Mathematical Modeling Template

What is your favorite?

Walking into Sweet Frog presented me with a dilemma. What flavor and topping should I choose?

http://sweetfrog.com/yogurt/flavors

http://sweetfrog.com/yogurt/toppings

Pose Questions

What math modeling task do you want to present?
Is it real-world and does it require math modeling?

Information gathered

What variables will you consider? What data/information is necessary to answer your question?

Assumptions and Constraints

What assumptions do you make? What are the constraints that help you define the problem?

Build Solutions

Generate solutions.

Validate Conclusions

Now, take your solution and apply it to the real world scenario. How does it fit? What do you want to revise?

SOL Math:

Contributions from Team Sweet

Kelly Cheatham, Brian Wiseman, Jenny Sample,

Michelle Santa, Tiffany Reed, Avery Ginn, Susan Foster

from Fairfax County Public Schools

Mathematical Modeling: Furnishing the apartment

Pose Questions

Your family is moving into a brand new apartment. There is no furniture in it. Your parents told you that you can furnish your room as you would like. You have a budget of $1,500 that can be spent only in Ikea. Can you plan the shopping list, so that your room is fully furnished and ready to move in?

Information gathered

Total amount of money: $1,500.

Shopping place: Ikea.

Assumptions and Constrains

Students will assume what kind of furniture they need to fully furnish the room. They will also decide what furniture is necessary for living.

Then students will go to the Ikea website and choose the furniture they need, keeping in mind that in sum the furniture cannot cost more than $1,500.

Build Solutions

Students will create a list of the furniture items with their prices. The total price must be less or equal $1,500. The list must include all necessary for living items.

Students might create:

• Pictures (plan of the room);
• Tables (items with prices).

Validate Conclusions

Students will check that (1) total amount of money needed to purchase all the items from their list is less or equal $1,500; and (2) all necessary for living items are included.

SOL Math:

5.5 The student will a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit).

Pose the Question:

We are welcoming a new teacher to our school that needs a wheelchair to move from place to place. How can we make our school more accessible to her?

Information for Teachers to Frame Problem for Students:

While newly constructed and renovated school buildings must be ADA compliant, structural modifications are only one way that an older public school can demonstrate that it meets the needs of students. From http://www.pacer.org/publications/adaqa/school.asp:

Making structural improvements to an existing building such as installing ramps or elevators is one way of achieving program accessibility. However, structural accessibility is not required if there are alternative means of achieving program access such as providing the service at an accessible site, relocating a class or activity to a different room in the building, or having library staff retrieve books for students or teachers who use wheelchairs. Auxiliary aids and services such as interpreters would have to be provided if necessary for effective communication at school programs, conferences and other activities.

School districts are not required to take any action that would result in a fundamental alteration of the nature of the program or activity or in undue financial and administrative burdens. However, public entities must take any other action that would not result in a fundamental alteration or undue burden but would ensure that individuals with disabilities receive the same benefits and services offered to others without disabilities.

 

Constraints

Assumptions

Budget:   How much funding do we have? ·Time: How much time are we given to complete the project? · County Building Codes · Safety

·       Must meet  building codes ·       Self-propelled wheelchair ·       Make the school accessible for her to function on a routine school day (not every room has to be wheelchair accessible). ·       Teacher weighs no more than 150 lb. ·       Teacher will come to school with a fully charged battery for wheelchair every day. ·       Students have other teachers for “specials” – music, art, P.E., library time

 

Variables

 

• Size of wheelchair, weight of wheelchair
• Budget
• Schedule for construction
• Number of steps that have to be negotiated by the wheelchair

 

 

Build Solutions: (Sample student work in blue)

 

• Survey the building to determine access points and necessary changes needed to be made.

 

Access Point	Number of Stairs or Steps	Width of Entryway	Space for teacher in wheelchair	Other considerations?	Solution
Front entrance	4	34 in or 86.4 cm		4 doors – stairs are wide enough to accommodate a ramp	Construct permanent ramp on left half of stairway.
Student’s classroom	0	34 in or 86.4 cm	Need to arrange desk spacing so that teacher can move throughout room		Create map for custodians and mark necessary furniture locations
Art room	0	N/A	N/A	Assume teacher does not need to enter room – no modifications	None
Music room	1	N/A	N/A	Assume teacher does not need to enter room – no modifications	None
Cafeteria	0				None
Gym	0	34 in or 86.4 cm		There is a P.E. teacher, but sometimes classes attend presentations in gym	None
Little Theater	2	40 in		Insufficient space for ramp – consider a motorized lift	Manual folding ramp – students transport
Computer Lab	0	34 in or 86.4 cm	workstation height too low for wheelchair
Media Center	0	34 in or 86.4 cm			None
Restroom	0	40 in		Faculty restroom is ADA compliant	None

 

 

2) Research the dimensions and weight of wheelchairs.

Specifications

Weight Capacity       250 lbs.

Weight           105 lbs.

Heaviest piece  37 lbs.

Seat Width       17″

Seat Depth       16″

Seat-to-Floor Height            19.5″ – 22.5″

Overall Width              25.5″

Overall Length            35″

Overall Height             36.5″

Front Wheel Size         6″

Rear Wheel Size           9″

Turning Radius         15.5″

Max Climbing Angle            6 degrees

Info Source: http://www.1800wheelchair.com/product/shoprider-jimmie-power-chair/

 

Notes: The maximum total weight (teacher + wheelchair) = 255 lbs.

Total width should include an extra 6 in.

 

From http://www.adaptiveaccess.com/home_changes.php – “The doors need to be at least 32” wide with a straight in approach. If the doors are located in a hallway you need plenty of turning space and 36” door. Everyone’s needs are a little different, so you may have to make a few changes to the plans to suit your individual requirements and physical limitations.”

 

• For the front entrance: Use manipulatives to construct a scale model of ramp

1. Use proportional reasoning (similarity)

Extension – Pythagorean Theorem

 

• For the Little Theater: Motorized vertical lifts are too expensive!

1. http://www.tigermedical.com/Products/Folding-Ramp__INVICR330-.aspx?gclid=CM6RzPPoqMcCFYiPHwodqX8K3A

Manual folding ramp is only $200 and weighs 14 pounds. Student helpers could be assigned to carry and set up the ramp!

 

 

• For classroom:             Use graph paper to create scale model of classroom

1. Cut out scaled furniture
2. Test designs checking for aisle width and turning radius
3. Teacher should be able to access student work at each desk

 

 

Validate Conclusions:

Invite architect or construction engineer from community to evaluate our designs.

 

Further study: How will our changes affect traffic flow for all the students?

Apply model to a new problem – student wheelchair access?