Part I: Choice of Task

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3rd TA 6

Part I: Choice of Task

Geometry is always an exciting unit in 3rd grade based on the students’ enthusiasm about using hands-on shapes and models. However, after they have spent precious instructional time building three-dimensional models of the shapes we are learning, I find myself telling the students, “Do whatever you want with it.” This has always seemed like a pointless task if the students are not working and learning for a greater purpose. Therefore, the task that I designed is one that incorporates analyzing three-dimensional shapes that the students have built first hand along with practical city planning and a review of coordinate grids. The students are asked to create a two-dimensional layout of their self-invented third grade city, Glitzburg. This layout must include specific buildings, roads and labels. They will then build two of their buildings and analyze them carefully, looking for faces, edges and vertices. Finally, the students must critique the roads and lines on their original map, answering specific questions in regard to their imaginary downtown. After this unit I feel that many of the students will see a purpose behind building three-dimensional figures and how they can relate to cartographers and architects in the real world.

Here is a sample of the project that I created:

Town Planning Project – Geometry and Data

Congratulations! You have been asked to become Glitzburg’s newest town planner. Your job is to lay out the new downtown area showing the community members what their new downtown will look like. Your task is very specific so follow the directions very closely. You would not want to upset any of the important town members!!!

Task 1 – Create a map of the community

Just like you have seen in our study of maps, you will need to create a map of the town, looking down at it as if you were a bird. Create this map on coordinate grid paper, making it easy to navigate and read. Each building should be located inside a specific box with its ordered pair listed (ex: library is located at A,6). To help the town members understand your plan for the town, you must label all buildings and name all street names. Your town must include the following items:

3 office buildings

Glitzburg Elementary School

Glitzburg Police Department

Glitzburg Fire Department

Glitzburg Town Hall

Glitzburg Groceries

Glitzburg Library

6 roads

You may also include items that you believe a downtown should include such as houses, a park, banks, restaurants, etc. This will be graded based on whether or not it includes the necessary buildings and how easy it is to read/understand.

Task 2 – Build Your City!!!

Now that you have a two-dimensional plan for your city, it is time to make it three-dimensional! Using your map as a guide, select 2 buildings from your city and build them using nets (outlines) of the three-dimensional shapes. Depending on how you drew the shape of the building or how tall you think it should be, your models must reflect this.

Task 3 – Analyzing Your City

Now that you have finished your models, you must give us a little information about your town and each of the buildings. Using the attached guide, please answer each question to the best of your ability. Be sure to check and double check to make sure you have identified everything you are supposed to.

Task 3 – Analyzing Your City

Buildings:

Building / # of faces / # of edges / # of vertices / Coord. Location
1.
2.

Roads:

1. How many roads are there in Glitzburg? ______

1. Name 2 sets of roads that are intersecting

1. ______

1. ______

1. Name 2 sets of roads that are parallel

1. ______

1. ______

1. Are any of the roads line segments? ______
2. If yes, which one(s)? ______

______

1. Select two locations on your map and create directions for how to get from one location to the next. Please write this once as if you were telling them the street names, then again as if you were explaining it on the coordinate grid moving north, south, east or west.

______

______

______

After reviewing the elements of this set of tasks, I believe that they should be considered doing mathematics. The students are first asked to create a downtown area for a community that they have created. The students are already familiar with this community and have a connection to its purpose. The layout of the town must be placed on a piece of grid paper, making it much like the maps that we have been studying. Having the students follow coordinate grids and ordered pairs provides a mathematical relationship to the seemingly “fun” and creative activity, allowing multiple pathways to an answer. Once the students have laid out the town with specific locations, they must create two of the buildings drawn, using the three-dimensional nets that we have studied. In order to put them together, the students must think through the study of three-dimensional nets, having them assess prior knowledge of their shape before building. Finally, the students must explore the relationship between what they created and the characteristics of geometric shapes and lines that are presented on their map. Due to their creation, their answers may be limited and the students must identify whether or not the roads that they have created meet the classifications of specific lines studied.

Part II: Thinking Through a Lesson Protocol

Selecting and Setting up a Mathematical Task

I currently have three goals for this lesson. My first goal is that the students will understand the relationship between city maps used in everyday society and the coordinate grids on which they are represented. The students see maps as social studies and coordinate grids as math. They are not making a larger connection between how different elements in mathematics can appear in other areas of life and I would like to stress the use of mathematics in many other fields of daily life. My second goal for the students is that they will better understand the concepts of faces, edges and vertices after building the shapes themselves. If the students choose to create a building that is composed of multiple three-dimensional shapes, the analysis of these features for that building could get much more complex than a simple cube. Finally, my third goal for this lesson is that it will solidify a concrete connection between various types of lines taught in math class and real life examples in their everyday life. Instead of the students memorizing figures and their definitions, I would like for them to see a purpose behind understanding various types of lines, for example on roads, and where they can be applied to a future career.

This task builds on the students’ previous knowledge in many ways. The students must first be familiar with coordinate grids, three-dimensional shapes, their characteristics and various types of lines. Without a clear understanding of how coordinate grids work, the students will not be able to follow directions from one location to the next as directed on question five. The students need to understand how a three-dimensional shape is classified so that they can describe it based on the number of faces, edges and vertices. Additionally, the students need to be able to describe how the roads in their city reflect various descriptions of interesting lines, parallel lines and line segments.

Considering the idea that students will be critiquing the work that they are creating themselves, there is no particular key with which to grade the accuracy of this assignment. Therefore, there is no concrete right or wrong way to complete these tasks, just as long as the students use the given materials and create their two-dimensional graph on coordinate grid paper. I believe that many of the students will first plug in the required buildings on their graph, then fill in roads or other areas around it. I am afraid that after the students lay out the map of the town, those who are still unclear on the characteristics of three-dimensional shapes may build two models that are too complex for their understanding. They may incorrectly identify the number of faces or edges if the buildings become concave or have rounded domes. I will work to keep the students’ building decisions challenging, yet within an attainable goal.

Once the students are busy working in pairs, I will expect them to be fully engaged for the duration of the work time, as each pair is free to move along at the speed most conducive to their learning style. If any of the students do not know how to move along to solve a task, they can first look to their partner for assistance. Next they will have another set of partners at their desk that they may refer to. Finally, the teacher is the last option when asking for help on this project. To help guide the students through a solid pace of work, I have created deadlines for each task. Therefore the students should understand how long to spend on each part. Looking at only creating two buildings from those listed on the map should not take a large amount of time. If various students spend more time decorating their building as opposed to moving on to their worksheet, they will be immediately redirected and reminded of their deadlines for each task.On the contrary, there are those few students who will finish first and then become disruptive. If this becomes the case I will ask them to do one of a choice of activities. That student may create another building to add to their chart, they may find more than the designated number of identified roads or they may create questions of their own based on book samples to match the map they created.

As the students work to complete this whole activity they will be working in pairs. The pairs will be decided based on where they are sitting in their groups. Each group is composed of one high, two average and one fragile student. This model is based on the Kagan (1994) model of cooperative learning strategies. Ideally, if the students take partners across from them at a table of four, pairs will either consist of a high and low average student or a high average and fragile student. Besides using each other for ideas and guidance, the students will have a variety of tools available to them for solving this problem such as notes from class, posters around the room, a glossary of terms in their math textbook and the teachers circulating throughout the room during the lesson.

Once the students have been introduced to all of the concepts necessary for sufficiently completing this task, they will be presented with the project outline. I will introduce the set of tasks by reviewing a coordinate grid from their text book that uses hypothetical places of interest, such as a book store, grocery store and bank. After the review of how to chart locations on a coordinate grid I will ask them to imagine what a grid would look like that included the key places of Chapel Hill. From there, I will present their task of creating a map of downtown Glitzburg. Since this town is a fictional community within the Ephesus 3rd grade classrooms, this should be realistic and tangible for all students. I will show them an example of charting key locations in Chapel Hill just as I mentioned previously, using the same coordinate grid paper that they will have to use. We will discuss landmark buildings, roads and intersections. We will also discuss what the particular buildings could look like using three-dimensional models and how the roads reflect the types of lines discussed previously in class. I expect to hear remarks of understanding such as answering impromptu questions or students asking questions for clarification when they do not understand. Through the written explanation as well as a map to follow as a guide that reflects my expectations, I feel that many, if not at least one of the partners from every group, will gain a clear understanding of their expectations.

Supporting Students’ Exploration of the Task or Set of Tasks

As the students are working in their groups, I will be continuously moving throughout the classroom to monitor their progress and see if they have any questions. In order to refocus their thinking and keep the students on track, I will occasionally ask them questions about each task as they are working on it. Possible questions for the coordinate grid activity could include asking them to identify the ordered pair for particular buildings plotted on their graph or asking them to analyze why they chose to place certain buildings in the town next to one another. This would target the students’ metacognitive skills, a higher order questioning strategy. Additionally, the response from the students regarding the ordered pair for their specific buildings will reinforce their understanding of how coordinate grids work. When looking at the students’ understanding of three-dimensional geometric shapes, I will listen for them to use proper vocabulary when describing and analyzing the shapes they have built (vertex versus corner) and check to see if they are accurately counting the characteristics of their newly created buildings. One specific way that will naturally advance their understanding of the three-dimensional shapes will be the students putting together multiple shapes to create more complex three-dimensional ones. From here it will be more difficult to accurately count the number of faces, edges and vertices based on how complex their buildings are. This will be more challenging for those students who simply memorized the number of characteristics required of each shape. In looking at this analysis of various shapes, I will expect the children to hold one another accountable for the work completed, as the final project reflects upon both students. This is something that I will make very clear to both partners. My intention is that the students will continually challenge their partners, questioning their decisions to place buildings on the map, create buildings a particular way, and more specifically rethink their answer for the summative questions in part three of the tasks.

Sharing and Discussing the Task or Set of Tasks

After the students have completed their final task of answering the questions, I would like to supply some time in the classroom for whole group discussion regarding the set of tasks, as well as time for the students to present their final project to their peers. Many of the students do not see math as a hands-on, presentation geared environment, but I am hoping that this activity will help open students up to the ways in which town planners and architects use mathematics and presentation in their every day lives. As we discuss the demands of their tasks and present their final product, I would like to discuss them in the same order that the tasks were arranged for their project. This will show the true to life stages of planning a city and creating a model to reflect the plan, helping the students to see the connection between the strategies applied and the mathematical ideas and processes it incorporates.

In watching the students’ presentations, I am less interested in the students sharing the number of corners that one building has or the number of intersections on their map, and more focused on using this as an opportunity for the students to share something valuable that they have learned. Looking over their summative questions I will be able to see that they understood the content material and were able to apply this knowledge to a self-created downtown area. In listening to the presentations, I will see how the students were able to make connections between the vocabulary learned in math class and the areas it appears in real life. Intersections, rays, line segments, vertices, edges and faces are all vocabulary that I hope to hear when the students are presenting.

To best orchestrate their presentations, I would like to use the school’s document camera so that the students can show off their coordinate grid maps of the downtown area. The students will easily be able to share their three-dimensional city buildings that they have created, allowing their peers to experience their building through seeing it up close as well as touching it. After each pair presents I will display their coordinate maps on the board, providing the students an opportunity to look for patterns within the maps created. I am also going to encourage the students to think deeply about which they would describe as the “best” planned downtown area and why. I want them to consider what makes a good plan for a business or residential area and why it is considered good or bad. This will tie nicely into our social studies discussion of communities and the many components that are included.