Unit 9, Lesson 3
Restaurant Floor Plan (Optional)
Grade 7
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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 from the dining area to the kitchen. Students choose their own scale for creating their scale drawing and choose tools strategically when deciding how to make their scale drawings (MP5).
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).
Monitor for students who design different styles of floor plans:
Food pick-up area in a corner, side, or the middle of the restaurant
Tables set up individually, in rows, or in groups
Indoor and outdoor seating
Each of the floor plans can fit the parameters of this activity. Highlight that there is not one exact floor plan that will be successful.
Provide access to a variety of materials, such as blank paper, index cards, graph paper, geometry toolkits, and compasses. Give students quiet work time followed by partner discussion.
Select work from students with different strategies, such as those described in the Activity Narrative, to share later.
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 labeled “A,” a rectangle labeled “B,” and a circle labeled “C” are indicated. A scale of one defined unit equals 1 foot is also indicated. The square has side lengths of 2 point 5 units. The rectangle has side lengths of 2 units and 4 units. The circle has a diameter of 3 point 5 units.
It is good to have about 15 ft2 of floor space per customer in the dining area.
Select an appropriate scale, and create a scale drawing of the outline of your dining area.
Using the same scale, what size would each of the tables from the first question appear on your scale drawing?
To make sure the service is fast, 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 pick-up 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.
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.
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.
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 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 large right trapezoid, that represents the shape of a refrigerator and freezer, with a longer top horizontal base. A horizontal line is drawn such that it divides the large trapezoid into two smaller trapezoids labeled “refrigerator” and “freezer.” The top trapezoid labeled “refrigerator” has a top horizontal base of 14 feet, a bottom horizontal base of 9 feet, a vertical leg of 7 point 5 feet, and a leg of 9 feet. The bottom trapezoid labeled “freezer” has a top horizontal base of 9 feet, a bottom horizontal base of 4 feet, a vertical leg of 7 point 5 feet, and a leg of 9 feet.
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 or not 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.)