When I was a student teacher, one of my and my associate teacher’s favourite lessons that we did in our Grade 9 applied (MFM1P) class was the mullet ratio lesson. Quick recap: students learn the index of a ratio by determining who has the best mullet among hockey players, celebrities, and even students in our class and in the school. Some of the students actually had mullets and were happy to be part of the lesson. Students had many ideas about what makes the best mullet (“how long it is in the back”, “how much longer it is in the back than front”, “how greasy it is”). The idea that we were leading into is that the best mullet is one with the highest ratio of party:business (as the saying goes, a mullet is a hairstyle with “business in the front, party in the back”). Hence, the index of a ratio: one number that you can use to compare ratios.
The students loved it! It was something they could relate to since most of them were from rural areas where mullets and country music were very popular. Even the students who were normally completely un-engaged were excited. I couldn’t wait until I had my own class so I could teach it again.
Fast-forward one year: I’m teaching Grade 7 math at an all-girls private school in the suburbs of the Greater Toronto Area. We are starting rates and ratios – my favourite topic! I was excited to break out the mullets again when I realized something: these city girls are not going to be interested in learning about mullets. Some of them might not even know what a mullet is. I needed a different approach. That’s when I came up with the chocolate milk lesson.
We started off with a quick review of the previous day’s material:
And then I posed the question:
We talked about whose chocolate milk is more chocolatey and how you can tell. Some students tried to guess. Some used similar reasoning to my Grade 9s with the mullet ratios: Sasha’s* has less milk, Kate’s has more chocolate powder. Some found equivalent ratios. I led into the idea of the ratio of chocolate powder to milk in each drink. We found the index of the ratio and determined that Sasha has the higher ratio, and therefore her drink was more chocolatey. We did some practice comparing other chocolate milk ratios:
In that class we only ever talked about ratios in terms of chocolate milk. On the test, I decided to throw in a thinking question to check if my students really understood the concept. Instead of chocolate milk, I asked student whose drink was more lemony. Almost all of them were able to make the transition to thinking about the index of a ratio in a different context.
Sarah and Mia are making lemonade.
Sarah uses 3 scoops of lemonade mix and 8 cups of water. Mia uses 5 scoops of lemonade mix and 11 cups of water.
a) [K/U – 1 mark] What is Sarah’s ratio of lemonade mix to water?
b) [K/U – 1 mark] What is Mia’s ratio of lemonade mix to water?
c) [T – 3 marks] Whose lemonade is more lemony? Explain how you know. Show all of your work.
Take away: it’s all about context. Put math into a context that students can relate to and can understand. This will vary depending on the culture and background of your students.
Another example: when I was teaching data management, I included this communication question which I got from an assessment at the school where I was a student teacher:
The price of bread and the price of canola oil both increase sharply after a long period of no rain in the prairies.
Explain the type of causal relationship that most likely exists between the 2 variables. Assume that the first variable is the independent variable, and the second variable is the dependent variable.
When my students got to this section of the test, I got so many questions from students about what canola oil was made of! I didn’t even consider that my suburban students might not make the connection that students who grew up on or around farmland wouldn’t think twice about.