Here is a math problem in honor of one of our family’s favorite movies…
Han Solo was doing much-needed maintenance on the Millennium Falcon. He spent 3/5 of his money upgrading the hyperspace motivator. He spent 3/4 of the remainder to install a new blaster cannon. If he spent 450 credits altogether, how much money did he have left?
Stop and think about how you would solve it before reading further.
Photo by Martin Thomas via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
When adding, we combine two addends to get a sum. For subtraction we are given the sum and one addend and must find the “missing addend”.
— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers
Notice that subtraction is not defined independently of addition. It must be taught along with addition, as an inverse (or mirror-image) operation. The basic question of subtraction is, “What would I have to add to this number, to get that number?”
Inverse operations are a very fundamental idea in mathematics. The inverse of any math operation is whatever will get you back to where you started. In order to fully understand a math operation, you must understand its inverse.
You may have seen this video making the edu-blog rounds:
[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…]
In case you’d like to try your hand at the problems before reading my solutions, I’ve put together a printable worksheet:
Continue reading Hobbit Math: Elementary Problem Solving 5th Grade
[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)…
More recent posts tagged ‘Word problems’
More recent posts tagged ‘Bar diagrams’
You can help prevent math anxiety by giving your children the mental tools they need to conquer the toughest story problems.
Check out Word Problems from Literature: An Introduction to Bar Model Diagrams—now available at all your favorite online bookstores!
And there’s a paperback Student Workbook, too.
Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.
[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.
I’ve put the word problems from my elementary problem solving series into printable worksheets:
Continue reading Narnia Math: Elementary Problem Solving 4th Grade
[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:
[Photo by One Laptop Per Child.]
Once again, I am adding to my Free (Mostly) Math Resources page. Here are a handful of helpful websites for teaching math…
[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?
[Oops! I found one more post from my old blog. It apparently slipped off the back of my metaphorical desk and has been sitting with the dust bunnies.]
Here is a math problem in honor of one of our family’s favorite movies…
Han Solo was doing some needed maintenance on the Millennium Falcon. He spent 3/5 of his money upgrading the hyperspace motivator. He spent 3/4 of the remainder to install a new blaster cannon. If he spent 450 credits altogether, how much money did he have left?
[Modified from a word problem in Singapore Primary Math 5B. Stop and think about how you would solve it before reading further.]
Denise Gaskins' Let's Play Math 