Real World Math: The Garden Stone Problem
I’m always on the lookout for ways to make Math seem “more real” for my students. I find one of the worst things that can happen in a child’s Math education is if they get the idea in their head that Math is an abstract concept, detached from everyday life. Under this mindset, doing Math is a dreary process of completing an assignment for the purpose of finding THE ANSWER (more on this mindset in my next blog post). My goal in the classroom is to help students realize that Math is really all around us, and if you know how to think mathematically, can really make many day-to-day tasks much easier and less prone to trial and error.
I find taking this approach to Math instruction helps engage kids more in the process of doing Math, and for some of them, contextualizes it and makes it easier to understand the concepts when they see how they can be applied in real world settings. Whenever I do an activity like this, I also find that inserting myself into the problem tends to give the activity a human connection that my students identify with. So without further ado, let’s move on to the Garden Stone Problem, how I used Math to solve it, and how a teacher might use the activity in the classroom to encourage real world Math thinking.
Intro: The Setup
As I often tell my students, when you use Math in a real world setting, it’s very rare that the actual question is presented for you in clear words. So I often begin a real world Math problem with a quick intro stinger like this one and have students brainstorm, “What Math questions does this video inspire?” The goal is to activate the student’s mathematical thinking and see ways in which they could potentially apply Math concepts to real life. I call it encouraging them to seek out the questions, because really in Math instruction, it is knowing and understanding the questions and how they might be answered that is more important than the actual answers (again, more on this later). Give students some time to discuss their Math questions, and most importantly, discuss what information they would need to answer the question.
Part 1: How many stones would it take to make a circle wall around the tree?
Next step in the activity is to pose the real world question: How many stones would you need to build a wall around the tree? Students can then be encouraged to come up with an estimate that they are sure is too small, and an estimate that they are sure is too large, and explain how they know. It’s important that students base their estimates on something they see in the photos and are not just wildly guessing. Next, students should brainstorm ideas on what measurements they would need to solve the problem with Math.
Part 2: Gathering important information
Next I would show these images with important information and pose the question, “Can you use the information here to answer the question? Do you need any additional information?” and see what they can come up with. Ask students to do some calculations to come up with a definitive answer. Remember, the wall needs to be two stones tall.
Next to pose another related question: How many bags of mulch would it take to fill in the wall? Once again, zeroing in on the necessary information to solve the problem is an important step in the process. What information do you need?
It’s also important to note that there are some factors that may affect our final outcome.
Part 3: Conclusion
Calculating the number of stones around the tree should be straightforward. If you take the distance across the tree ring (or the diameter of our intended ring of stones) and multiply it by PI (3.14) you will find the distance around the stone wall, or its circumference.
Then it’s a matter of dividing the circumference by the length of one of the stones. Variations may occur if you use the length of the inner or outer edge of the stone (25 cm versus 30 cm). I used the inside edge of the stone, getting a circumference of about 450 cm, meaning it will take 18 stones to go around the tree. Multiply by two and you get 36. So when I returned to the hardware store, I made sure I had 36 stones in total. If you watch the conclusion video, posted below, you’ll see that I only actually used 34 stones. This may be a good concluding activity with students. Why is it that the actual stone wall only took 34 stones when our calculations suggested we needed 36?
I really like the idea of creating real world Math problems to use in the classroom. I really hope eventually to encourage students to see real world Math in their own day-to-day lives and to document them in the same way as I have in this blog post. Maybe it would be beneficial for students to maintain a Math Blog for this very purpose. Something to think about.
Thank you very much for reading, and I’ll see you next time.
Side note: I really rushed to get this job finished towards the end. I was so absorbed in my work, that I didn’t notice these rolling in.
Considering all my calculations were written in sidewalk chalk, I was really glad that I had taken the time to document everything with pics and vids! Five minutes after I finished, the skies opened up.
Originally posted on Tim Boudreau’s EDU Blog.