- How will you calculate the total cost of your building?
- How will you determine the amount of people who will attend Friday night games?
- What are the standard dimensions of a high school basketball court?
- How can the court be used for different sports?
- What sports will be using the facility?
- How much is the material for the gym floor?
- What type of flooring should be used on the court?
- What is the best type of flooring for the locker rooms and cost per square foot?
- What type of flooring will last the longest and have the best quality?
- How many people will the facility hold?
- What percentage of the students are female/male?
- How many people can fit on one row of bleachers?
- How many bleachers will you install?
- How many students and staff are in this building?
- How many lockers will be needed in each locker room?
- How many showers and toilets will be needed in each locker room?
- How many changing rooms will be needed in each locker room?
- How many sinks will be needed in each locker room?
- How many benches will be needed in each locker room?
- What type of storage will the staff need for their tools and necessities?
- Will you have one floor, two stories, etc?
- What are amenities?
- How can you determine what amenities are necessary for a high school gym and locker room?
- What are the size constraints of space to build?
- How will the number of people the gym will hold affect the number of restrooms needed?
- How high should your ceiling be above your basketball court?
ACS (Real world applications; career connections; societal impact)
Real World Applications
Students will learn how to develop equations for determining the amount of square footage a building can use. Students will design the layout which will help them conceptualize space and functionality (certain designs are done for a reason) keeping scale factors in mind.
Interpreting graphs and being able to provide valid reasons using math is helpfully for everyone
in society. Being able to use equations to determine how much a building would cost or being able to determine the maximum number of square feet needed for a certain budget. You can also determine length of payments on a mortgage.
Architects, contractors and architectural and mechanical engineers would be the careers associated with this challenge.
Individuals need to understand the concept of cost and ways to maximize space in work areas. This will help in building future homes as well as bigger facilitates. Many individuals struggle with the concept of organization. Designing a space that must maximize space is a great way of using organization, not only to organize your notes in school, but your files in an office, your files on your computer or your equipment for sports games.
Engineering Design Process (EDP)
Challenge – Students will have to design a gym and locker rooms for their school given a workspace and determining the equations associated with initial costs and the additional variable costs.
Research – Students will use websites to find useful data for designing their space; for example, what are the dimensions of a high school basketball court?, What are the dimensions of where the tape should be placed for out of bound lines?, What variables would add cost to the final project? What percentage of the gym is used for seating? How many people on average attend Friday night games? How many of those people are men/women? How many restrooms are needed? Will there need to be more stalls in the men’s or women’s restrooms? Etc.
Brainstorm and Essential Questions – Students will use their background knowledge in addition to the math concepts gained from the activity and apply to calculate the cost for a certain size building as well as the area of the space needed.
Build – A paper sketch drawing that shows the gym space, locker room space, and dimensions. Use excel to calculate the cost of different size buildings with the different amounts of restrooms, tiles, lockers, bleachers and so on, using equations, charts, graphs on Microsoft Excel.
Redesign – After each group presents their findings on the costs of their portion of the construction including the arithmetic/geometric sequence; each group will then take all research into consideration when finalizing their design.
Final Conclusion – Students will give a presentation that must show and explain all of their findings in the fashion of a pitch/sale. Students will present in front of the individuals who have the final say decision in the design of the new 2015 Hughes STEM High School Gymnasium with locker rooms; therefore, students must convince the board to choose their design based on the numbers that make their design work.
Unit Academic Standard
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Lesson 1: Introduction to the components of Challenge Based Learning
Hook plus PowerPoint introduction (1 class period, 55 min); Pre-assessment (30 min)
Students will watch the video of one of the best gyms and locker rooms. Students will answer questions and class will hold a quick discussion. Students will take a pre - assessment that will provide a way to gather key information about what students know and are able to do prior to instruction. We will then move into the introduction PowerPoint that focuses on the big idea, essential questions, and guiding questions and finally I will present the challenge.
Activity 1: Hook- A combination of two videos will be shown and two questions will be posted. Students will have 5 minutes to individually answer the questions and then the class will have a quick discussion.
Activity 2: Pre-Assessment- Students will take a pre assessment to gather data about what students know prior to the lesson. Data will be recorded for further use.
Activity 3: PowerPoint Introduction -The big idea will be introduced to the students. I will ask students to think of two essential questions that relate to the big idea (3 min). We will share out as a class and I will chart the responses on the board. Once I guide the class to the essential question I have in mind we will start brainstorming ideas for guiding questions. Each student must brainstorm at least 4 guiding questions individually (5 min) and we will share out and chart in the same fashion as for the essential question.
Lesson 2: Determine variable costs and derive equations.(4 bells)
Students will work through an activity to develop an understanding of the extra costs associated with certain materials. Students will be placed in groups of three and will use the Engineering Design Process to begin solving their challenge. Students will present their findings to the entire class and other groups will choose to use the information provided or decide to change some parts depending on their research and their specific design.
Activity 4: Construction Cost of Tiles (1 bell, 55 min)
Students will use given dimensions of an area to calculate the number of tiles needed to tile the area, as well as, the number of boxes of tile, the total cost of the area and the cost per square foot of tiled area. Students will have to research how the cost of this room could be decreased.
Activity 5: Groupings with given variables ( 3 bells, 165 total min)
Students are grouped and given a specific variable to research. Students will start to develop an understanding of cost variances dependent on the change of materials as they research prices for restrooms, hallways, lockers, showers, basketball court, storage closets, bleachers/seating, sinks, entrance, and stairs; as well as, researching the percentage of gymnasiums that are restrooms, bleachers, walls, etc. (List might change depending on discussion with students) Once research is complete students will present their findings with the class. Each group will take the research their classmates discovered and use them to finalize their design including formulas of percentages and costs of specific rooms in addition to the entire gym. Students will present their final findings in an Excel spreadsheet including: equations, cost, data tables, graphs and percentages of specific areas of the design. Students will need to present understanding of information included in their excel document. Each student will need to have a part on speaking during the presentation.
Knowledge that all sequences are not arithmetic but when asked to give examples they can only give arithmetic examples.
Sequences only containing whole positive numbers.
Pre-Unit Assessment Instrument
Post-Unit Assessment Instrument