Children have such a wonderful way of looking at the world. They are naturally curious and question everything. What a great asset to the world of mathematics! If we can tap into these qualities by using the mathematics that we see or experience in the life around us, we will find that all students are wonderfully positioned to learn high levels of math.
During some downtime over the holiday break, I came across an article titled “The Truth About A&W’s Third-Pound Burger and the Major Math Mix-up.”(Anonymous, 2025) The article tells a story about an ad campaign promoted in the 1980s about a new third-pound burger priced the same as the quarter-pound burger. Essentially, the campaign was a massive flop because most adults believed that a third-pound burger was less meat than a quarter-pounder and thought it was ridiculous that they should pay the same amount for less food. How fascinating! It made me wonder what students would have to say about this. If I brought this article to students, they could weigh in and use mathematics to prove their point. I partnered with Mrs. Casey in her 5th-grade classroom. We decided to use this opportunity to return to previously learned content and try different methods for engaging students in mathematics.
Mrs. Casey thought it would be a fun experience for the students and give us some great information about how her students had internalized the fraction work they had been doing. We started by standing at the Promethean with the article displayed for students to see.
Mrs. Burwell: Have any of you been to A&W™ or other restaurants that serve cheeseburgers?
Many hands went up.
Mrs. Burwell: Well, I came across this story about the A&W™ restaurant back in the 1980s, where they decided to introduce a new type of burger, and it did not go well.
Student 1: What happened?
Mrs. Burwell: The restaurant had always had a quarter-pound cheeseburger.
Student 2: Oh! I’ve had that! I get that at McDonald’s.
Student 3: Me too. But I don’t get it with all of that stuff on it.
Mrs. Burwell: I see many of you have had a similar burger. Can someone explain why it’s called the quarter-pounder?
Student 4: it’s a burger that weighs a quarter of a pound.
Student 1: I think it’s the meat that weighs that.
Student 4: Oh yeah. It’s just the meat.
Mrs. Burwell: Well, A&W™ decided to bring in a third-pound burger and would charge people the same price as the quarter-pound burger.
Many students at the same time: What? That’s not right. How can you charge the same amount?
Student 5: Was that the mix-up?
Mrs. Burwell: It actually wasn’t. The third-pound burger wasn’t selling well. The company held a forum with some adults to find out why they thought it wasn’t selling well. All of the participants said they wouldn’t pay the same amount for a third-pound burger because it’s less meat; therefore, it should cost less.
Many hands went up with a lot of excitement.
Mrs. Burwell: For your task today, I want you to make a case for why there was a mix-up. You might prove your thinking with a picture, a model, numbers, and words.
Students were given a large sheet of paper and markers for the task and encouraged to talk with those around them to support their thinking. Many students began by drawing a representation of the two hamburgers. Mrs. Casey and I prompted students to provide labels and detailed explanations so others could understand their reasoning.
Other students used representations such as fraction pieces, fraction bars, and number lines to model the fractions in the problem context.
As expected, the students in Mrs. Casey’s class had a variety of ways they approached the task. They used many unique representations to prove their thinking, such as drawings of physical tools (fraction pieces), semi-concrete models such as the number line, and written language. In the end, the class agreed that the mix-up resulted from most people thinking that ⅓ is less than ¼. In the number line drawing above, one student recognized this by stating that “people thought the ¼ was bigger because the numbers are bigger, but ⅓ is a bigger fraction.”
What Mrs. Casey and I learned about her students was that their understanding of basic fractions was solid, and students had a deep toolkit of knowledge and strategies they could pull from to talk about and solve a real-world problem. We ended the session by discussing what A&W™ might have done to convince their patrons better that they were getting a good deal. Solutions ranged from pricing the quarter-pounder lower but keeping the same price for the third-pound burger to providing people with an accurate visual representation of the burgers.
Mrs. Casey and I also discussed the impact of using a real-world example where students use mathematics to solve a problem. The engagement was high throughout the task, and students demonstrated agency in selecting their strategies and tools, which helped them build positive mathematical identities. We were also intentional in how we presented the task to students. Peter Liljedahl, author of Building Thinking Classrooms (2021), found in his research that when and where you give a task matters. By gathering around the teacher, in this case, standing at the board and beginning right as class started, students were highly engaged, asked very few questions on how to get going, and immediately left for their desks to start proving their thinking.
The world is full of mathematics, and it’s magical. When we notice something interesting, our students will likely find wonder in it. They are born with an incredible curiosity, and we can lift them in their efforts to make sense of the world around them through mathematics. Happy mathing!
Holly
Liljedahl, P. (2021) Building Thinking Classrooms in Mathematics. Corwin
No author. “The Truth About A&W’s Third-Pound Burger and the Major Math Mix-Up.” A&W. https://awrestaurants.com/blog/aw-third-pound-burger-fractions Date of Access January 10, 2025.
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