Multiplication, division, trig, telling time, order of operations, negative numbers, infinity, and even more — it must be the Math Teachers at Play blog carnival! Check out the latest edition:
Enjoy!
Do Your Students Understand Division?
[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.
How to Solve Math Problems
[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.]
Math Teachers at Play #15b via MathFuture
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:
- Math Teachers at Play Blog Carnival #15
[This is the second “MTaP #15.” For an explanation of the numbering glitch, see Math Teachers at Play #19.]
You may also enjoy Heather’s post:
And if you teach high school students, don’t miss the upcoming MathNotations contest:
Mental Math: Addition
[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…
Math Teachers at Play #15a via Homeschool Math Blog
Wow! It’s hard to believe we’re up to the 15th edition already:
- Math Teachers At Play — Sep 4, 2009 edition
“It is again a very engaging and interesting assortment of posts, so feel free to stay a while and relax. Thank you for everyone who submitted! We’ll start out in the early years of kindergarten. What happens when a research mathematician goes into a kindergarten class? Something interesting, creative … “
Click over for a visit, and enjoy yourself!
Math Teachers at Play #14 via Math Mama Writes
The Carnival is posted:
- Math Teachers at Play #14
“We have money problems (doesn’t everyone?), a dish of art with math on the side, probability and statistics, factors and primes, problem-solving, and a miscellaneous bunch at the end…”
Check it out!
Math Teachers at Play #13 via Blog She Wrote
The carnival is up and running, with fun math for all levels. Check it out:
Math Teachers at Play #12 via Number Warrior
- Update: Math Teachers at Play #12 is up and running, with a pleasing variety of posts to browse. Enjoy!
Wednesday night is the deadline for submitting to this week’s Math Teachers at Play blog carnival, to be posted on Friday at The Number Warrior. Send in your thoughts, ideas, tips, or tricks about K-12 math using this handy submission form.
Continue reading Math Teachers at Play #12 via Number Warrior
Math Teachers at Play #11 via Math Mama Writes
Math Teachers at Play #11 is now posted for your browsing pleasure. So click on over to Math Mama Writes and enjoy!
If you would like to host the carnival, there are many dates still open. Just comment or email me, and I’ll get you set up.
Denise Gaskins' Let's Play Math 