MEDIA RESOURCES FROM THE GET THE MATH WEBSITE
- The Setup (video) Optional
An introduction to Get the Math and the professionals and student teams featured in the program.
- Math in Restaurants: Introduction (video)
Sue Torres, chef and owner of a Mexican restaurant, describes how she got involved in the cooking world, gives an introduction to the mathematics used in menu costs, and poses a math challenge related to menu pricing.
- Math in Restaurants: Take the challenge (web interactive)
In this interactive activity, users try to solve the challenge posed by Sue Torres in the introductory video segment, by examining avocado prices from the past three years to suggest a menu price for guacamole.
- Math in Restaurants: See how the teams solved the challenge (video)
The teams solve the restaurant challenge in two distinct ways by using algebra to examine costs of avocados and suggest a menu price .
- Math in Restaurants: Try other menu pricing challenges (web interactive)
This interactive provides users additional opportunities to set future menu prices for three dishes in Sue Torres’ restaurant, based on trends in costs over recent years.
For the class:
- Computer, projection screen, and speakers (for class viewing of online/downloaded video segments)
- One copy of the “Math in Restaurants: Take the challenge” answer key (DOC | PDF)
- One copy of the “Math in Restaurants: Try other challenges” answer key (DOC | PDF)
For each student:
- One copy of “Math in Restaurants: Take the challenge” handout (DOC | PDF)
- One copy of the “Math in Restaurants: Try other restaurant challenges” handout (DOC | PDF)
- One graphing calculator (Optional)
- Rulers, grid paper, chart paper, whiteboards/markers, overhead transparency grids, or other materials for students to display their math strategies when solving the challenges in the Learning Activities.
- Colored sticker dots and markers of two different colors (Optional)
- Computers with internet access for Learning Activities 1 and 2. (Optional)
(Note: These activities can either be conducted with handouts provided in the lesson and/or by using the web interactives on the Get the Math website.)
BEFORE THE LESSON
Prior to teaching this lesson, you will need to:
- Preview all of the video segments and web interactives used in this lesson.
- Download the video clips used in the lesson to your classroom computer(s) or prepare to watch them using your classroom’s internet connection.
- Bookmark all websites you plan to use in the lesson on each computer in your classroom. Using a social bookmarking tool (such as delicious, diigo, or portaportal) will allow you to organize all the links in a central location.
- Make one copy of the “Math in Restaurants: Take the challenge” and “Math in Restaurants: Try other restaurant challenges” handouts for each student.
- Print out one copy of the “Math in Restaurants: Take the challenge” and the “Math in Restaurants: Try other restaurants challenges” answer keys.
- Get rulers, graph paper, chart paper, grid whiteboards, overhead transparency grids, etc. for students to record their work during the learning activities.
- Get colored stickers (optional) and colored markers, for students to mark the points and construct the trend lines in the scatter plots in the learning activities.
- Ask students to discuss their favorite foods and whether they have ever prepared a meal. Ask students to brainstorm how mathematics is used in cooking and food preparation (measurements, proportions, etc.) Ask students to discuss how they use math when purchasing and selecting food items in a store or restaurant (determining the prices of items, calculating the “best buy” by comparing items of different quantities, etc.).
- Explain that today’s lesson focuses on the use of math in restaurants. Ask students to brainstorm how mathematics might be used in restaurants, in ways other than those mentioned in the previous discussion. (Paying employees, paying for costs of operating a business, pricing menu items, etc.)
- Explain that today’s lesson features video segments and web interactives from Get the Math, a program that highlights how math is used in the real world. If this is your first time using the program with this class, you may choose to play the video segment The Setup, which introduces the professionals and student teams featured in Get the Math.
- Introduce the video segment Math in Restaurants: Introduction by letting students know that you will now be showing them a segment from Get the Math, which features Sue Torres, chef and owner of Sueños, a restaurant in Chelsea, New York. Ask students to watch for the math that she uses in her work and to write down their observations as they watch the video.
- Play Math in Restaurants: Introduction. After showing the segment, ask students to discuss the different ways that Sue Torres uses math in her work. (Sample responses: She uses math to make recipes with many ingredients; collects data about the costs of ingredients; looks for trends in the data over time; makes predictions about prices using decimal estimations; sets the menu prices using a rule of thumb that involves using addition and multiplication of rational numbers.)
- Ask students to describe the challenge that Sue Torres posed to the teens in the video segment. (Sue must set a menu price for guacamole for the coming year. Avocado is the main ingredient. The challenge is to look at avocado prices from the past 3 years to predict what avocados might cost in the next 14 months. Then, using this prediction, , as well as Sue’s Rule of Thumb for establishing menu prices, recommend a menu price for guacamole for next year at Sueños.)
LEARNING ACTIVITY 1
- Explain that the students will now have an opportunity to solve the problem, which will require them to graph and analyze the data, look for possible relationships, and make a prediction to determine the price of guacamole using Sue’s Rule of Thumb.
- Ask students to think of situations in their daily life where they may need to apply the concepts of analyzing data and finding a “trend line” to make a prediction. (Sample responses: Analyzing the number of hits a baseball player makes each game or a runner’s times at a particular distance; looking at how many customers come to at a popular restaurant or store at different times of day to predict when would be the best time to eat or shop there; looking at the number of hits your blog is getting to see if there is a trend over time; collecting and analyzing the quality and water temperature of a lake over time to see when it is safe to swim; collecting local census data over time to predict the need for a new school or additional youth programs; analyzing the amount of money you might save each year to make a prediction about how much you will have when you graduate high school.)
- Discuss why you would need to find an average to determine the menu price of an appetizer, main course, or dessert item. (Sample responses: to calculate the average cost of an ingredient, or several ingredients, over time; to locate the median cost in the data set; to set one price that can remain the same over a period of time, even though the costs might be lower or higher at different times.)
- Review the following terminology with your students:
- Coordinates: an ordered pair of numbers that identify a point on a coordinate plane.
- Scatter Plot: a graph that displays the relationship between two different sets of data. The values on the horizontal axis represent one data set and the values on the vertical axis represent the other data set. The coordinates of each point represent the ordered pair of these data values.
- Trend line: a line on a scatter plot that shows a correlation between two sets of data.
- Correlation: a relationship between two sets of data that can be positive, negative, or none.
- Line of best fit: the trend line that most accurately models the relationship between the two sets of data. It has about the same number of data points above it and below it. It is used to make a prediction based on a scatter plot that appears to be linear.
- Linear: in a straight line.
- Extrapolation: Predicting a value outside the range of known values.
- Interpolation: Predicting a value between two known values.
- Slope: a ratio or rate of change. Slope represents the change in the y-values to the change in the x-values on a coordinate graph using any two points on a line. It is a ratio of the vertical change to the horizontal change.
- Box and whisker plot: a display that summarizes one set of data along a number line. It shows a 5-number summary of a data set. The left “whisker” or segment extends from the minimum to the first quartile; the box extends from the first quartile to the third quartile, with a line segment through the median; the right “whisker” or segment extends from the third quartile to the maximum.
- 5-number summary: five numbers in a data set that show how the data is spread. The numbers represent the boundary points: the minimum and maximum, the median, the first quartile (median of the first half), and the third quartile (median of the second half).
- Median: the middle value in a data set with an odd number of values that have been listed in order. If there is an even number of values in the data set, the median is the mean of the two middle values after they have been listed in order.
- Average: a measure of central tendency that is often displayed as the mean of the data values. It is calculated by finding the sum of the values and dividing by the number of data values in the set.
- Distribute the “Math in Restaurants: Take the challenge” handout. Let your students know that it is now their turn to solve the challenge that Sue Torres posed to the teams in the video.
- Explain that in the activity, students will use the Avocado Cost Chart and scatter plot to analyze the real world data for avocados. Students need to decide on a strategy to find a model that will show the general direction of the data. After constructing a line that will appear to “fit” the data, called a “line of best fit” or “trend line,” they will need to make a prediction about the cost of avocados in the next 14 months. Then, using “Sue’s Rule of Thumb,” they will make a recommendation for the menu price of guacamole.
- Ask students to work in pairs or small groups to complete the “Math in Restaurants: Take the challenge” handout. Use the “Math in Restaurants: Take the challenge” answer key as a guide to help students as they complete the activity. Note: The handout can be used by itself or in conjunction with the “Math in Restaurants: Take the challenge” activity on the website.
- If you have access to multiple computers, ask students to work in pairs to explore the interactive and complete the handout.
- If you only have one computer, have students work in pairs to complete the assignment using their handouts and grid or graph paper and then ask them to report their results to the group and input their solutions into the online interactive for all to see the results.
- Review the directions listed on the handout.
- As students complete the challenge, encourage them to use the following 6-step mathematical modeling cycle to solve the problem:
- Step 1: Understand the problem: Identify variables in the situation that represent essential features (For example, students may use x to represent the number of months over time and y to represent the cost of a case of avocados.)
- Step 2: Formulate a model by creating and selecting multiple representations (For example, students may use visual representations in graphing, algebraic representations such as slope and an equation of a line of best fit, a box and whisker plot, or an explanation/plan written in words.)
- Step 3: Compute by analyzing and performing operations on relationships to draw conclusions (For example, operations include solving for slope– the relationship between the change in y-values and the change in x-values that allows a student to conclude the rate of change for the line of best fit. Several strategies can be used to find the lines of fit including finding the slope of the line between two representative points, then graphing the slope-intercept or point-slope form of the line of fit; finding the 5-number summary and using Q-points (the x-coordinate of the first or third quartile in the data set and the y-coordinate of the first or third quartile to form a rectangle); finding the average cost of the main ingredient and adding the additional ingredients, then calculating the menu price using a “Rule of Thumb.”)
- Step 4: Interpret the results in terms of the original situation (The results of the first three steps should be examined in the context of the challenge to determine a menu price for the guacamole dish.)
- Step 5: Ask students to validate their conclusions by comparing them with the situation, and then either improving the model or, if acceptable,
- Step 6: Report on the conclusions and the reasoning behind them. (This step allows a student to explain their strategy and justify their choices in a specific context.)
- How can you use the line of best fit to predict the cost of avocados in the future?
- Is there only one value for the price of avocados that can be used to set the menu price? How do you know? (You may wish to have students solve graphically to determine that there are several possibilities for the trend lines and equations, and, therefore, menu price. An extension would be to have students solve the problem using another method, such as the method of least squares, linear regression, or the median-median method.)
- After students have completed the activity, ask students to share their solutions and problem-solving strategies with the class through discussion and visual materials, such as chart graph paper, grid whiteboards, overhead transparency grids, etc. Encourage students to discuss how their strategy helped (or didn’t help) them predict the cost of avocados for next year and recommend a menu price for guacamole. Ask students to discuss any difficulties they faced in completing the challenge and how they overcame those obstacles.
- As students present their solutions, ask them to discuss the mathematics they used in solving the challenge. (Sample responses: Using coordinate graphs and scatter plots to solve problems, identifying variables and writing expressions and/or an equation of a line, finding slope or rate of change, representing a trend between two sets of data using a line of best fit, displaying data using a box and whisker plot and calculating a 5-number summary, finding the average of the cost of one ingredient and determining the menu price by multiplying this price times four.)
- Introduce the Math in Restaurants: See how the teams solved the challenge video segment by letting students know that they will now be seeing how the teams in the video solved the restaurant challenge. Ask students to observe what strategies the teams used and whether they are similar to or different from the strategies presented by the class.
- Play Math in Restaurants: See how the teams solved the challenge. After showing the video, ask students to discuss the strategies the teams used and to compare them to the strategies presented by the class. How are they similar? How are they different? During the discussion, point out that the two teams in the video solved the restaurant challenge in two distinct ways. Discuss the strategies listed in the “Math in Restaurants: Take the challenge” answer key, as desired.
LEARNING ACTIVITY 2:
- Go to the Math in Restaurants: Try other challenges interactive. Explain to your students that they will use the web interactive to solve a series of problems similar to the one Sue Torres presented in the video segment. In this activity, students are challenged to use a Cost Chart and scatter plot to analyze the real world data for three different main ingredients: beef, shrimp, and chicken. Students decide on a strategy to find a model that will show the general direction of the data. After constructing a line that will appear to “fit” the data, a “line of best fit” or “trend line,” they will need to make a prediction about the cost of the main ingredient in the next 12 months. Then, using “Sue’s Rule of Thumb,” students will make a recommendation for the price of three menu items: Shredded Beef Mini Tacos with Queso Fresco and Pico de Gallo, Shrimp Flautas with Guajillo Sauce and Guacamole, and Organic Chicken & 3-Cheese Quesadilla with Avocado Tempura and Chipotle Cream. [Note: As in Learning Activity 1, you can conduct this activity with one computer and an LCD projector in front of the entire class or your students can work in small groups on multiple computers. This can also be assigned to students to complete as an independent project or homework using the accompanying handout as a guide.]
- Distribute the “Math in Restaurants: Try other challenges” handout. Clarify and discuss the directions.
- Ask students to complete the handout as they explore the online challenges. [Note: If you are using one computer, have your students work in pairs to analyze the given scatter plot (or plot the points on graph or chart paper), identify the trend line, and to write the equation of the line of best fit for the data. Have students take turns inputting their responses into the web interactive to test their choices. Partners should complete the Cost Chart and predict the average cost of one serving of the main ingredient, using Sue’s Rule of Thumb to recommend a menu price.]
- As in Learning Activity 1, encourage your students to use the 6-step mathematical modeling cycle as they develop a strategy to solve the challenges.
- After students have completed the activity, lead a group discussion and encourage students to share their strategies and solutions to the challenges. Ask students to discuss how they selected the trend lines and lines of best fit, as well as the average cost per serving for the menu item.
LEARNING ACTIVITY 3 (OPTIONAL)
- Ask students to brainstorm situations where they can apply a line of best fit (including the ways they mentioned in the introductory activity)
- Ask students to collect data over a certain period of time. (Encourage students to go online to find existing stats, such as stats for professional sports teams and athletes.)
- Ask students to graph this data. If it is linear, ask them to come up with a line of best fit, calculate an equation for the line, and make conclusions based on their findings. (Note: If the data is not linear, a different fit may be required.)
- Ask students to share their findings with the class.
- Assess deeper understanding: Ask your students to reflect upon and write down their thoughts about the following:
- How did you determine an effective strategy for solving the challenges in this lesson? What are your conclusions and the reasoning behind them? (Sample answer: First you can determine whether the data is linear and has a positive or negative correlation. Then, after choosing a method to find a line of best fit, you can use the y-coordinate representing the cost of the main ingredient to predict an average price for the next year. Finally, you can use this price for one serving to set the menu price by using the Rule of Thumb.)
- Compare and contrast the various algebraic and graphical representations possible for the problem. How does the approach used to solve the challenge affect the choice of representations? (Sample answers: If you decide to graph the points and then use two representative points to find the slope, you can use the point-slope form of the line algebraically to find the average cost as the median of the data in the next year. You could use your line of best fit graphically without an algebraic equation by determining the coordinates on the graph and arrive at the same solution using visual representations. Using a third method, you could represent the line of best fit as the diagonal in the rectangle formed by the Q-points as determined by the 5-number summaries and box and whisker plots.)
- Why is it useful to represent real-life situations algebraically? (Sample responses: Using symbols, graphs, and equations can help visualize solutions when there is more than one, such as different lines of fit that can be used to predict the cost of an item, as well as using different averages for each serving.)
- What are some ways to represent, describe, and analyze patterns that occur in our world? (Sample responses: patterns can be represented with graphs, expressions, and equations to show change.)
- After students have written their reflections, lead a group discussion where students can discuss their responses. During the discussion, ask students to share their thoughts about how the algebra concepts and problem-solving skills they used in this lesson (including recognizing trends in data and determining a line of best fit) are used in restaurants and how these concepts and skills can be applied to other real-world situations.