Every now and again, you’re watching the news or reading the newspaper, and then all of a sudden – bam! Math slaps you upside the head. Histograms or some other strange phenomena appear right out of nowhere. And usually, when you least expect it. Suddenly, real world data are being used to make a point in the media. And if you’re a math teacher, you immediately seize on the data and think about how you can turn it around with your kids.
Math in a Burrito
On a discussion forum, I ran across a post that linked to this article in an interactive from February 2015’s New York Times online. The article compared the nutritional information from meals you can purchase at the national restaurant chain, Chipotle. Now, I’m a good Texas boy, so an article about nutrition that you can get from a burrito (or its relative, a burrito bowl) got my attention. And, since this isn’t my first encounter with Tex-Mex cuisine, I had a suspicion that the nutritional information wouldn’t end up suggesting that burritos are health food. If you scroll through the article, you see this histogram:
Note: This histogram is (c) The New York Times and is presented here for educational purposes only. If you want to use this diagram with your students or your colleagues, use the full article.
In the revised math TEKS, histograms appear in 6th grade (6.12A and 6.13A), so I started thinking about the sixth graders that I’ve been working with recently at a school in Houston. If I placed this histogram on the SMART board, I wonder what the kids would notice? What inquiry questions might this data generate? A graph like this just screams to be used in a warm-up style, “What do you notice? What do you wonder?” activity.
What do you notice? What do you wonder?
This activity is a gem that should be in every teacher’s toolkit. It’s a short, sweet activity that sparks student interest and helps provoke student discourse.
- Arrange students in pairs.
- Have students make a T-chart with two columns: I notice and I wonder.
- Select an interesting diagram, problem, or data display (like the Chipotle histogram) and show it to students.
- Give students 1-2 minutes to look at the diagram, problem, or data display.
- Students will first make a list of things they notice about the diagram, problem, or data display. To do so, they will alternate roles while you time this part of the activity. Set the timer for 2 minutes. Student A brainstorms what she/he notices and Student B records it on the chart. After the 2 minutes ends, students switch roles for 2 more minutes.
- Next, students will make a list of things they wonder about the diagram, problem, or data display. Repeat the timed brainstorm roles – Student A brainstorms what she/he wonders for 2 minutes while Student B records it on the chart. After 2 minutes, students switch roles and repeat.
- Once student pairs have a list of what they notice and what they wonder, facilitate a whole-class sharing. Each student pair can share out one thing they noticed. Allow student pairs to share out something different. Then, have student pairs, one at a time, share out one thing they wondered.
Part of the power of the I Notice-I Wonder activity is that it gets students’ brains thinking about math on their terms. Students get to generate inquiry questions based on what they know about the topic and what they are interested in. This means you have the chance to let students self-differentiate based on both ability and interest. Histograms are very useful graphs for real-world data. But sometimes, they are hard to teach and for kids to understand. Real-world connections make seemingly abstract topics like interpreting histograms accessible.
The teacher benefits from this activity as well. Teachers have the opportunity to listen to students as they describe what they are naturally curious about when they see a set of data, a diagram, or a problem. Teachers gain insights into what students know and what they are genuinely interested in learning more about.
Paul’s Take-Home
Mathematical processes really are an important part of the learning experience. They are specialized types of knowledge that help students understand mathematical content. The burrito histogram, paired with a cooperative learning activity such as I Notice-I Wonder, touches on many of the K-12 mathematical process standards.
- 6.1A – Apply mathematics to problems arising in everyday life, society, and the workplace. Yep – lunch at Chipotle definitely qualifies for applications to everyday life.
- 6.1D – Communicate mathematical ideas, reasoning, and their implications using multiple representations. A T-chart is a diagram with which you can record ideas and reasoning.
- 6.1E – Create and use representations to organize, record, and communicate mathematical ideas. The histogram is a representation that communicates the mathematical idea of caloric content of certain meals and the T-chart is a representation that organizes mathematical ideas of noticings and wonderings.
- 6.1F – Analyze mathematical relationships to connect and communicate mathematical ideas. Students have to analyze the data presented in the histogram and then use their T-chart to communicate their mathematical ideas (noticings and wonderings).
- 6.1G – Display, explain, and justify mathematical ideas and arguments. Students are displaying their ideas by committing them to paper, sharing with a peer, and then sharing with the whole class. The mathematical vocabulary may not be precise for this activity, but the communication pieces are present.
I’m also intrigued by how math continues to amaze me by showing up in strange places. There is an abundance of opportunity for real-world connections that we can help our students make! Part of the art of teaching is developing fine-tuned eyes and ears to learn how to spot those connections when we see them.
Bonus Histograms
If you haven’t done so by now, take a look at the Chipotle article. Really – please do! It’s very informative and gets you thinking about the math that really is all around us. Plus, if you scroll down through the article, there’s a beautiful pair of histograms that you can have your kids compare and contrast, foreshadowing to 7th grade math when they will be looking at comparative graphs.
