Lesson 4

Restaurant Floor Plan

4.1: Dining Area (25 minutes)

Optional activity

The purpose of this activity is for students to create a scale drawing for a restaurant floor plan. Students use proportional reasoning to consider how much space is needed per customer, both in the dining area and at specific tables. They try to find a layout for the tables in the dining area that meets restrictions both for the distance between tables and to the kitchen. Students choose their own scale for creating their scale drawing.

When trying to answer the last two questions, students might want to go back and modify the shape of their dining area from their previous answer. This is an acceptable way for students to make sense of the problem and persevere in solving it (MP1).

Launch

Provide access to graph paper, geometry toolkits, and compasses. Give students quiet work time followed by partner discussion.

Student Facing

  1. Restaurant owners say it is good for each customer to have about 300 in2 of space at their table. How many customers would you seat at each table?

    A square, rectangle, and circle. 
  2. It is good to have about 15 ft2 of floor space per customer in the dining area.

    1. How many customers would you like to be able to seat at one time?
    2. What size and shape dining area would be large enough to fit that many customers?

    3. Select an appropriate scale, and create a scale drawing of the outline of your dining area.

  3. Using the same scale, what size would each of the tables from the first question appear on your scale drawing?

  4. To ensure fast service, it is good for all of the tables to be within 60 ft of the place where the servers bring the food out of the kitchen. Decide where the food pickup area will be, and draw it on your scale drawing. Next, show the limit of how far away tables can be positioned from this place.

  5. It is good to have at least \(1\frac12\) ft between each table and at least \(3\frac12\) ft between the sides of tables where the customers will be sitting. On your scale drawing, show one way you could arrange tables in your dining area.

Student Response

Student responses to this activity are available at one of our IM Certified Partners

Student Facing

Are you ready for more?

The dining area usually takes up about 60% of the overall space of a restaurant because there also needs to be room for the kitchen, storage areas, office, and bathrooms. Given the size of your dining area, how much more space would you need for these other areas?

Student Response

Student responses to this activity are available at one of our IM Certified Partners

Activity Synthesis

Ask students to trade with a partner and check that the layout meets the requirements for spacing between tables and maximum distance between the tables and the food pickup area.

Display these questions for students to discuss with their partner:

  • Is the scale drawing easy to interpret?
  • Does it say somewhere what scale was used for the drawing?
  • Is there anything that could be added to the drawing that would make it clearer?
Speaking, Listening, Conversing: MLR7 Compare and Connect. After students have prepared their scaled drawings of a floor plan, display the drawings around the room. Ask pairs to discuss “What is the same and what is different?” about the scale drawings. To help students make connections between drawings, ask, “What do you observe about our scale drawings that is easier to interpret?”. This will help students reflect on how precise and understandable their drawings are for others to interpret.
Design Principle(s): Cultivate conversation; Maximize meta-awareness

4.2: Cold Storage (15 minutes)

Optional activity

The purpose of this activity is for students to apply proportional reasoning in the context of area and volume to predict the cost of operating a walk-in refrigerator and freezer.

Launch

Arrange students in groups of 2. Give students 1 minute of quiet think time followed by time to work with their partner to solve the problem.

Action and Expression: Internalize Executive Functions. Chunk this task into more manageable parts for students who benefit from support with organizational skills in problem solving. Check in with students within the first 2-3 minutes of work time to ensure that they have understood the directions. If students are unsure how to begin, suggest that they consider each statement for the refrigerator first, and then for the freezer.
Supports accessibility for: Organization; Attention
Writing, Reading, Conversing: MLR5 Co-craft Questions. Begin by displaying only the initial text describing the context of the problem and the information about the monthly costs of standard refrigerators and freezers (i.e., withhold the scale drawing and question about the walk-in refrigerator and freezer). Ask students, “What mathematical questions can you ask about this situation?” Give groups 2–3 minutes to write down questions they have. As students share their questions, focus on questions that address how to evaluate costs in relationship to the volume of the refrigerator or freezer. This will help students understand the context and identify any assumptions they are making prior to solving the problem.
Design Principle(s): Cultivate conversation; Maximize meta-awareness

Student Facing

Some restaurants have very large refrigerators or freezers that are like small rooms. The energy to keep these rooms cold can be expensive.

  • A standard walk-in refrigerator (rectangular, 10 feet wide, 10 feet long, and 7 feet tall) will cost about \$150 per month to keep cold.
  • A standard walk-in freezer (rectangular, 8 feet wide, 10 feet long, and 7 feet tall) will cost about \$372 per month to keep cold.

Here is a scale drawing of a walk-in refrigerator and freezer. About how much would it cost to keep them both cold? Show your reasoning.

A right trapezoid. 

Student Response

Student responses to this activity are available at one of our IM Certified Partners

Activity Synthesis

The goal of this discussion is for students to practice explaining the assumptions they made and the strategies they used to solve the problem.

First, poll the class on their estimates for the cost of operating the refrigerator and freezer. Discuss whether the different answers seem reasonable.

Next, select students to share their strategies for breaking the problem up into smaller parts.

Discuss what assumptions students made about proportional relationships while solving the problem. (For example, there is a proportional relationship between the volume of a walk-in refrigerator and the cost to keep it cold.)