Lesson plan
Inside mathematics
https://www.illustrativemathematics.org/content-standards/tasks/84
video clip- Insider Traffic Jam
https://www.youtube.com/watch?v=y__bLEDh4eg
Reference to Math Modeling http://www.sciencedaily.com/releases/2007/12/071219103102.htm
Traffic Jam is costly for everyone
http://uproxx.com/life/2015/11/worst-traffic-bottlenecks-report/
SOL Math: What have students learned that will support them in developing this model? What do they need to know to be successful on this task? Consider both content and processes.
What will students be working on?
| ANTICIPATE |
| Describe two strategies students might use to model this problem. |
| STREATEGY 1 – |
| What are the strengths and limitations of this approach? |
| STRATEGY 2 |
| What are the strengths and limitations of this approach? |
| Identify three challenges students might encounter when working on this problem. |
| ENACTING A MODELING TASK |
| ASK |
| What information will students need in order to begin their work?The problem:
What questions will you ask in order to support students as they investigate the problem? Is this question posed as a mathematical problem? Why or why not? |
| MONITOR |
| What do you want to see and hear from students as they progress? |
| REGROUP |
| What ideas do you want to make public in order to advance students’ work?(1) A strategy that draws explicitly on the student’s background knowledge
(2) A strategy that focuses on xyz… (3) A strategy that focuses on xyz…. (4) A strategy that focuses on xyz… |
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:
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
Build Solutions: (Sample student work in blue)
| 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.”
Extension – Pythagorean Theorem
Manual folding ramp is only $200 and weighs 14 pounds. Student helpers could be assigned to carry and set up the ramp!
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?
Mathematical Modeling Wonders
http://www.intmath.com/blog/videos/friday-math-movie-the-rice-show-6312
http://news.bbc.co.uk/2/hi/science/nature/7617191.stm
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