A friend emailed me, frustrated with her child’s math lesson on bar diagrams: “Why do they have to make it so complicated? Why can’t we just solve the blasted problem?”
I told her bar models themselves are not the goal. The real question for parents and teachers is:
- What can you do when your child is stumped by a math word problem?
To solve word problems, students must be able to read and understand what is written. They need to visualize this information in a way that will help them translate it into a mathematical expression.
Bar model diagrams are one very useful tool to aid this visualization. These pictures model the word problem in a way that makes the solution appear almost like magic.
It is a trick well worth learning, no matter which math program you use.
Visualization
https://www.youtube.com/watch?v=HKsYDzQK8Zw
“Visualization is the brain’s ability to see beyond what the eyes can see, and we can develop visualization in many ways.”
The Bar Model Explained
https://www.youtube.com/watch?v=I6Ipio8JntU
“A bar model is a way to represent a situation in a word problem using diagrams — in particular, using rectangles.”
https://www.youtube.com/watch?v=i7LAHc1qvig
“This is one of the ideas that children learn in mathematics: the use of diagrams to represent quantities, especially quantities which are unknown.”
Word Problems from Literature
I’ve written a series of blog posts that explain bar model diagrams from the most basic through to solving multistep word problems. Check them out:
- Penguin Math: Elementary Problem Solving 2nd Grade
- Ben Franklin Math: Elementary Problem Solving 3rd Grade
- Narnia Math: Elementary Problem Solving 4th Grade
- Hobbit Math: Elementary Problem Solving 5th Grade
- Solving Complex Story Problems
- Solving Complex Story Problems II
I’ve started working on a book about bar model diagrams, and I’d love to hear your input. Have you tried using them? Do they help your children? What questions do you have?
Update: My New Book
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.
CREDITS: Videos and quotations from Dr. Yeap Ban Har’s YouTube channel. “Girl doing homework” photo (top) by ND Strupler and “math notebooking equal fractions” by Jimmie via Flickr (CC BY 2.0).
Denise Gaskins' Let's Play Math 
I work with adults, many of whom dropped off the math train early. Word problems are like 500 pound weights to be lifted: it’s not going to happen.
http://www.ncsall.net/fileadmin/resources/fob/2008/fob_9a.pdf is an article about a teacher who focuses on “parts and wholes” with her students; we’ve adopted this approach and end up with bar models to represent the parts and the wholes.
It helps a lot, in part because it’s different than the usual procedural drill, so it doesn’t carry the emotional baggage of “doing kiddie arithmetic” AGAIN, but also because it takes an abstract idea and breaks it into manageable ideas.
Another great way to help learners of all ages is to take the numbers OUT of the word problems. This forces students to pay attention to the problem situation and apply their real-world intuition to figuring it out. For example, see Brian Bushart’s Numberless Word Problems post.
I agree 🙂 Since I’m in a tutoring lab, I don’t get that option, but … when I design my blended learning course…