GeoCities Project - Mr. David A. Peterson

Transcription

GeoCities Project
Project Overview
Name:_________________
Team Mates’ Names:_________________
Date:_________________
Teacher:_________________
Introduction:
You and your team will build a model city using 3D geometric shapes. Here’s a picture of the kind of city you might build: Major Tasks:
You and your team will work through several phases of design and construction. The major phases of the project are: 1. City Planning 2. Architectural design 3. Construction The details of each of these steps and how will be broken down in greater detail the booklet as you work through it. 1 of 39 GeoCities Project
City Planning Phase
Name:_________________
Date:_________________
Teacher:_________________
Step 1: Choosing a Site The first step in planning any city is deciding where to build it. Cities are often built near rivers, lakes, or oceans though not always. City planners must think about how the site may or may not meet the city’s needs. Task: Considering Features of a Good Site (5 points) In your team brainstorm at several (at least 5) traits that make a particular site a desirable place to build a city. List these in the table below. 2 of 39 Task: Selecting a Site (2 + 3 points) In your team, sketch a site which you think would be a good place to build a city. Use scrap paper. Once you have a site that you agree on, sketch your site below. Be sure to label lakes, rivers, mountains etc: Write a brief paragraph justifying why your site is a good one for a city. ______________________________________________________________________________
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______________________________________________________________________________ 3 of 39 Step 2: Zoning It would be awful having a house next door to a smelting plant. For this reason Cities are typically broken up into different zones for different purposes (e.g. residential, industrial, downtown business core, park land etc.). Think about what zones will be in your city. Task: Choosing how to zone and zone needs (5 points) In your team, think about what the sorts of zones you will divide your city into. For each zone, consider the geographic considerations for your zone. For instance you may place parks in “pretty” areas, industries in less pretty areas near water, etc. 4 of 39 Task: Zoning your city (2 + 3 points) Resketch the your site from Step 1 on some scrap paper. In your team, divide the site up into zones, taking into consideration the needs you listed above. Once you have a zoning that you agree on, sketch your zoned site below: Write a brief paragraph explaining why you chose to zone your city as you did. ______________________________________________________________________________
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____________________________________________________________________________ 5 of 39 Step 3: Planning for Community Needs & Wants Imagine you are injured, you had better hope your city has a hospital! Do you like to play hockey? Maybe an arena is in order. Think about what you would like to include in your city. Task: Identifying Needs and Wants (5 points) In your team, create a list of at least 8 features you would like to include in your city. Unfortunately, you probably won’t be able to build everything, so categorize items into needs and wants to help you prioritize. Also consider which zone you would build them. 6 of 39 GeoCities Project
Architectural Design Phase
Name:_________________
Date:_________________
Teacher:_________________
While we could make our entire city out of cubes, this would make your math teacher pretty sad and wouldn’t be as interesting to look at. As an architect you will combine basic 3D shapes to make interesting looking buildings. It is important for you shapes a lot since you will have to be able to calculate the capacity of buildings and the quantities for the building supplies list! Step 1: Investigating Properties of Shapes
Let’s practise our skills with a couple of examples. Use a ruler to measure to the nearest 0.1 cm and answer in either cm2 or cm3 as appropriate. Task: Calculate the Volume of a Cylinder (2 points)
Get a copy of the cylinder net from your teacher, as well as a ruler, scissors, gluestick/tape so that you can assemble your shape and do the calculation. 7 of 39 Task: Calculating the Surface Area of a Triangular Prism (5 points)
Get a copy of a triangular prism net from your teacher. Describe how to decompose the net into simpler shapes:
Calculate the area of the simple shapes:
Determine the total surface area:
Task: Calculate the Surface Area and Volume of a Hexagonal Prism (8 points)
Now for a more challenging one! Get a hexagonal prism sheet and a glue stick from your teacher. But I don’t know the area of the hexagon base of the prism! I need this to
calculate both the volume and the area!
True enough, but you can approximate it. Cut up the hexagonal base and try to arrange the pieces into a rectangle (and maybe a partial row) on the grid paper on the next page. Glue the pieces in place. Be careful to fill squares up entirely but not to overlap pieces! 8 of 39 9 of 39 What is the approximate area of the hexagonal base? (2 points)
Calculate approximate surface area of the hexagonal prism. Be sure to
explain what your numbers mean! (2 points)
Calculate the volume of the hexagonal prism. (2 points)
Either ask you teacher for the exact formula or Google “volume of a
hexagonal prism” to calculate the volume precisely. How close was your
estimate? (2 points)
10 of 39 Step 2: A Prototype Building
Now it’s time for you to build your own prototype building! Task: Build a prototype building (4 points)
Combine two or more 3D shapes together to make a building. You may use prisms and cylinders, or more exotic shapes if you are feeling adventurous! Sketch your building below What shapes did you use and how did you put them together? ______________________________________________________________________________
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____________________________________________________________________ 11 of 39 Task: Drawing Different Perspectives of Your Building (6 points)
Draw a front, side and top view of your shape. Indicate approximate lengths of different sides in your drawings: 12 of 39 Task: Calculate the Volume of Your Building. (5 points)
If you just used prisms, go ahead and use the formulas that you know. If you used more exotic shapes, describe how you might find an approximate volume, then ask your teacher or Google the formula to find the actual volume. Be sure to state any formulas that you use and to show all of your work! 13 of 39 Task: Calculate the Surface Area of Your Building. (5 points)
Use extra nets and cut out one of each of the faces in your shape. Glue them below with some extra space for calculations. IMPORTANT: Only include external faces. If you you know the formulas to find the areas of the faces, go ahead and calculate. To find the approximate area of weird shapes, get extra grid paper from your teacher and use the technique we practised in step 1. 14 of 39 What is the total surface area?
Bonus Task: Calculating Construction Cost (1 bonus point)
Suppose the surface area of the final building is 400 m2 and is to be made out of sheet metal costing $45 per m2. What is the total cost in building supplies? 15 of 39 GeoCities Project
Construction Phase
Name:_________________
Date:_________________
Teacher:_________________
It’s Time to Build Your City!
Finally, you’re ready to begin construction. Work together with your team to build a beautify city. Keep in mind your earlier work, especially at the city planning stage, so that you can make your city the best place that it can be. Materials:
You can get shape templates, scissors, glue, and tape from your teacher. Feel free to bring things from home like markers, construction paper, and other things to beautify your city. If you find other shape templates, you can use them, just make sure you know the name of the shape! Marking Criteria: Do read this, an interview is part of it.
Item
Detailed Description
You used at least: ● 1 cylinder ● 1 cube ● 1 pyramid Variety of Shapes Used ● 1 triangular prism ● 1 rectangular prism ● 1 cone ● 1 composite shape Aesthetically Pleasing Design You incorporated all of the following: ● Attractive use of colour ● Neat folding of shapes ● Interesting road layouts ● Incorporation of unusual and interesting shapes Score Value
5 points if all present 4 points if missing one 3 points if missing two … 1 point ≤ 3 distinct shapes used 5 points if all present 4 points if missing one 3 points if missing two … 1 point if at least it doesn’t cause instant blindness Continued Below 16 of 39 Marking Criterion (continued):
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Detailed Description
Score Value
You ensured that all of the following criteria were met: ● Reasonable scale (e.g. houses are smaller than schools & hospitals) ● The construction is strong enough to be moved. Up to 2 points for reasonable scale + up to 3 points for strong construction. You are able to confidently answer your teacher’s questions about: ● City planning Decisions ● Engineering Decisions ● Shape Types ● Aesthetics ● How to fortify your city against possible Godzilla attack, zombie apocalypse, or similar random unforeseen situation. 5 points if all questions answered with appropriate justification. 4 points if most questions answered with appropriate justification. 3 points if some questions answered with appropriate justification. 2 points if a few questions answered with appropriate justification. 1 point if only few questions are answered, but without justification. Sound Engineering Individual Interview (3 minutes ish) The Interview: The interview be an informal Q&A session with your teacher that will happen while you are building your city. The goal is to see you thinking on your feet. If you are asked something that you don’t understand, feel free to ask! This is not something to fear, your teacher doesn’t bite!
17 of 39 18 of 39 19 of 39 20 of 39 21 of 39 22 of 39 23 of 39 24 of 39 25 of 39 26 of 39 27 of 39 28 of 39 29 of 39 30 of 39 31 of 39 32 of 39 33 of 39 34 of 39 35 of 39 Lesson Title: GeoCity Project
Lesson #: ______________
Date: __________________ Name: Derek, David, Kate
Subject: Mathematics
Grade: 8 Rationale: The purpose of this lesson is to have students apply their geometric knowledge to an interdisciplinary realworld problem. Hopefully, by introducing students to the world of cityplanning and architecture they will appreciate the importance of Geometry in everyday tasks. Prescribed Learning Outcome(s): Math 8: C2 Draw and construct nets for 3D objects C3 Determine the surface area of
− right rectangular prisms
− right triangular prisms
− right cylinders
to solve problems
C4 Develop and apply formulas for determining the volume of right prisms and right cylinders
C5 Draw and interpret top, front, and side views of 3D objects composed of right rectangular prisms Social Studies 8: Describe how physical geography influenced patterns of settlement, trade, and exploration Instructional Objective(s): Students should be able to: Construct 3D objects from 2D nets Calculate volumes and surface areas of basic 3D shapes Calculate surface areas of simple composite shapes Plan and construct a simple city layout using basic 3D shapes Defend decisions made regarding city layout on the basis of application such as: access to necessary city features, resource exploitation, aesthetics,etc…. Prerequisite Concepts and Skills: From previous lessons,students should be able to:

Calculate Volume and Surface areas of basic 3D objects (cubes, prisms) Understand the effect physical geography has on settlements 36 of 39 Materials and Resources: Teacher Students 1. Sample Geocity (or picture) 1.
Pens, Pencils, and erasers 2. Geometry notes package 2.
Geocity student package 3. GeoCity student package 3.
Scissors and tape 4. Extra scissors 4.
Pencil crayons 5. Extra pencil crayons 5.
Calculator 6. Tape 7. Computer and projector (for displaying
slides/overview of GeoCity project on overhead Lesson Activities: Teacher Activities Introduction (anticipatory set): The teacher will start off the lesson by introducing the new Geometry unit. The teacher will hand out introductory notes for the unit. Body: The teacher will introduce volumes and surface areas to the class. They will go over several examples of surface area and volume calculations. The teacher will hand out the package for the GeoCity project to the students and outline the basics of the project to the class. They will show the students an example of a completed GeoCity for comparison. The teacher will assemble the students into their groups for the GeoCity project. The teacher will give the students time to get started on their project. During this time the teacher will circulate and make sure that all of the students understand the Student Activities Students will take note of the new unit that they will be studying. Students will take notes and ask questions. After one or two guided examples, students will be given time to complete “on your own” practice questions. Students will ask questions about the project and take note of what they will be expected to do. Students will get together in their new groups.
The students will familiarize themselves with the assignment and determine the roles of each member in the group. After the Time 5 min 20 min 10 min 5 min 37 of 39 assignment and what is expected of them. Additionally, the teacher will ensure that the
students stay ontask and will be formatively assessing the students’ understanding as they work. Closure: In the last 5 minutes of class, the teacher will ask students to clean up their projects. If students have gotten to the point of actually working with a cardboard sheet for their landscape, the teacher collect them and keep them safe until next class. The teacher will remind the students that they should be working with their group mates outside of class to begin to plan their GeoCities so they can continue working on it next class. The teacher will dismiss the students at the bell. groundwork has been laid, they will work through their handout and begin the first phase of the project (site planning and design). Depending on their productivity, they
may even begin planning their GeoCities. Students will clean up their workstations and give any progress they have made on their physical GeoCities to the teacher for safekeeping. Students will take note of their group mates and will arrange to talk after class to discuss their GeoCity plans. Students will leave for their next class. 33 min 5 min 2 min It is understood that the GeoCities project will be done over multiple days, this lesson plan is just for the first day. The activity booklet is designed to so that it can be picked up and put down as needed by the teacher, likely over at least 3 days, one for each phase. Universal Design for Learning (UDL) and Differentiated Instruction (DI): Learning activities in the workbook are designed to engage students in multiple ways. Multiple intelligences are incorporated in the following ways: ● Visual Spatial: Students are building shapes and drawing different perspectives. ● Verbal Linguistic: Activities include written components as well as an interview at the end ● Logical Mathematical: The Architectural Design Phase has students doing calculations in various ways ● BodilyKinesthetic: Many of the activities are very hands on. Students are manipulating “real” objects ● Interpersonal: Most of the activities involve group work Many of the tasks are sufficiently open as to be very tailorable to different students’ levels. For instance the “Build a Prototype” step gives students the freedom to choose relatively simple buildings (e.g. rancher style house) or very complex ones. The teacher will encourage students to choose appropriately. The interview portion of assessment is also very adaptable to student ability. 38 of 39 Organizational Strategies: This activity is intended to be spread over a number of lessons. Since this is an activity that takes a lot of preparation time, classes can be structured so that phases of this activity can be completed on different days after some other main lesson (on a related geometry topic). For example, in this particular lesson, the teacher will introduce the new geometry unit. After learning about volumes and surface areas, and explaining how to construct a composite object, the teacher introduces the GeoCity project and gives students a chance to get started on it. This way, as the students learn the grade 8 geometry curriculum they can work on their project and apply the skills they learned each day. This allows the students to have plenty of class time to complete the project while still spending class time covering new content and having students solve problems on it (as well as the problems incorporated into the project). This also allows the teacher to use his or her discretion when deciding how much time to allow students to work on the project on a given day based on how productive (or unproductive) they will likely be. Behavioural Management Strategies: Groups of 34 , preferably heterogeneous, will be chosen that the teacher expects will work based on past experiences. The hope is to minimize the amount of discord within groups as to avoid having to deal with this. Should minor squabbles occur, most of the activities can be done reasonably independently except for the final placement of buildings in the city. In the worst case scenario, the teacher can always split a group up and give each subgroup responsibility for a particular zone, then rejoin the city at the end. The teacher will have to manage the noise level, though it is expected that the noise level will be higher than normal. The teacher may wish to check with surrounding colleagues and close some doors to minimize disturbances to others. Assessment and Evaluation: The Assessment and Evaluation criteria are detailed in the student workbook. This activity assesses students in a variety of ways, and has aspects that target a variety of think, write, do, and say tasks. Assessment components have been chosen to target a variety of intelligences with several tasks targeting several intelligences simultaneously. Most of the tasks have been designed so that they are adaptable to suit student needs without radically changing evaluation criteria. Extensions: The majority of tasks in the section are made to that they can be pushed far beyond their basic state. Indeed the prototype building task is actually relating to a MATH 9 PLO, but it is hoped that the authenticity of the task will drive students to challenge themselves (the teacher can scale it back if needed). There are all kinds of other ties between geometry and architecture that can be explored, as well as between geometry and the surveying. For those who just like making shapes, the mathematics behind origami folding is pretty neat too and very hands on! Reflections (if necessary, continue on separate sheet): 39 of 39