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).
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People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math. 