[Photo by internets_dairy.]
Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest. Let’s start the mathematical fun with an arithmetic card game in honor of our 24th edition and a few number puzzles:
I thought I knew math fairly well.
I thought arithmetic was boring.
I thought the reason other nations beat America in international math tests was that their students worked harder than ours.
I thought all sorts of silly things before I read Liping Ma’s Knowing and Teaching Elementary Mathematics. Now this must-read book is coming out in a new edition, due in bookstores next week.
I can hardly wait!
In American elementary mathematics education, arithmetic is viewed as negligible, sometimes even with pity and disdain—like Cinderella in her stepmother’s house. Many people seem to believe that arithmetic is only composed of a multitude of “math facts” and a handful of algorithms. . . Who would expect that the intellectual demand for learning such a subject actually is challenging and exciting?
— Liping Ma
Arithmetic in American Mathematics Education: An Abandoned Arena?
[Photo by mape_s.]
I’m afraid that Math Club may have fallen victim to the economy, which is worse in our town than in the nation in general. Homeschooling families have tight budgets even in the best of times, and now they seem to be cutting back all non-essentials. I assumed that last semester’s students would return, but I should have asked for an RSVP.
Still, Kitten and I had a fun time together. We played four rounds of Tens Concentration, since I had spread out cards on the tables in the library meeting room before we realized that no one was coming. Had to pick up the cards one way or another, so we figured we might as well enjoy them! She won the first two rounds, which put her in a good mood for our lesson.
I had written “Prime numbers are like monkeys!” on the whiteboard, and Kitten asked me what that meant. That was all the encouragement I needed to launch into my planned lesson, despite the frustrating dearth of students. The idea is taken from Danica McKellar’s book Math Doesn’t Suck.
[Photo by armigeress.]
In 4th grade, math problems take a large step up on the difficulty scale. Students are more mature and can read and follow more complex stories. Multi-step word problems become the new norm, and proportional relationships (like “three times as many”) show up frequently. As the year progresses, fractions grow to be a dominant theme.
As a math teacher, one of my top goals is that my students learn to solve word problems. Arithmetic is (relatively) easy, but many children struggle in applying it to “real world” situations.
In previous posts, I introduced the problem-solving tools of word algebra and bar diagrams, either of which can help students organize the information in a word problem and translate it into a mathematical calculation. The earlier posts in this series are:
In this installment, I will continue to demonstrate the problem-solving tool of bar diagrams through a series of ten 4th grade problems based on the Singapore Primary Math series, level 4A. For your reading pleasure, I have translated the problems into the universe of a family-favorite story by C. S. Lewis, The Lion, the Witch and the Wardrobe.
UPDATE: Problems have been genericized to avoid copyright issues.
Continue reading Narnia Math: Elementary Problem Solving 4th Grade
[Photo by shonk.]
Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.
Let’s start the mathematical fun with a couple of puzzles in honor of our 20th edition: First, the shape to our right is an icosahedron, one of the Platonic solids. Each face is an equilateral triangle — can you count them? For more fun, make your own model.
[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?
[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:
[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:
How could you use this relationship (without using long-division) to discover the answer to:
[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.
[Photo by Aaron Escobar. This post is a revision and update of How to Solve Math Problems from October, 2007.]
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.]
[Photo by jaaron.]
Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! We accept entries from anyone who enjoys playing around with math, as long as the topic is relevant to students or teachers of preK-12th grade mathematics.
Some articles were submitted by their authors, other were drawn from the back-log in my blog reader, and I’ve spiced it all up with a few math jokes courtesy of the Mathematical humor collection of Andrej and Elena Cherkaev.
Let the mathematical fun begin…
Denise Gaskins' Let's Play Math 