I think that most people who know me are aware that I teach math. Few are probably aware of what an actual math nerd I am. As a point of reference, do you know how helpful it is to describe to someone where an itch on your back is by having them picture a coordinate grid on your back and giving them the coordinates of the itch? No? Well, put that in your bag of tricks, and get those itches scratched. Do you play the “make an alien” game in the car with your kids, where you use mathematically correct terminology to describe some crazy alien? Ex: My alien has a purple pyramid head with three square eyes, a rotini noodle for a nose, no mouth, a red cylindrical body, and 5 sticks for arms. Try it – my 5 year old loves it, and he’s learning all kinds of geometry terminology (while having fun!) Because he can’t picture this alien until he asks me, “What does a cylinder look like again?” What’s incredibly rewarding is when he describes his alien, and uses some words that I’ve been tossing around.
In any case, the point of those examples was to give you a little glimpse into how the brain of a math geek works. We like to do other things besides solve math problems because we are also living, breathing, functioning human beings (most of us!), but math seems to creep its way in to everyday tasks – like driving. Sometimes I will calculate in my head how much time I will actually save by going 5 mph over the speed limit on a drive. Spoiler alert – it’s not worth it on most drives! Drive safely y’all! I am not always thinking about math, but I would definitely say I am often thinking about math.
One of my hobbies is cake decorating. I like making things with my hands – crochet, cake decorating, painting, etc. I’ve always said I am not at all creative, just patient. I’ll be the first to say that my best work is usually not done when I have to create the design totally from scratch. These tasks all take a lot of patience. This weekend I had a cake order for a cute little mermaid cake for a 6 year old’s birthday party. I made this cake, sent it on its way, and then met up with it later after it was the victim of a cake-tastrophe on the car ride home. It turned out pretty well, especially considering what it looked like post car ride!
Check out all of those circles! The coloring of the fondant, rolling and cutting circles, and placing circles all took quite a bit of time. However, it’s not work that requires a lot of thought, so my mind wandered as I colored, rolled, cut, and placed. And you guessed it – my mind was wandering to all of the ways I could use this cake as a prompt for various math problems. I even drafted a few and used them in the process. I used equations to calculate how much turquoise and white fondant to mix together to create each shade for the hombre effect. I initially intended to go from a 75% saturation to 50%, 25%, then pure white (and do 2 rows of each color). It turned out that I did not want the dark 75% color going up very high on the cake, so I actually went with a 75%, 50%, 30%, 16%, and 8% before switching to white! I weighed my balls of fondant on a food scale for accuracy. I finished each row (bottom up) with more than enough left over, so I just calculated how much white to add to the mix to end up with my desired saturation. I thought about the diameter of the circles compared to the circumference of the cake to see how many circles of each color I would need. I used the diameter of the circles compared to the height of the cake to figure out an estimate of how many rows I would have (estimate because I did not know exactly what the overlap situation would be until I was actually in it!) This is thrilling, no?
Was math necessary to complete this cake? Ummmm no. The hombre effect I did could have been done by just adding turquoise/white fondant gradually until the color variations looked good. In fact, I’ve done it this trial and error way before with great results, I was just feeling extra mathy on this day. All of this got me thinking though, “Would this application of mixture problems be more engaging than the ones I’m currently using in my class?”
As a math instructor, I’m often met with resistance. My husband and I both teach college level courses, but I often joke that we have two completely different jobs. He teaches Criminal Justice courses, which is a field that people choose to sign up for. I ask him all the time what it’s like to have a class full of students that are, at least on some level, interested in the subject matter. In a math course, I’m feeling like a champ if like 10% of the class would say they ‘enjoy’ or ‘like’ or ‘are interested in’ the subject on the first day. Sometimes I too get bogged down with the feeling that if my students are bakers, they probably are going to wing it rather than work a mixture problem to figure out how much of each material to use. That maybe the complainers have a point – a lot of what we do in a college level math course is just not necessary for a large portion of the population. But I have a job to do, and if talking about cake decorating makes mixture problems a little less blah for someone out there, then by golly I’m going to give it a go.
I decided that I would create a few lessons based on this cake, and I’ll be posting them here. Some of my favorite lessons that I’ve done with kids have been when I give them about 3-5 sentences describing a scenario and turn them loose. So, that’s how these lessons have been derived. If actually used with students, you should note that there are many ways to skin the math cat. (Is that an actual saying?) Your students may not use the “desired” method of solving the problems without prompting. I’d encourage you to be okay with that, and leave the “desired” method of solving for the discussion after everyone has presented their findings. I promise, kids love it when “their way” hasn’t been talked about yet – even if they got the same answer as the presenter before!
I’ve drafted an activity that, from my experience, I believe students in grades 4-6 (and up) have the reasoning skills to take on. They may not know how to multiply with decimals or two digit numbers, but I have experienced in multiple classrooms that when students are given a chance to reason, they will take it and run. They may not “set up a proportion” to solve as you might, but it is important to note that that is 100% okay. If your goal is to create problem solvers, then with some coaching as necessary, your students will succeed. In my classroom, I would have available any materials that I had – whether I found them helpful or not – and put the students in groups of 3-4. Oftentimes, we create graphic organizers, give students “the” manipulative, and let them “problem solve” – our way. In fact, I almost included a table to record fondant amounts in, and thought better of it! My most rewarding experiences as a math teacher have come when I allow the students to attack a problem and make their own decisions.
Your students will likely have questions about this problem due to lack of experiences and vocabulary. It is important to read through the problem as a group and get all of those questions answered prior to turning them loose. You do not want to be explaining what “50% saturation” means and what fondant is 6 different times before anyone can begin! If your students have absolutely NO idea how to calculate the amount of each color needed for the various shades, I’d encourage them to start by figuring out the 50% saturation first, and see if they can reason from there. And it’s okay if some students just. don’t. get it. The struggle makes the explanations that much more rewarding.
This lesson may seem like it will take too much time if you just let them go without guidance, and it will take time. I would allow 30-40 minutes for exploration, and 15-20 minutes for presentation – depending on your allotted class time. I have been in the panic mindset where any deviation from the set plan seems like it will be impossible to make up. The strains of standardized tests and countless learning objectives can send us into a frenzy. But I’d encourage you to take time for this type of lesson at least once per 6-weeks period. Your students will thank you, and you may find that you enjoy it and they gain more than you anticipated. Give it a shot! If you do, please let me know how it goes. I’d love to hear it!
I’ve included two handouts, and a link to a widely circulated page that discusses serving amounts for different sizes of cakes. You will need all three pieces for this activity! Enjoy!!