How to Understand Fraction Division

Posted on by Denise Gaskins

photo by Scott Robinson via flickr

A comment on my post Fraction Division — A Poem deserves a longer answer than I was able to type in the comment reply box. Whitecorp wrote:

Incidentally, this reminds me of a scene from a Japanese anime, where a young girl gets her elder sister to explain why 1/2 divided by 1/4 equals 2. The elder girl replies without skipping a heartbeat: you simply invert the 1/4 to become 4/1 and hence 1/2 times 4 equals 2.

The young one isn’t convinced, and asks how on earth it is possible to divide something by a quarter — she reasons you can cut a pie into 4 pieces, but how do you cut a pie into one quarter pieces? The elder one was at a loss, and simply told her to “accept it” and move on.

How would you explain the above in a manner which makes sense?

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Probability Issue: Hints and Answers

Posted on by Denise Gaskins

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. If you’re stuck, read the hints. Then go back and try again. Figure them out for yourself — and then check the answers just to prove that you got them right.

This post offers hints and answers to puzzles from these blog posts:

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Hobbit Math: Elementary Problem Solving 5th Grade

Posted on by Denise Gaskins

[Photo by OliBac. Visit OliBac’s photostream for more.]

The elementary grades 1-4 laid the foundations, the basics of arithmetic: addition, subtraction, multiplication, division, and fractions. In grade 5, students are expected to master most aspects of fraction math and begin working with the rest of the Math Monsters: decimals, ratios, and percents (all of which are specialized fractions).

Word problems grow ever more complex as well, and learning to explain (justify) multi-step solutions becomes a first step toward writing proofs.

This installment of my elementary problem solving series is based on the Singapore Primary Mathematics, Level 5A. For your reading pleasure, I have translated the problems into the world of J.R.R. Tolkien’s classic, The Hobbit.

UPDATE: Problems have been genericized to avoid copyright issues.

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Narnia Math: Elementary Problem Solving 4th Grade

Posted on by Denise Gaskins

[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

Tangrams and Other Dissection Puzzles

Posted on by Denise Gaskins

tangram-cat[Photo by jimmiehomeschoolmom.]

One of the things I meant to do with my elementary math class (the one that got canceled due to low enrollment):

And then we would play around with Tangram puzzles, and perhaps make up a few of our own.

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Math History on the Internet

Posted on by Denise Gaskins

[Image from the MacTutor Archive.]

The story of mathematics is the story of interesting people. What a shame it is that our children see only the dry remains of these people’s passion. By learning math history, our students will see how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge we today take for granted.

In a previous article, I recommended books that you may find at your local library or be able to order through inter-library loan. Now, let me introduce you to the wealth of math history resources on the Internet.

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Math Games by Kids

Posted on by Denise Gaskins

Photo by Mike Licht, NotionsCapital.com.

The cold came back and knocked me flat, but there are compensations. The downtime gave me a chance to browse my overflowing bookmarks folder, and I found something to add to my resource page. Princess Kitten and I enjoyed exploring these games and quizzes from Ambleweb.

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