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February 4, 2011

2-D, 3-D, and Beyond: Developing Geometric Thinking and Spatial Sense

By Angela Bunyi

    If you are responsible for teaching students about moving from 2-D to 3-D and 3-D to 2-D, and creating and understanding nets, surface area, and/or volume, then I have THE lesson for you. Read on to learn how you can quickly help your students master 2-D, 3-D, and beyond! 

    2-D, 3-D, and Beyond!

    Time: 1 hour

    Grade Level(s): 3–12

    Materials: 10–12 plastic plates, hot glue gun, 80–100 building blocks, graph paper and/or isometric grid paper (allows you to draw dimensions), and computer access

    Prep Time: 20–30 minutes 

    Directions: Using a hot glue gun, glue a set of blocks to a clear, plastic plate in a personally created arrangement. I used 7-13 blocks on most arrangements (see photo). Assign each set with a number that will signify the "front" of the block set and help you identify answers for assessment. It took me fewer than 20 minutes to create 12 sets at home. The clear plates are important; you need to be able to see the bottom view.

     

    From 3-D to 2-D

    Time: 15–20 minutes

    3d_1_key
    Choose one of the sets as a class example and display the front. What would it look like in a 2-D drawing with no depth? How about on the bottom? Without moving the plate, have students stretch their spatial skills by rotating it in their heads and creating that image on graph paper. The fun part is checking it; you simply have to move the block set and show the class if they are indeed correct. Complete all the sides with the class using graph paper and the block set. 

    Then it's time for students to try it on their own. After distributing one set for every two students, challenge your class to create all the 2-D views possible without moving the set. (Of course, students who need extra support should be allowed to move it.) Students can check their work by moving the block set and checking.

     

    3-D to 2-D

    Time: Whole group: 15 minutes; independent practice: 30+ minutes

    Whole Group

    My teaching friend, Stacey Burt, shared an AMAZING site, NCTM Illuminations, with me last year. It allows you to create and investigate three dimensional objects with ease, and your students will be fascinated with it. 

    Iso_1

    After opening up the site, we displayed the class example block set used above and embarked on creating a three-dimensional version of it on isometric grid paper. The three buttons we began with included the cube on the left side of the screen, the eraser on the top left, and the eye icon. The eye icon is what will really impress your students. 

    Once you believe you have created your block set, click on the eye icon. Here is what you will first see:

    Iso_2

    If you are using a SmartBoard, you can simply touch the object and move it around with your finger. Otherwise, three rotational bars allow you to see every angle of your created object. 

    But then it gets better. Uncheck the 3-D button and you will see this:

    Iso_3

    Yes, it quickly converts your online three-dimensional object into a mat format. This is the birds-eye view of the arrangements and number of blocks in each section. How amazing is that? I was impressed enough, but unclick the "mat plan" button and be amazed one more time:

    Iso_4
    "Well, how about that?" I thought the first time I saw it. You now have a site that allows your students to move quickly between 3-D and 2-D. 

    Independent Practice

    Using a block set and a computer (each of our students has a laptop) challenge students to create their three-dimensional object online. When I completed this lesson, I discovered that a few students had incredibly sharp and advanced spatial skills. It was really fun to watch. Then challenge them to create the 2-D views on grid paper. They can check their work using the eye icon. 

    Depending on the time you have left, create a set of 2-D views on the board and ask students to move from 2-D to 3-D using the Illumination site. 

     

    Surface Area and Volume

     

    If you take the time to play around with the site, you can also teach surface area and volume. This allows you to challenge your brightest students, yet provide your "not there yet" kids with the hands-on/visual support they need to excel. 

    Geometry Unit

    If you are addressing these geometric skills, you may be interested in looking at the geometry unit I  created for Scholastic (2008). It includes three lessons and three printables. 

    Three Dimensional Geometry: Sing It, Move It, Film It!

    Geometry turns cross-curricular, as students take a geometry tour around the world!
    Geometry turns cross-curricular, as students take a geometry tour around the world! 

    In this unit, learn how to make the teaching of geometry multi-dimensional. With the power of music, the health benefits of movement, and the application of geography and geometry through film, teaching has never been so much fun.

    OBJECTIVE

    1. Identify, compare, and analyze attributes of two-and three-dimensional shapes and develop vocabulary to describe the attributes.
    2. Classify two- and three- dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids.
    3. Explore congruence and similarity.
    4. Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.

    LESSONS FOR THIS UNIT
     Lesson 1: Geometry: Let's Get Moving!
     Lesson 2: Teaching Geometry through Geography
     Lesson 3: Geometry: Sport's Edition

    REPRODUCIBLES
    Geometry lyrics (PDF) 
    Geometry sports examples (PDF) 
    Geometry puzzles (PDF) 

    Feedback

     

    Do you have any tips or suggestions on helping your students grasp these geometric skills? Please share your thoughts below.  

     

    If you are responsible for teaching students about moving from 2-D to 3-D and 3-D to 2-D, and creating and understanding nets, surface area, and/or volume, then I have THE lesson for you. Read on to learn how you can quickly help your students master 2-D, 3-D, and beyond! 

    2-D, 3-D, and Beyond!

    Time: 1 hour

    Grade Level(s): 3–12

    Materials: 10–12 plastic plates, hot glue gun, 80–100 building blocks, graph paper and/or isometric grid paper (allows you to draw dimensions), and computer access

    Prep Time: 20–30 minutes 

    Directions: Using a hot glue gun, glue a set of blocks to a clear, plastic plate in a personally created arrangement. I used 7-13 blocks on most arrangements (see photo). Assign each set with a number that will signify the "front" of the block set and help you identify answers for assessment. It took me fewer than 20 minutes to create 12 sets at home. The clear plates are important; you need to be able to see the bottom view.

     

    From 3-D to 2-D

    Time: 15–20 minutes

    3d_1_key
    Choose one of the sets as a class example and display the front. What would it look like in a 2-D drawing with no depth? How about on the bottom? Without moving the plate, have students stretch their spatial skills by rotating it in their heads and creating that image on graph paper. The fun part is checking it; you simply have to move the block set and show the class if they are indeed correct. Complete all the sides with the class using graph paper and the block set. 

    Then it's time for students to try it on their own. After distributing one set for every two students, challenge your class to create all the 2-D views possible without moving the set. (Of course, students who need extra support should be allowed to move it.) Students can check their work by moving the block set and checking.

     

    3-D to 2-D

    Time: Whole group: 15 minutes; independent practice: 30+ minutes

    Whole Group

    My teaching friend, Stacey Burt, shared an AMAZING site, NCTM Illuminations, with me last year. It allows you to create and investigate three dimensional objects with ease, and your students will be fascinated with it. 

    Iso_1

    After opening up the site, we displayed the class example block set used above and embarked on creating a three-dimensional version of it on isometric grid paper. The three buttons we began with included the cube on the left side of the screen, the eraser on the top left, and the eye icon. The eye icon is what will really impress your students. 

    Once you believe you have created your block set, click on the eye icon. Here is what you will first see:

    Iso_2

    If you are using a SmartBoard, you can simply touch the object and move it around with your finger. Otherwise, three rotational bars allow you to see every angle of your created object. 

    But then it gets better. Uncheck the 3-D button and you will see this:

    Iso_3

    Yes, it quickly converts your online three-dimensional object into a mat format. This is the birds-eye view of the arrangements and number of blocks in each section. How amazing is that? I was impressed enough, but unclick the "mat plan" button and be amazed one more time:

    Iso_4
    "Well, how about that?" I thought the first time I saw it. You now have a site that allows your students to move quickly between 3-D and 2-D. 

    Independent Practice

    Using a block set and a computer (each of our students has a laptop) challenge students to create their three-dimensional object online. When I completed this lesson, I discovered that a few students had incredibly sharp and advanced spatial skills. It was really fun to watch. Then challenge them to create the 2-D views on grid paper. They can check their work using the eye icon. 

    Depending on the time you have left, create a set of 2-D views on the board and ask students to move from 2-D to 3-D using the Illumination site. 

     

    Surface Area and Volume

     

    If you take the time to play around with the site, you can also teach surface area and volume. This allows you to challenge your brightest students, yet provide your "not there yet" kids with the hands-on/visual support they need to excel. 

    Geometry Unit

    If you are addressing these geometric skills, you may be interested in looking at the geometry unit I  created for Scholastic (2008). It includes three lessons and three printables. 

    Three Dimensional Geometry: Sing It, Move It, Film It!

    Geometry turns cross-curricular, as students take a geometry tour around the world!
    Geometry turns cross-curricular, as students take a geometry tour around the world! 

    In this unit, learn how to make the teaching of geometry multi-dimensional. With the power of music, the health benefits of movement, and the application of geography and geometry through film, teaching has never been so much fun.

    OBJECTIVE

    1. Identify, compare, and analyze attributes of two-and three-dimensional shapes and develop vocabulary to describe the attributes.
    2. Classify two- and three- dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids.
    3. Explore congruence and similarity.
    4. Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.

    LESSONS FOR THIS UNIT
     Lesson 1: Geometry: Let's Get Moving!
     Lesson 2: Teaching Geometry through Geography
     Lesson 3: Geometry: Sport's Edition

    REPRODUCIBLES
    Geometry lyrics (PDF) 
    Geometry sports examples (PDF) 
    Geometry puzzles (PDF) 

    Feedback

     

    Do you have any tips or suggestions on helping your students grasp these geometric skills? Please share your thoughts below.  

     

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