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Algebra: A Problem in Translation

Posted on by Denise Gaskins

[Photo by *Irish.]

In my post Elementary Problem Solving: The Tools, I introduced word algebra as a way to help students think their way through a story problem. In the next two posts, I showed how the tool worked with simple word problems.

Now, before I move on to focus exclusively on bar diagrams, I would like to show how word algebra can help a student solve a typical first-year algebra puzzle.

A homeschooling friend who avoided algebra in high school, trying to help her son cope with a subject she never understood, posted: “Help! Our answer is different from the book’s.” Here is the homework problem:

Josh earned $72 less than his sister who earned $93 more than her mom. If they earned a total of $504, how much did Josh earn?

Continue reading Algebra: A Problem in Translation

Contest: Write a Number Story

Posted on by Denise Gaskins

numberstoriescover

Math Mama is hosting the next Math Teachers at Play blog carnival (submit your post here) on Friday, and she writes:

The Math Teachers at Play blog carnival came out twice as #15. Since then we’ve had #16 and #17. We’d like to iron out the numbering, and so the upcoming issue will be #19. I am personally sponsoring a contest for the best little (ie, very short) story written about how the numbers got mixed up this way…

For more details, check out her blog post:

Beginning next month, the MTaP carnival will change its schedule, coming out on the third Friday of every month.

If you are interested in hosting an upcoming carnival, please let me know! Carnival posts are a lot of fun to put together, you get to discover new (or new-to-you) bloggers, and you almost always get a bit of a traffic spike. And don’t worry if you’ve never hosted a blog carnival before — just ask for my very detailed “how to” email to help you get started.

Elementary Problem Solving: Review

Posted on by Denise Gaskins

[Bill Watterson identifies the trouble with math problems, through the eyes of Calvin and Hobbes.]

It’s time to revive and (hopefully!) finish my long-neglected series on solving word problems in elementary mathematics. I’ve been having fun making up the problems, so now I just have to write the posts. Coming up soon:

Since it has been more than two years since the last entry, however, I wanted to take a few minutes to recap our progress so far and to refer new readers back to the original posts:

Continue reading Elementary Problem Solving: Review

My New Project: Blogging 2 Learn

Posted on by Denise Gaskins

Beginning in January, I will teach a 4th-12th grade Blogging 2 Learn class through our local homeschool co-op. For now, here is my research blog, testing ideas and trying to imagine myself as a new blogger:

Have you used blogs with your students? If so, I would love to hear your suggestions and comments. And whether you are an experienced or a wanna-be blogger, please share: What do you think a “Blogging to Learn” class should cover?

Math Teachers at Play #17 via MathRecreation

Posted on by Denise Gaskins

Check out the action-packed blog carnival at mathrecreation:

There is plenty of humor, a few movies, some great activities and explorations, and lots of math in Math Teachers at Play 17. Hope you enjoy reading these as much as I did….

I think this may be our longest edition yet, with plenty of mathematical fun for all ages. Enjoy!

Do Your Students Understand Division?

Posted on by Denise Gaskins

Cheerios by sixes
[I couldn’t find a good picture illustrating “division.” Niner came to my rescue and took this photo of her breakfast.]

I found an interesting question at Mathematics Education Research Blog. In the spirit of Liping Ma’s Knowing and Teaching Elementary Mathematics, Finnish researchers gave this problem to high school students and pre-service teachers:

We know that:
498 \div 6 = 83
How could you use this relationship (without using long-division) to discover the answer to:
491\div6=?
[No calculators allowed!]

The Finnish researchers concluded that “division seems not to be fully understood.” No surprise there!

Check out the pdf report for detailed analysis.

Continue reading Do Your Students Understand Division?

How to Solve Math Problems

Posted on by Denise Gaskins

[Photo by Aaron Escobar. This post is a revision and update of How to Solve Math Problems from October, 2007.]

HowToSolveIt2

What can you do when you are stumped by a math problem? Not just any old homework exercise, but one of those tricky word problems that can so easily confuse anyone?

The difference between an “exercise” and a “problem” will vary from one person to another, even within a single class. Even so, this easy to remember, 4-step approach can help students at any grade level. In my math classes, I give each child a copy to keep handy:

[Note: Page 1 is the best for quick reference, especially with elementary to middle school children. Page 2 lists the steps in more detail, for the teacher or for older students.]

Continue reading How to Solve Math Problems

Math Teachers at Play #15b via MathFuture

Posted on by Denise Gaskins

The new math carnival is up and running, with explorations in pure and applied math, “bestest” resource lists, and tips on teaching technical skills and basic facts. Check it out:

You may also enjoy Heather’s post:

And if you teach high school students, don’t miss the upcoming MathNotations contest:

Mental Math: Addition

Posted on by Denise Gaskins

[Photo by woodleywonderworks.]

The question came from a homeschool forum, though I’ve reworded it to avoid plagiarism:

My student is just starting first grade, but I’ve been looking ahead and wondering: How will we do big addition problems without using pencil and paper? I think it must have something to do with number bonds. For instance, how would you solve a problem like 27 + 35 mentally?

The purpose of number bonds is that students will be comfortable taking numbers apart and putting them back together in their heads. As they learn to work with numbers this way, students grow in understanding — some call it “number sense” — and develop a confidence about math that I often find lacking in children who simply follow the steps of an algorithm.

[“Algorithm” means a set of instructions for doing something, like a recipe. In this case, it means the standard, pencil and paper method for adding numbers: Write one number above the other, then start by adding the ones column and work towards the higher place values, carrying or “renaming” as needed.]

For the calculation you mention, I can think of three ways to take the numbers apart and put them back together. You can choose whichever method you like, or perhaps you might come up with another one yourself…

Continue reading Mental Math: Addition