photo by Carla216 via flickr

Reblog: The Case of the Mysterious Story Problem

[Feature photo above by Carla216 via flickr (CC BY 2.0).]

Here’s a blast from the Let’s Play Math! blog archives: Seven years ago, I blogged a revision of the first article I ever wrote about homeschooling math. I can’t even remember when the original article was published — years before the original (out of print) editions of my math books. I hope you enjoy…


Case-of-the-Mysterious-Story-Problem
I love story problems. Like a detective, I enjoy sifting out clues and solving the mystery. But what do you do when you come across a real stumper? Acting out story problems could make a one-page assignment take all week.

You don’t have to bake a pie to study fractions or jump off a cliff to learn gravity. Use your imagination instead. The following suggestions will help you find the clues you need to solve the case…

[Click here to go read the original post.]


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10 Questions to Ask About a Math Problem

[Photo by CourtneyCarmody via flickr.]

It’s important to teach our children to ask questions, about math and about life. As I wrote in my series about homeschooling with math anxiety, “School textbooks only ask questions for which they know the answer. When homeschoolers learn to think like mathematicians, we will ask a different type of question.”

So I was delighted to see this new post from Bon Crowder: Ten Questions to Ask About a Math Problem. Click the link and read the whole thing!

Why a list of questions about math problems? Before creating them, I decided the questions should do the following:

  • Allow the student to dig in deeper to the math problem, and the math behind the problem.
  • Help the student to think about the problem in ways they wouldn’t normally.
  • Let the student get creative in thinking about the problem.

And of course doing these things regularly will train them to continue to do this with all math problems through their lives.

— Bon Crowder
Ten Questions to Ask About a Math Problem


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Family

Tell Me a (Math) Story

feature photo above by Keoni Cabral via flickr (CC BY 2.0)

My favorite playful math lessons rely on adult/child conversation — a proven method for increasing a child’s reasoning skills. What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?

As soon as your little ones can count past five, start giving them simple, oral story problems to solve: “If you have a cookie and I give you two more cookies, how many cookies will you have then?”

The fastest way to a child’s mind is through the taste buds. Children can easily visualize their favorite foods, so we use mainly edible stories at first. Then we expand our range, adding stories about other familiar things: toys, pets, trains.

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More Than One Way to Solve It, Again

photo by Annie Pilon via flickr

We continue with our counting lessons — and once again, Kitten proves that she doesn’t think the same way I do. In fact, her solution is so elegant that I think she could have a future as a mathematician. After all, every aspiring novelist needs a day job, right?

If only I could get her to give up the idea that she hates math…

Permutations with Complications

How many of the possible distinct arrangements of 1-6 have 1 to the left of 2?

Competition Math for Middle School, by J. Batterson

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How to Translate Word Problems

Hooray! The MathCounts Mini videos are back. September’s edition is all about translating word problems into algebra:

Download activity sheets and answers.

Do your students like making videos? This year, MathCounts is challenging students in grades 6-8 to create a math problem video. Check out the details:


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by Eirik Newth via flickr

More Than One Way to Solve It

Photo by Eirik Newth via flickr.

In a lazy, I-don’t-want-to-do-school mood, Princess Kitten was ready to stop after three math problems. We had gotten two of them correct, but the last one was counting the ways to paint a cube in black and white, and we forgot to count the solid-color options.

For my perfectionist daughter, one mistake was excuse enough to quit. She leaned her head against me as we sat together on the couch and said, “We’re done. Done, done, done.” If she could, she would have started purring — one of the most manipulative noises known to humankind. I’m a soft touch. Who can work on math when there’s a kitten to cuddle?

by tanjila ahmed via flickr

Still, I managed to squeeze in one more puzzle. I picked up my whiteboard marker and started writing:
DONE
DOEN
DENO
DNOE
DNEO
ONED
ODNE

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photo by George Parrilla via flickr

The (Mathematical) Trouble with Pizza

Photo by George Parrilla via flickr.

Kitten complained that some math programs keep repeating the same kind of problems over and over, with bigger numbers: “They don’t get any harder, they just get longer. It’s boring!”

So we pulled out the Counting lessons in Competition Math for Middle School. [Highly recommended book!] Kitten doesn’t like to compete, but she enjoys learning new ideas, and Batterson’s book gives her plenty of those, well organized and clearly explained.

Today’s topic was the Fundamental Counting Principle. It was review, easy-peasy. The problems were too simple, until…

Pizzas at Mario’s come in three sizes, and you have your choice of 10 toppings to add to the pizza. You may order a pizza with any number of toppings (up to 10), including zero. How many choices of pizza are there at Mario’s?

[The book said 9 toppings, but I was skimming/paraphrasing aloud and misread.]

  • Can you figure out the answer?

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Quotable: What to Do When You’re Stuck

When a kid is feeling bad about being stuck with a problem, or just very anxious, I sometimes ask him to make as many mistakes as he can, and as outrageous as he can. Laughter happens (which is valuable by itself, and not only for the mood — deep breathing brings oxygen to the brain). Then the kid starts making mistakes. In the process, features of the problem become much clearer, and in many cases a way to a solution presents itself.

Maria Droujkova
Natural Math discussion of math club activities

Does It Work?

While I was collecting entries for the Math Teachers at Play #35 blog carnival, I ran across this post by Dave Lanovaz:


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Photo by Raphael Goetter via Flickr

Babymath: Story Problem Challenge III

<a href="http://www.flickr.com/photos/goetter/2352128932/"Photo by Raphael Goetter via Flickr

Alex and Leon enjoyed their baby sister, but they were amazed at how much work taking care of a baby could be. One particularly colicky night, everyone in the family took turns holding the baby, rocking the baby, patting her back, and walking her around before she finally succumbed to sleep.

Then Alex collapsed on the couch, and Leon sank into the recliner. They teased each other with these story problems.

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Probability Issue: Hints and Answers

Alexandria JonesRemember 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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Rate Puzzle: How Fast Does She Read?


[Photo by Arwen Abendstern.]

If a girl and a half
can read a book and a half
in a day and a half,
then how many books can one girl read in the month of June?

Kitten reads voraciously, but she decided to skip our library’s summer reading program this year. The Border’s Double-Dog Dare Program was a lot less hassle and had a better prize: a free book! Of course, it didn’t take her all summer to finish 10 books.

How fast does Kitten read?

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dragon and moon

Hobbit Math: Elementary Problem Solving 5th Grade

[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.

[Note: No decimals or percents here. Those are in 5B, which will need an article of its own. But first I need to pick a book. I'm thinking maybe Naya Nuki...]

Printable Worksheet

In case you’d like to try your hand at the problems before reading my solutions, I’ve put together a printable worksheet:

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Best Articles about Solving Word Problems


[Photo by scui3asteveo.]

I’m still working on that Best of Blog page. [It's done! :D] Here are the 20 best Let’s Play Math! blog articles about solving word problems (also known as story problems)…

Solving Word Problems

More recent posts tagged ‘Word problems’

Bar Diagrams Help Students Think

More recent posts tagged ‘Bar diagrams’

Other Post in the Best of Blog Series


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dwarfswolves

Narnia Math: Elementary Problem Solving 4th Grade

[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

I’ve put the word problems from my elementary problem solving series into printable worksheets:

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Burnt Algebra

Algebra: A Problem in Translation

[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?

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Calvin and Hobbes, math atheist

Elementary Problem Solving: Review

[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:

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Math, Math, Math, math, mathh,,,,maaah,,,,by Aaron Escobar

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.]

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More Backwards Math


[Photo by *clairity*.]

Have you ever noticed how very different little girls are from little boys, in the way they play and in the way they think about things? Princess Kitten has been playing around with Backwards Math again, and my first thought was, “No boy would ever have done this with numbers.”

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The Olympics: Math Puzzles and a Game


[Photo by striatic.]

Maybe it’s because school is out for the summer, but there don’t seem to be all that many Olympics-related math resources on the Web. I did find one cool game, however, and a nice stack of word problems. I hope you enjoy them!

Update: Be sure to see my blog post Olympic Logic for more links and puzzles!

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flower-flag

Christmas in July Math Problem

[Photo by Reenie-Just Reenie.]

In honor of my Google searchers, to demonstrate the power of bar diagrams to model ratio problems, and just because math is fun…

Eccentric Aunt Ethel leaves her Christmas tree up year ’round, but she changes the decorations for each passing season. This July, Ethel wanted a patriotic theme of flowers, ribbons, and colored lights.

When she stretched out her three light strings (100 lights each) to check the bulbs, she discovered that several were broken or burned-out. Of the lights that still worked, the ratio of red bulbs to white ones was 7:3. She had half as many good blue bulbs as red ones. But overall, she had to throw away one out of every 10 bulbs.

How many of each color light bulb did Ethel have?

Before reading further, pull out some scratch paper. How would you solve this problem? How would you teach it to a middle school student?

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jaycoxfilm-if-every-picture-tells-a-story

Math Game: What Number Am I?

Photo by jaycoxfilm.

Math concepts: mental calculations, math vocabulary, and anything else you want to include
Number of players: any number, but I think it works best with two players who alternate asking questions
Equipment: imagination and, if necessary, scratch paper

Many years ago, I read a magazine article by mathematical music critic Edward Rothstein, wherein he described a game he invented for his daughter:

  • “What number am I? If you add me to myself, you get four.”

Rather than explaining the rules of the game, let me tell you a story…

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Word Problems in Russia and America

Andrei Toom calls this an “extended version” of a talk he gave a few years ago at the Swedish Mathematical Society. At 159 pages [2010 updated version is 98 pages], I would call it a book. Whatever you call it, it’s a must-read for math teachers:

Main Thesis: Word problems are very valuable in teaching mathematics not only to master mathematics, but also for general development. Especially valuable are word problems solved with minimal scolarship, without algebra, even sometimes without arithmetics, just by plain common sense. The more naive and ingenuous is solution, the more it provides the child’s contact with abstract reality and independence from authority, the more independent and creative thinker the child becomes.

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