1. World’s Largest Burger:
Using Ratios & Proportions in a Real-World Context
A lesson study by: Brittney Ermatinger, Lauren Martinelli, Lauren Taube, and Valerie Weage
Lessons Learned…
Scaffolding and Introduction is ESSENTIAL. Teacher needs to provide adequate directions, supplies, and motivation.
Observing how unfamiliar students struggle and how the host teacher copes can give observers new strategies.
Open-ended tasks make it more difficult to anticipate misconceptions.
Teachers should not only anticipate conceptual misconceptions, but also how students might misinterpret directions, etc.
It’s important to always use consistent and familiar language to avoid confusing students.
Lesson Goal
The learner will understand how to set up and solve a proportion by picking out important information from a presented situation and analyzing the language used in the problem set-up.
The learner will understand how a unit rate is associated with a ratio and how a unit rate may be beneficial when attempting to scale up or down a ratio to fit different constraints.
The learner will understand how a real world situation can be applied to ratios and proportions.
Revisions…
The directions were not very clear for students of where to place the 30, 10, and 4 pound burger in their ratio table.
Therefore, the teachers decided that it needed to be specific in the directions.
When the teacher began revising the lesson taught in other classes, she specifically told them where the numbers would need to be placed.
Another revision that was made from the lesson was the amount of time given to the students to explore with proportions.
Many students began the explore portion of the lesson by filling out the column by using various proportions.
This method would work for completing the table, but it would take a lot of time using this method. Therefore, one revision to be made is to let the students explore for about 7-10 minutes and then ask the class if they discovered a different way to fill out the table besides setting up proportions and then solving them.
Many students discovered the use of a unit rate that you could divide every number by from the 360 pound burger to figure out what the numbers would be for a 30 pound burger, etc.
However, some students were able to explore with proportions for awhile and then figure out a rate they could divide every number by for the 360 pound burger to receive the 30 pound burger and so on.
If needed, the teacher did decide to pair up some groups after the revision was made to help some students who were still only focused on proportions to discover a different method that could be used.
“I want to eat that burger!”
Hypothesis
“I want to visit this place.”
Highlights…
Throughout the lesson study, students were able to practice their set up of proportions. They were able to remind themselves that they must line up the context of the ratios in the proportions. During this practice, students were able to develop this process into and understanding to rely on. As the explore begins, students work on solving proportions to complete the table, but quickly realize this is a long process. Some students attempt to discover different avenues to expedite their work. Students begin to see the scaling that is happening between various rows of the table. They are using observation skills and analyzing their work to determine patterns, which they find. Students find that they can divide an entire row by the same number to scale the numbers down. Some begin to make connections that they are using their understanding of equivalent ratios so know that their method is correct. Throughout the explore, some students were not able to make this connection and continued to solve proportions to complete their table. During the discussion, students were able to see the thought process of their peers and learn from them. Students who had made the connection between proportions to scaling and equivalent ratios helped students at all different levels build connections to the different methods demonstrated in the explore.
students have a grasp of how to write ratios as a fraction
solid understanding that a ratio shows the comparison between two numbers that represent a topic, usually found in the context of the problem.
students tend to question the proper set up of the proportion.
students may struggle to line up their proportions correctly due to confusion/lack of noticing the difference between uncooked vs. cooked weight
students struggle with understanding the connections between ratios, proportions, and rates
Most students will complete the task using a procedural knowledge of cross multiplication of proportions
Students may also use a unit rate to determine the different amounts for each sized hamburger, but still struggle with connecting unit rate to the process of cross multiplication.
There can be connections made about scaling down the original values of the larger burger and comparing that to the unit rate as well as cross multiplication. This may be difficult for students without a deep understanding behind the mathematics they are performing.
The real-world context of the problem helped students achieve the goal. The activity was very interesting to the students since the restaurant they would be looking at was in Michigan and some students had been to the restaurant. The students were also intrigued by the biggest burger being made at the restaurant and it helped them relate what they have learned about ratios and proportions to the real world scenario.
Also, it always helps the students when they are able to see the scenario on screen. The students watched a YouTube video from Man vs. Food to see how the burger was created with the ingredients.
Launch…
Summary…
To launch this delicious lesson the teacher began by playing a video clip that showcased the creation of the world’s largest burger at a nearby Detroit restaurant, Mallie’s Sport’s Grill. Following the video clip the teacher probed the students for ideas about how this might be related to their current unit, ratios and proportions.
The class completed questions 1 and 2 together with the teacher to think about how proportions can be used to cook the world’s largest burger. The teacher focused on introducing critical thinking required to complete the task, scaffolding the work they would be completing later.
Next, the teacher read the prompt and explained the directions for part 3 in which students were to use a ratio table to “scale down” the world’s largest hamburger to make a proportionally correct burger that was instead 30 pounds, 10 pounds, or 4 pounds.
Students explored this task with the help of a partner and a calculator for about 20 minutes. Several different approaches were used to solve and the teacher was careful to monitor thoroughly and answer questions from groups.
After a sufficient amount of time, the teacher interrupted the groups’ work to discuss their findings. The teacher had sets of partners explain how they found their perfectly proportional burger. Two methods were highlighted; using proportions to solve for each new value and finding and using common factors to reduce each component of the burger.
The lesson concluded with the students completing an exit slip to show their understanding of the day’s lesson. “If I use two ketchup packets on a 2/3 lb burger, how many packets will I need on a 360 lb burger?”
Explore…