Did you know that over 50% of Americans over 18 years of age drink coffee every day?! And that among these 150 million coffee drinkers, the average coffee consumption in the United States in 2010 was 3.2 cups of coffee per day! (Data gathered from the 2010 National Coffee Association Drinking Trends Study.) Since coffee consumption is such a huge consumer market in the United States and using an interactive video to represent a real-world scenario, the Hot Coffee math problem by Dan Meyer is a great math problem to do with your students!

The Hot Coffee math problem follows the Gourmet Gift Basket team as they try to Guinness World Record for the biggest cup of coffee! This compelling math problem can be found on Dan Meyer’s 3-Act Math task website using the following link: http://mrmeyer.com/threeacts/hotcoffee/. This problem is also a great way to address several high school geometry Common Core State Standards!

The High School Geometry: Geometric Measurement and Dimension: Common Core State Standards that are addressed in this problem are:

G-MG.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

G-MG.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

G-MG.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Act One

In the first act students will watch a one-minute short video of the Gourmet Gift Basket team building, transporting, setting up, and beginning to fill up their coffee cup! Then, students will be given the questions shown below:

1. The Gourmet Gift Baskets team wants to break the record for the biggest coffee cup. Will that cup be enough to break it? How many gallons of coffee do you think will fit inside?
2. Guess as close as you can. Write your guess down.
3. Write down a guess you know is too high.
4. Write down a guess you know is too low.
5. How long do you think it’ll take them to fill up the cup?
6. How many regular-size cups of coffee would fit inside that super-size cup of coffee?

After making their individual guesses for questions 2 through 4, by the end of the problem students should be able to answer questions 1, 5, and 6.

During this lesson, it is up to your digression whether you would like your students to work individually, in pairs, or in teams. My recommendation, however, and how I would group up my students would be in pairs or groups of three. So, students can challenge and work together to answer the problem’s questions.

Act Two

In the second act, students will ask themselves and answer the question: What information will help solve this problem?

First, I would have my students brainstorm in their small groups the type of information they think they need to complete the problem. While students are coming up with ideas, I will be going around and listening in to conversations and helping students who need assistance. After it seems that all students have finished their list, I will hold a whole class discussion. Where I will ensure that students understand the facts of the problem (shown below) and understand what procedures need to be taken in order to solve the Hot Coffee’s questions.

Information students need to solve this problem: 

The dimensions of the cup: 7 feet by 7 feet

The rate the cup is filling up:2.1 gallons/minute

The conversion from cubic feet to gallon: 1 cubic foot = 7.48052 gallons

The conversion from gallons to cups: 1 gallon = 16 cups

Information on the old record: Which can be reviewed as a class during whole class discussion and handed out in paper form to each student or small group as a resource

Information on the Guinness World Record guidelines: Which can also be reviewed as a class during the whole class discussion or handed out in paper form to each student or small group to serve as a resource

Act Three

In act three students solve for the size of cup needed to break the old largest cup of coffee record, solve for the amount of coffee gallons that would fit in the cup, how long it would take the Gourmet Gift Basket team to fill up the cup, and how many regular-size cups of coffee fit inside of that super-size cup of coffee.

Students will meet the first standard when they are able to solve for the size of cup needed to break the Guinness World Record for the largest cup of coffee. Students will show evidence of meeting the second standard when they solve for the volume and area of the coffee cup to figure out how many gallons it will take to fill the inside of the cup. Students will meet standard three by using ratios to solve how many regular-size cups fit in their recording breaking coffee cup.

This is a great lesson because this 3-Act Math problem is exciting to solve! It really helps students stay engaged and motivated to solving the several answers pertaining to the cup of coffee, but probably the most interesting and conclusive question being: Did Gourmet Gift Baskets actually beat the old Guinness World Record for the largest cup of cup?! On the Dan Meyer’s webpage there are also great sequel ideas that align to other Math Common Core State Standards that you can do!