of yarn I’ll need to make the muffler and then share them later.

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