**The Essential Question**

- What design makes the sturdiest bleachers?
- How much space does the average person need?
- What should the slope be?
- How high up should the bleachers go?
- How can I build cost effective seating?

**The Hook**

Students will be given the following math problem:

''Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?"

Students will work with a partner/small group to solve the problem. Students will share their method for solving. Afterwards, Teacher will start a discussion by asking the difference between a grandstand and bleachers. She will show pictures of stadiums at local high schools. The Athletic Director will take students on a short tour of the athletic facilities. Students will then propose a challenge as their Exit ticket.

**Anticipated Guiding Questions **

- How much space is needed for each person to sit comfortably?
- How many people can fit on a bleacher?
- How many rows should the seating be?
- What is the best material for building outdoor seating?

**Engineering Design Process (EDP)**

Students will implement their solution by building a scale model. They will know their solution worked by mathematically showing what the actual dimensions would be and that they adhere to human ergonomic factors. Also, by evaluating to see if the model adheres to safety and ADA guidelines.

Students will create a written proposal to present to the Athletic Director. Power Point will be used to write the Proposal. Students will be provided with guidelines to assist them in writing their proposal.

What academic content is being taught through this Challenge?

**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.6** Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

**8. EE.B.5** Graph proportional relationships, interpreting the unit rate as the slope of the graph.

##### Misconceptions

Students tend to want to write slope as run/rise, because they learn when graphing on a coordinate plane you move along the x-axis first.

Students often see scaling as enlarging something. They do not consider decreasing the size of something.

##### Unit Activities

Pre-Test - will be given prior to the start of this unit. It is presumed that students are familiar with slope, scales, and finding area.

Day 1:

a) Hook: Give students *Ticket Problem* to solve with a partner or small group. Have two groups share their method of solving. Ask students questions about the types of seating (grandstand, and bleachers) mentioned in the problem. Ask which types of seating is present at our school. Show students pictures of seating arrangements at other local schools. Have the Athletic Director take class on a quick tour of the athletic facilities at our school.

Day 2: Present Challenge: Create a scale model of an outdoor seating arrangement that can accommodate 75 fans.

Begin brainstorming ideas

Day 3:

a) Students go the gym to make observations and take measurements

b) Students go outside to take measurements of field and surrounding area

c) Students use graph paper to make a sketch of outdoor area and proposed placement of bleachers

Day 4:

a) Students research information about bleachers

b) Teams work on sketches and math calculations

Day 5:

a) Students finalize sketches and submit to teacher for approval.

Day 6: Build model of seating according to scale drawing specs

Day 7: Finish scale model of seating design

Day 8: Students write a Seating Design Proposal to the Athletic Director

Day 9: Students present their proposals to the Athletic Director/Principal/Assistant Principal

Day 10: Post-test

##### Pre-Unit and Post-Unit Assessment Instrument

Pre-Test/Post-Test