In my last post, I linked to a really cool vintage resource called Problems Without Figures. As I pointed out, I decided to update it so I could use it with my kids more easily. I didn’t update the whole work because it was very long. I did the first 150 problems, which is a little less than half, but I thought I’d share my update here with you. It’s free to download. For more about the types of problems, the reasons to use a book like this, and how to use the book, have a look at my previous post. Below, I’m going to talk a little more about the changes I made to the book and why. I can’t promise that every problem in here is perfect. I’m pretty sure I thought through everything, but I didn’t have a professional editor. Feel free to send me any corrections and do tweak any problems to make them make more sense for your kids if needed. Note that the nature of these problems is to include superfluous information, have answers that are impossible to get without more information, have multiple potential solutions or paths to a solution, and to have “trick” problems where the answer is much simpler than the problem implies. None of those things are necessarily errors. Again, see my previous post for more about these problems.
I changed the problems in a couple of ways. A large number I left the same or simply updated a word or two to be less old fashioned (such as “shall”), including some of the old fashioned problems about farms and orchards and the like, simply because it’s nice to have different perspectives occasionally. I updated the language in a few problems. For example, instead of buying marbles and penny candy, kids are buying Legos and other contemporary items. For others, I changed the situation or the measuring units for a problem to be more up to date but tried to keep the spirit of the question. However, for several problems, I couldn’t come up with a modern equivalent so I completely rewrote the problem to be more contemporary.
Doing this was an interesting process for me. It let me think about how math has changed over time. Much of the original book was out of date because of the situations it portrayed. It assumed the readers were familiar with agriculture and farm animals. However, much of what has changed is the math. There were several measurement units that are simply not used anymore, such as the rod as a measurement of length. Other measurement units are in use today and students may have a general sense of what a bushel or an acre is, but they are less a part of everyday life. In general, while measurement math is still a key component of everyday math and we have the complexity in the US of having to go between customary and metric measurements, this book drove home for me how it was an even bigger share of the everyday math people used a century ago. For one thing, we tend to deal with standardized sizes of things much more often. Doors, windows, pieces of paper, tablecloths, picture frames, etc. are all standardized. If we want to know how much land we own, we look it up instead of measuring. If we build something, we tend to follow preset directions instead of making them up ourselves with all the accompanying measurement challenges.
On the other hand, there are types of math that were never or almost never covered in the original book. For example, there were only a couple of problems involving averages. There were no problems involving estimation. There were no problems involving statistics or ratios. Very few problems involved fractions or percents, which surprised me. There were no problems involving permutations or combinations.
Life today is more complex with more choices. We tend to need to know more about combinations and permutations just to order off a menu or decide how to buy something or what to wear. We have to evaluate more complex data and statistics to understand a news article or a scientific claim on the internet. We’re used to bigger numbers. None of the numbers in the original book were very big. These days we’re used to hearing about numbers in the millions and billions. Our tax code and economy are much more complex, meaning that percentages come into play a lot more often. When the original book was written, people lived with a cash economy and prices were more straightforward. It’s different now.
When I tossed out those few problems from the original, I tried to replace them with ones that asked kids about making the sort of decisions that we often have to make using math these days. So there are problems about how to make basketball matchups, how to choose which toilet paper to buy, how to know if a statistic is reasonable, and other more modern conundrums than how many acres in your fields or how many fence posts you need.