Stadium Seating and Circles

 

Name: Nicole Williams

 

Title of Lesson: Stadium Seating and Circles                       

 

Date of Lesson:  N/A

 

Length of Lesson:  1-2 class periods (50 min each)

 

Description of Class: Regular or Honors Geometry

 

Source of Lesson:  N/A

 

TEKS addressed:

            111.34.a.2-Geometric thinking and spatial reasoning. Spatial reasoning plays a critical role in geometry; shapes and figures provide powerful ways to represent mathematical situations and to express generalizations about space and spatial relationships. Students use geometric thinking to understand mathematical concepts and the relationships among them.

            111.34.a.4-The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems.

            111.34.d.1-The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems. Following are performance descriptions.

 

 

The Lesson:

I.         Overview Students will be exploring the area and circumference of circles under the topic of seating in their stadiums.  They will be expected to find the exact seating capacity for each of their stadiums.

 

II.            Performance or learner outcomes

Students will be able to:

            -use blueprints and find the total area of seating for a stadium (the area of a larger circle with a smaller circle of area taken out in the center.)

            -use circumference and area to find the exact number of seats for any stadium within their project.

            -determine whether a particular number of seats for a stadium is reasonable.

 

III.         Resources, materials and supplies needed

-stadium blueprints from previous lessons

-rulers/meter sticks

 

IV.          Supplementary materials, handouts

 

 

Five-E Organization

 

Teacher Does

Student Does

Engage:

Each stadium that you are working on needs to hold a certain number of spectators.  Do you think that each stadium will have the same number of seats?

Which stadiums do you think will require the most seating?

Which will require the least?

Among your group you should start discussing these ideas.

 

 

Hoped for student response:

 

-no

 

-answers will vary (track, gymnastics, etc)

 

-answers will vary (volleyball, tennis, etc)

 

 

 

 

 

 

                                                                

Evaluate

Teacher will make sure that students are coming up with logical and feasible answers within their group.

 

Explore:

The teacher will write on the board the minimum number of seats for each stadium.  The students will be asked to work in their groups and decide if these numbers are feasible for each stadium layout.  

 

 

 

Students will decide if each minimum seating works for each stadium.  Students may need to measure some chairs around the room to get an idea of how much space each seat should take up.

 

 

 

 

 

 

 

 

 

 

 

    

Evaluate

The teacher will walk around and assist students in the right direction.  Teacher will make sure that students are working together and thinking about everything they know about circles.

Explain:

 

The teacher will ask the class to discuss how they worked through this task. 

 

 

 

 

Tennis- (main) 7,000

(others) 3,000

Swimming (outdoor main)-10,000

(indoor)-6,000

Gymnastic/basketball 15,000

Main/track  70,000

 

 

As a class the students will come together and discuss how they came up with their answers. 

 

Expected Student Response:

 

We know that the space between these two circles on our blueprint is the space set aside for seating.  We also know that each row will take up approximately (depends on what the students came up with) amount of space.  So in this particular stadium we could fit (number depends on the group and stadium) rows.  We noticed that the circumference of about the middle of this section was (some number) so we could fit (some number) of seats on this row and just to average we said this would be the same for every row.  So this stadium (does or does not) fit the criteria.

    

Evaluate

Teacher will ask several groups to demonstrate what they have done to the class even if they worked the problem the same.  This is to ensure that all groups are on the right track.

 

 

Extend / Elaborate:

 

 

Questions:

Now as a group you should decide exactly how many seats will fit in each stadium.  Remember that you should account for isles to walk down to get to your row.  If your stadium does not hold enough seating you may want to decide if this is enough seating or if you need to build an upper deck.  How many seats will be necessary for this upper deck and is this feasible for your budget?

 

 

 

 

 

 

 

 

 

Expected Student Response

 

 

This will vary for each group and each stadium within each group.

   

Evaluate

Teacher will collect blueprints and all work done on each stadium for seating.  Teacher will make sure that each group is making feasible blueprints.