# Probably Probability

We had never covered probability, so I felt like it was time to dive in with a little bit of a focus. Now that we’ve done a good bit of it, I feel like we would have been fun and totally possible to have done it a few years ago as well and then returned to it with a stronger focus before moving into pre-algebra. It’s one of those topics that’s not really covered in books for younger kids, yet kids are constantly encountering probability in their lives, in part because of games. I think it makes a huge amount of sense to cover it earlier.

Picture Books
There are a couple of good picture books for younger students about probability. The first is the MathStart book Probably Pistachio by Stuart J. Murphy. This is really not one of my favorites in the series, but it does introduce the concepts, especially about using probability to predict what comes next. It’s Probably Penny by Loreen Leedy is similar in concept, and readers who like Leedy’s classic picture book about measuring will recognize the same characters. However, my favorite was A Very Improbable Story by Edward Einhorn from Charlesbridge. This one is more clever and introduces a lot more basic vocabulary to start talking about probability, not only for what happens next but also for games.

Chapter Book
Of course there’s a Murderous Maths book for kids who are just a little older. Are You Feeling Lucky? is yet another excellent resource. We have been loving the Murderous Maths series. This one, like the one about shapes, asks readers to try a number of things out and I think it’s best when you do the activities with the book, such as flipping a coin or rolling a die. The book also covers some combinations math, which is nice for us as a follow up to some of the Beast Academy combinations math. If you haven’t yet discovered the Murderous Maths books, know that they often cover some surprisingly complex and difficult math, far beyond what kids would typically do before high school. However they cover it in such a friendly and humorous way that it feels approachable and enjoyable.

Activities
The GEMS guide In All Probability is an excellent one. It’s intended for students grades 3-5. I think the activities could be done more quickly for older kids who need an introduction to the subject as well and perhaps beefed up a little. There are five sets of activities that include flipping coins, making spinners, rolling dice, and making game sticks based on a Native American game. I really like the thought behind the GEMS Guides in general, however, as always, you have to adapt them to homeschool use since they’re really set up for a large class. In this book, some of the activities assume that you’ll gather lots of data from the games. Also, I wish the books were organized with the math more clear and more in depth. There is a teacher section in the back that explains the math behind the activities in more depth, but, for example, the number of chances in the Native American game sticks activity is tied to Pascal’s Triangle, yet it never mentions that. Still, I like the way the investigations are set up for real discovery math and Mushroom and BalletBoy both enjoyed building the spinners, making game sticks, and playing all the various games.

I wanted some pages to practice probability problems, so I had Mushroom do some of the pages from MEP Math that deal with probability. You can find them in the 5b book at the end of this section and the beginning of this one. An alternate source of probability problems and text could have been the NCERT 7th grade math book chapter on data, which covers a variety of concepts, including probability. You can find that here, if you’re interested.

Of course, since probability is in our lives so much, it’s good to look at other places it appears. We started with something greatly revered in our house: game shows. In case you didn’t know, the Husband won us the down payment on the rowhouse many years ago on a game show. Thus the game show’s exalted place in our hearts. It’s fun to look at the odds on nearly any game show. However, the classic game show problem is the Let’s Make a Deal problem, which has been written about a ton, most famously by Marilyn Vos Savant and Martin Gardner (if you’d like to be a math nerd and don’t know who Martin Gardner is, you need to remedy that, by the way). It’s great to actually watch the show and learn about the problem. I saw a great demonstration of it by Ed Zaccaro of the Challenge Math books at a conference once, using envelopes instead of doors. With three envelopes, it’s not clear which one to choose. However, with a hundred envelopes, it’s almost immediately clear. We tried that and talked a little about how probability is one of those things that can be tricky to think about sometimes. This was followed up on nicely by the Murderous Maths book when it talked about how pennies don’t have memories.

If you look up probability lessons on Pinterest, you’ll find lots of options. However, the classic probability lesson that I wanted to be sure to do was with M&M’s. There are many variations, but essentially you have students calculate the probability of drawing an M&M out of the bag. The more bags you calculate, the closer you can start to get to what is, presumably, the actual ratio in which M&M’s are actually produced. You’re finding the experimental probability, so this is a good activity to introduce this term. The theoretical probability can also be found just by looking up in what ratios the M&M/Mars company actually makes the M&M colors. It’s slightly different for each type of M&M, but you can find it easily online.

Finally, we simply tried to be more alert to probability in our lives, such as in weather forecasts, board games, video games, and random events. It’s nice when kids can see math in the real world, especially when it’s things that aren’t money. Overall, this was a good unit for us.

# Do More Math Projects

I think when we think of projects, history, science, nature studies, electives, and so forth are the first things that come to mind. However, I’ve been making a concerted effort to do more math projects lately and I really want to advocate for engaging with math in that way. It’s fun and adds another dimension to math. It helps show how math is relevant to other subjects and everyday life. It shows how math can be artistic and useful.

So far, we’ve been enjoying a few different resources for math projects and I thought I’d highlight them here.

Time Travel Math
This is a great book from Prufrock Press, intended to be used for gifted fourth and fifth graders. There is a loose story about a pair of twins, Harriet and Thomas, who find a secret way to travel in time, but only if they’re wondering about math. The story is cheesy, but it’s not at all poorly written, which helps it work. They travel in time three times, first to learn about ratio with a young Leonardo da Vinci, next to learn about geometry and tessellations with a young M.C. Escher, and finally to learn about area in ancient Egypt with Imhotep. Each section has questions for students to think about as the text tells the story and reveals the math. Those are followed by either short math labs or activities about the topic and then finally by a much longer project. For ratio, students make a giant object. For tessellations, students make a quilt out of tessellations. For area, students make a mobile to balance shapes. I highly recommend this book. We’ve finished the first two sections and are looking forward to the third. I think the recommended ages on the book is probably a little too narrow. The projects and math could be right for kids any time from third grade to before formal algebra, at which point the concepts would be too simple.

Math Projects Series
This series is out of print, but most of the titles can be found inexpensively. There are titles about making math games, making kites, designing playgrounds, and designing houses. We have tried out two of them – one about designing playgrounds and one about designing houses. I especially liked the way that the playground book led the kids forward with different activities, considering how playgrounds are used and playing around with simple shapes for design. This is the piece of doing a math project that I think I didn’t initially understand. Doing questions beforehand and practicing the concepts isn’t busywork or wasted time. It’s time kids need to understand the math and get the most out of the project. Unfortunately, when we went to use the houses book, we were very disappointed by the vagueness of the instructions and ended up ditching it. Still, I would like to see the math behind the kites and bridges books because I like the goal of the series.

GEMS Guides
These are math and science guides for elementary and middle school with hands on projects for kids. There are ten math guides in all with different age ranges and topics, including combinations, probability, algebra, and polyhedra. We used Math on the Menu, which is about combinations and have a couple more on tap and are looking forward to them. Again, the key thing provided is support for how to think about the math as you do the project. The projects for the ones I have are much more process oriented with less of a final product at the end. For example, in the combinations one we did, there was a story and a number of problems revolving around it, but no product at the end to show off. These books require more tweaking for the homeschool classroom since part of the GEMS philosophy is having kids all share their methods and approaches in finding different answers. Two of the GEMS Guides, about cooperative logic problems, are probably not really adaptable.

Amazing Math Projects You Can Build Yourself
This book is filled with many different ideas for math projects, such as making your own abacus or playing around with polyherdra models. Unlike the other books mentioned, there’s less building up of specific skills by slowly structuring the project to have more meaning. Instead, there are just many different ideas for every sort of math all thrown together. This is more like a book of ideas than a guide. It’s written to the student with text about the projects that explains the math or the connections with history, art, or other subjects. Some of the “projects” are extremely fast and simple while others are more involved. If you’re looking for something to get the juices flowing for doing more hands on math and mini-projects, then this is probably a very good starter book.