Restaurant Floor Plan

25 min

Teacher Prep
Setup
Access to geometry tool kits, graph paper, and compasses. Quiet work time followed by partner discussion.

Narrative

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.

This activity uses the Compare and Connect math language routine to advance representing and conversing as students use mathematically precise language in discussion.

Launch

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.

Student Task

  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. 
    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.

  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 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.

  5. It is good to have at least 1121\frac12 ft between each table and at least 3123\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.

Sample Response

Sample responses:

    • Table A could seat 3 customers because 30⋅30=90030 \boldcdot 30 = 900 and 900÷300=3900 \div 300 = 3.
    • Table B could seat 3 or 4 customers because 48⋅24=115248 \boldcdot 24 =1152 and 1152÷300=3.841152 \div 300 = 3.84.
    • Table C could seat 4 or 5 customers because π⋅212≈1385\pi \boldcdot 21^2 \approx 1385 and 1385÷300=4.616‾1385 \div 300 = 4.61\overline{6}.
    1. About 80 customers
    2. The dining area could be a rectangle with sides 30 ft and 40 ft. This would give an area of 1,200 ft2, which is enough space for 80 customers because 80⋅15=120080 \boldcdot 15=1200.
    3. Using a scale where 1 cm represents 2 ft, the scale drawing would be a rectangle 15 cm wide and 20 cm long.
    • Table A would be a square with sides 1.25 cm.
    • Table B would be a rectangle with length 2 cm and width 1 cm.
    • Table C would be a circle with a diameter of 1.75 cm.
  4. The food pickup area could be a point in the top left corner of the rectangular dining area. A circle centered on this point with a radius of 30 cm represents the maximum distance to a table.

<p>A rectangular dining area floor plan.</p>
A rectangular dining area floor plan is indicated with 14 identical rectangular tables, 7 identical square tables, and 3 identical circular tables. At the top left corner is a dot with the label, “food pick up.” Along the top and bottom sides of the rectangular floor plan are 4 rectangles on each side, all spaced out equally, with the shorter side aligned with the sides of the floor plan. Along the left side of the floor plan are 3 rectangular tables, spaced out equally, with the shorter side aligned with the left side of the floor plan. Along the right side of the floor plan are 2 circular tables in each of the two corners and in the center of the right side are 3 rectangular tables aligned shorter side to shorter side. In the center of the floor plan, there are 3 rows of 7 square tables, where the first row has 2 equally spaced tables, the second row has 3 equally spaced tables, and the third row has 2 equally spaced tables. An arc is indicated underneath the lower right side of the floor plan indicating the maximum table distance.

Activity Synthesis (Teacher Notes)
Use Compare and Connect to help students compare, contrast, and connect the different approaches. Invite students to prepare a display that shows the strategy they used to create their floor plan. Encourage students to include details that will help others interpret their thinking. For example, specific language, use of different colors, shading, arrows, labels, notes, diagrams or drawings. Give students time to investigate each others’ work. During the whole-class discussion, ask, “What did the floor plans have in common? How were they different?” “Are there any benefits or drawbacks to one floor plan compared to another?”
Extension

The dining area usually takes up about 60% of the overall space of a restaurant, but 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 be needed for these other areas?

Extension Response

Sample response: If the dining area is 1,200 ft2, then the other areas would need about 800 ft2 of space. The fact that the dining area takes up about 60% of the entire restaurant area can be represented with the equation 0.6x=12000.6x = 1200, where xx represents the area of the entire restaurant. The entire restaurant would cover about 2,000 ft2, because x=1200÷0.6=2000x = 1200 \div 0.6 = 2000. The other areas of the restaurant would be about 800 ft2, because 2000−1200=8002000-1200=800 or 0.4⋅2000=8000.4 \boldcdot 2000 = 800.

Standards
Addressing
  • 7.G.1·Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
  • 7.G.4·Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
  • 7.G.A.1·Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
  • 7.G.B.4·Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
  • 7.NS.2.d·Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
  • 7.NS.A.2.d·Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
  • 7.RP.3·Use proportional relationships to solve multistep ratio and percent problems.
  • 7.RP.A.3·Use proportional relationships to solve multistep ratio and percent problems. <span>Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.</span>

15 min