As I mentioned yesterday, my new book includes links to online resources to help you play with word problems. So this week, I’m sharing a few of my favorites.
Today we examine a time-tested method to help kids reason about math: Leave out the numbers.
First up, there’s Brian Bushart’s numberless problem bank for young students. Then we’ll look at Farrar Williams’s modern revision of a math teaching classic with problems for upper-elementary and middle school students.
Have fun thinking math with your kids!
Word Problem Bank
Word problems are commonplace in mathematics classrooms, and yet they regularly confound students and lead to frustrated teachers saying things like:
- “They just add all the numbers! It doesn’t matter what the problem says.”
- “They don’t stop to think! They just start computing as soon as they’re done reading the problem.”
Brian Bushart offers a collection of ready-to-go slide presentations that walk through the steps of making a word problem make sense.
Math With No Numbers
Discover Farrar Williams’s book Numberless Math Problems: A Modern Update of S.Y. Gillian’s Classic Problems Without Figures, available in ebook or paperback.
Williams writes: “In order to answer the question, they’ll have to explain it, because the problem doesn’t give you anything to calculate with. The only way to answer is by explaining your process. See how sneaky a numberless problem is? It makes students really think about the process of solving the problem.”
“When students face a word problem, they often revert to pulling all the numbers out and “doing something” to them. They want to add, subtract, multiply, or divide them, without really considering which operation is the right one to perform or why.
“When you don’t have numbers, it sidesteps that problem.
“For students who freeze up when they see the numbers, this can be a really good way to get them to think about their process with math.”
—Farrar Williams, Math With No Numbers
CREDITS: Feature photo (top) by saeed karimi via Unsplash.com.
In this 4-video series, Tanton presents five key principles for brilliant mathematical thinking, along with loads and loads of examples to explain what he means by each of them. A call for parents and teachers to be mindful of the life thinking we should foster, encourage, promote, embrace and reward — even in a math class!
Essays and videos showing how to approach math puzzles in a way that a) is relevant and connected to the curriculum, and b) revels in deep, joyous, mulling and flailing, reflection, intellectual play and extension, insight, and grand mathematical delight.
Here are some essays illustrating astounding tidbits of mathematical delight. And here are some purely visual puzzles to surprise.
The best way to practice math is to play with it—to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.
My book Prealgebra & Geometry: Math Games for Middle School is scheduled for release to regular bookstores in February, 2021. Because no publisher wants to send a new book into the world during such hectic, unsettled times as a big election, the winter holidays, or during inauguration season.
Denise Gaskins' Let's Play Math 