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Quotations XV: More Joy of Mathematics

Mathematics is a vast adventure; its history reflects some of the noblest thoughts of countless generations.

Dirk J. Struik
A Concise History of Mathematics

Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!

Constance Reid

Continue reading Quotations XV: More Joy of Mathematics

Number Bonds, Number Rainbows

Basic bar diagram

Many of us use the idea of number bonds with our young students. A number bond is a mental picture of the relationship between a number and the parts that combine to make it.

Now we have a new, colorful way to show these relationships, thanks to Maria at Homeschool Math Blog. If you teach math to young children, check this out:

Continue reading Number Bonds, Number Rainbows

Looking Ahead with Alexandria Jones

We have now finished three back issues of my old Mathematical Adventures newsletter. Our next story will be from the November/December 1998 issue: Alexandria Jones and the Christmas Present Quandary. I plan to take a couple of months off to find my rhythm with co-op and homeschooling classes, and we will pick up Alex’s adventures (and meet her mother, Maria Jones) in November.

In case you missed any of them, here are all the Alexandria Jones stories so far…

Continue reading Looking Ahead with Alexandria Jones

Bloglines Potluck “Carnival”

Blog carnival graphic 2

One last, long weekend before we dive full-speed into school and co-op classes and swim lessons and karate and art lessons and…well, this may be my last chance to catch up on the backlog in my Bloglines folders.

With over 100 feeds, there is no way I will keep up with all of you during the school year. So here is my end-of-summer fling, a sort of unofficial “Best of (my) Bloglines” carnival, in which I share my personal favorites from the last few weeks of RSS.

I hope you enjoy these posts as much as I have.

Continue reading Bloglines Potluck “Carnival”

Penguin Math: Elementary Problem Solving 2nd Grade

The ability to solve word problems ranks high on any math teacher’s list of goals. How can I teach my students to reason their way through math problems? I must help my students develop the ability to translate “real world” situations into mathematical language.

In a previous post, I analyzed two problem-solving tools we can teach our students: algebra and bar diagrams. These tools help our students organize the information in a word problem and translate it into a mathematical calculation.

Now I want to demonstrate these problem-solving tools in action with a series of 2nd grade problems, based on the Singapore Primary Math series, level 2A. For your reading pleasure, I have translated the problems into the universe of one of our family’s favorite read-aloud books, Mr. Popper’s Penguins.

UPDATE: Problems have been genericized to avoid copyright issues.

Continue reading Penguin Math: Elementary Problem Solving 2nd Grade

Egyptian Math: The Answers

Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original posts. Figure them out for yourself—and then check the answers just to prove that you got them right.

Continue reading Egyptian Math: The Answers

High School Math Challenge

The USA Mathematical Talent Search (USAMTS) has posted its current set of challenge problems, the first of four rounds scheduled for the 2007-2008 school year. USAMTS is a free competition open to all United States middle school and high school students. Young mathematicians have a little over a month (until October 9) to write and send in solutions for the five questions.

According to the USAMTS website:

Student solutions to the USAMTS problems are graded by mathematicians and comments are returned to the students. Our goal is to help all students develop their problem solving skills, improve their technical writing abilities, and mature mathematically while having fun. We wish to foster not only insight, ingenuity and creativity, but also the virtue of perseverance, which is equally essential in scientific endeavors.

A mere five questions. How hard can it be? (Ha!)

A Very Short History of Mathematics

This paper was read to the Adams Society (St. John’s College Mathematical Society) at their 25th anniversary dinner, Michaelmas Term, 1948. [Warning: Do not attempt to read this while drinking coffee or other spittable beverage!]

Hat tip: I found this through the math carnival at a mispelt bog.

Update: The original page has disappeared from the internet, or at least I cannot find it any more, but the Internet Archive Wayback Machine came to the rescue. After my plea for help, James Clare pointed me to the article’s new home.