Several years ago, I read about someone asking for more math problems without numbers and thought to myself, huh? What’s that even mean? What would it look like? From there, I discovered the vintage book Problems Without Figures by S.Y. Gillian.
Reading on, I discovered exactly what a math problem with no numbers looked like.
If you know the width of one stripe on a United States flag, how can you find the total width of the red stripes?
See what I mean? In order to answer the question, students need to know how many stripes are on the flag and how many are red. They need to understand that to find the total width, they’ll need to choose an operation. In this case, they need multiplication. And in order to answer the question, they’ll have to explain it, because the problem doesn’t tell you the width. The only way to answer is by explaining your process.
See how sneaky a numberless problem is? Sometimes numbers worm their way in there, and several of the problems in the original book did include a number or two. However, most of them were like the problem above. They made 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, sometimes 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.
That’s been an increasing focus in the wake of Common Core to get kids to be able to show that they understand the math they do. This is a very old fashioned approach that does exactly that.
However, when I first read Problems Without Figures, I saw that Denise Gaskins, the author of the excellent Let’s Play Math, pointed out that it could really use a rewrite. Excited to give it a try before using it with my own kids, I did just that for the first few dozen problems and went on to use them off and on with my kids over the last few years.
Recently, I pulled out the book again and decided to give it a full facelift and publish it. Some of the problems just have updated language. However, for many others, updating didn’t seem to make a ton of sense. Take this gem:
I know the length of a field in rods and the width in feet, how can I find how many acres it contains?
Kids are barely familiar with acres today and rods are entirely bygone as a system of measurement. Some problems like this got rewritten. I added problems with meters, for example. However, some of the problems just needed a totally new take. I tried to add a lot more problems about figuring out how to navigate all the choices we have nowadays.
If you plan to leave approximately a 20% tip on your restaurant bill, what’s a quick way to calculate that amount?
Overall, this was a really fun project. I hope other people find it useful! You can find it on Amazon.