Remodel, Replace, or Maintain?, The Locker Issue


Author:

Barbara Kenney

Unit Title:

Remodel, Replace, or Maintain?, The Locker Issue

Grade:

7th

Subject:

Mathematics

Estimated Duration:

12 days (50-55 minute periods)

Unit Activities:

Activity 1: Proportion and Scale Factor

Activity 2: Composite Shapes

Activity 3: Nets

Activity 4: Pearson: Surface Area of Right Prisms

Activity 5: Challenge:  Remodel, Replace, or Maintain?, The Locker Issue

Background Knowledge: 

Students should be able to work with basic operations of rational numbers, writing and solving proportions, precise measuring, converting measurements within the same unit system, and application of area formulas for circles, triangles, and parallelograms before starting this unit.  

Date:

July 2013

Unit Summary

Students will determine a need to replace lockers at their school, determine the amount of lockers the school needs for all students, and determine the amount of space available for lockers.  In groups, students will then design, sketch, and build a scale model of a locker that they would like to see installed at their school and present their design, scale drawings, scale models and cost analysis to a school improvement committee.

The Big Idea (including global relevance)

Remodel, Replace, or Maintain?

Students will look at their school and talk about structural needs for repair or replacement in relationship to needs such as safety, environmental, and aesthetic purposes.  They will then look specifically at the issues of lockers in their building.

(Global Relevance)

Populations are growing and there is constant demand for rebuilding or remodeling existing structures for safety, environmental needs, technological advances, and aesthetic purposes with time and financial constraints.     

The Essential Question

What design is the most efficient and cost effective locker for Glen Este Middle School students?

Possible Student Essential Questions:

  1. Do we need to replace the current lockers?
  2. Can we repair the current lockers?
  3. How is a locker made?
  4. What is the most cost efficient material to make a locker from?
  5. How do you figure out how much material we will need?
  6. How many lockers do we need?
Justification for Selection of Content

The current lockers at Glen Este Middle School are very outdated, small, and damaged.  The students complain every year about the state of these lockers, therefore, a great opportunity for them to see how much it would cost to replace these lockers, have input on what new lockers should have in them, and if possible seek out funding to replace the existing ones.  It is also a great application of the 7th grade geometry standards for problem solving with scale models, surface area and volume. 

The Challenge

Glen Este Middle School is taking bids from locker companies to replace or repair the lockers they currently have.  You own a locker company and want to place a bid.  

As part of the bid process, Glen Este Middle School is asking all companies to present their bids to the School Improvement Committee so they can make their final decision on what locker company they will be choosing.  In your presentation be sure to include highlights of all the features of your locker, scale diagrams of your design, a scale prototype of your locker, and how you specifically determined the cost you will be charging.  

The Hook

The hook in this circumstance is personal relevance because the current lockers at Glen Este Middle School are damaged, outdated, and aesthetically unpleasing. As an opening day activity, students will put together a short commercial that highlights their locker replacement company and identifies and justifies the need to replace lockers at Glen Este Middle School.   

Teacher's Guiding Questions
  1. How do you make a locker?
  2. What are the essential parts of a locker?
  3. How much does a locker cost to make?
  4. Who uses a locker?
  5. What goes in a locker?
  6. What are the minimum and maximum dimensions a locker can have to hold necessary school supplies, (book bag, coats, lunch boxes etc.), yet have 1200 lockers fit in the building?
  7. What shape must a locker be?
  8. What material is the most cost efficient to use?
  9. What features do the people who use the locker want the locker to have?
  10. Can I reuse and/or recycle current lockers?
ACS (Real world applications; career connections; societal impact)

Applications:  Students will encounter many problem solving situations in life where a knowledge of fitting items in a given specific space with specific dimensions will be important.  For example, carpet in a room, tile on floor, stacking items on a shelf, pouring concrete, and many, many other examples.  In addition, students will also encounter many problem solving situations where scale factors and converting from scale to actual size will impact their lives like reading a map or reading blueprints.

Career connections:  Engineers such as Construction Engineers, Civil Engineers, Environmental Engineers and Architectural Engineers, would use these concepts on a regular basis. In addition, anyone who owns a home or works in the design or construction field would use these concepts on a regular basis.

Societal impact:  Our society relies on detailed, accurate scale drawings to function.  For example we use blueprints for identifying major components such as utilities for cities and infrastructures, and design implementations of bridges, buildings, and highways.  In addition, we must apply properties of two and three dimensional shapes daily for the building and design process of residential dwellings, office buildings, retail outlets, hospitals, schools, and other buildings.  Finally, we must consider reducing, recycling, and reusing materials to minimize environmental impact. 

Unit Academic Standard

7th grade Mathematics

  • Domain: Creating, Comparing, and Analyzing Geometric Figures
  • Cluster:  Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
  • Standard:  7.G.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.

7th grade Mathematics

  • Domain:  Geometry
  • Cluster:  Draw, construct, and describe geometrical figures and describe the relationships between them.
  • Standard: 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.

6th grade Mathematics

  • Domain:  Geometry
  • Cluster:  Solve real-world and mathematical problems involving area, surface area, and volume.
  • Standard: 7.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Unit Activities

Day 1: Introduction to the Unit

A.     Pretest

B.    Hook: Students brainstorm big idea and essential questions

C.    Students create commercials on current status of GEMS Lockers

Days 2:  Scale factors and scale drawings (Lesson 1, Activity 1)

A.    Scale factors and proportions

i.    Using Scale Factors on Maps

ii.    Cookie Conversions

iii.    Gummi Bear Basketball (Each group will get a different basketball court user: –Barbie, Gummi bear, Little people, army man, etc)

Days 3:  Scale factors and scale drawings (Lesson 1, Activity 1)

A.    Scale factors and proportions

i.    (continued from Day 2) Gummi Bear Basketball (Each group will get a different basketball court user: –Barbie, Gummi bear, Little people, army man, etc)

B.    Students will measure the current locker space at Glen Este Middle School.  Each team will draw scale drawings of the hallways and its dimensions with detail of current available locker space.

Day 4:  Composite Shapes (Lesson 1, Activity 2)

A.    Review of calculating area with formulas (Circles, parallelograms, and triangles)

B.    Finding the area of irregular shapes (Composite Shapes)

http://illuminations.nctm.org/LessonDetail.aspx?ID=L583

Day 5:  Nets of three dimensional prisms (Lesson 2, Activity 1)

A.     Nets:  Geofix shapes

http://www.didax.com/shop/searchresults.cfm/Keyword/geofix.cfm

Day 6:  Surface area of three dimensional prisms (Lesson 2, Activity 1)

A.    (Continued from Day 5)  Nets:  Geofix shapes

B.     DIGITS 13-1 Surface Area of Right Prisms

https://successnetplus.com/

Day 7:  Surface area of three dimensional prisms (Lesson 2, Activity 1)

A.     (continued from Day 6) DIGITS 13-1 Surface Area of Right Prisms

https://successnetplus.com/

Day 8:  Challenge, (Lesson 2, Activity 2)

A.    Engineering Design Process

a.     Identify the need

§  As a team, the students have already identified the need to replace and/or repair lockers and described the problem in their own words.  In addition at this point every team has already created a video commercial ad for their locker company that highlights the need for the lockers that is between 30 and 60 seconds long.   This will be shown during their presentation to the committee. 

b.    Brainstorm

§  Students will now find and record as many solutions to the locker issues their team can find and what needs they are considering with those solutions.  They will have computers and/or Ipads for research at their disposal if wanted. 

c.     Generate ideas and explore possibilities

§  Students will supply 3 detailed scale sketches, listing materials in each sketch and the pros and cons of each design.  (Label materials locker will made of, different views, and specific dimensions)

Day 9:  Challenge, (Lesson 2, Activity 2)

A.    Engineering Design Process (continued from Day 8)

a.     Students will select an approach

§  Select their best design of their 3 sketches

§  Describe why they chose that design

§  Plan to build it

b.    Students will build scale prototype

§  Students will discuss any issues/successes in building

§  Plan for testing

Day 10:  Challenge, (Lesson 2, Activity 2)

A.    Engineering Design Process (continued from Day 9)

a.     Students will refine prototypes

§  Students will talk about what worked, what didn’t work and what could work better

§  Students will make more prototypes if necessary

§  Students will turn in final sketch and prototype

b.    Students will write out an itemized cost analysis of their locker design

c.     Students will create a presentation for the “School Improvement Committee”

Day 11: Challenge, (Lesson 2, Activity 2)

A.    Students will present bids to the School Improvement Committee.  Each presentation should be less than 5 minutes. 

Day 12: Post test

A.    Post test

Day

Description

1

Unit Pre-test, Introduction to Unit:  Hook and Locker Company Video

2

Scale factors and proportions

3

Finish scale factors and proportions; Find current locker space

4

Composite Shapes

5

Nets

6

Nets (continued); DIGITS 13-1 Surface Area of Right Prisms

7

DIGITS 13-1 Surface Area of Right Prisms (continued)

8

Challenge(Identify the need, brainstorm, generate ideas)

9

Challenge (Select an approach, build prototype)

10

Challenge (Refine prototypes, cost analysis, presentation)

11

Presentations

12

Post-test

Where the CBL and EDP appear in the Unit

Lesson 2, Activity 4 (Days 8-12)

Misconceptions

Students will confuse volume and surface area formulas and appropriate uses of each.  It helps to have them draw the nets and refer back to finding the area of composite shapes so they are breaking down the problem into smaller steps.  Another misconception is converting square units.  For example, often students will try to convert square inches into square feet by dividing by 12 instead of 12 squared, or 144 square inches.  

Additional Resources

Scale Factor Activity: 

  • Composite Shape Activity:  NCTM Illuminations website

http://illuminations.nctm.org/LessonDetail.aspx?ID=L583

  • Math Manipulatives:  Geofix Shapes

http://www.didax.com/shop/searchresults.cfm/Keyword/geofix.cfm

  • Surface Area Activity:  Right Prism Surface Area

https://successnetplus.com/

  • Web resources for free 3D Cad programs for middle school students

http://www.ncs-tech.org/?p=7696

Pre-Unit Assessment Instrument

Pre-test

Post-Unit Assessment Instrument

Post-test