Silhouettes of Cube Buildings
Name: Elaine Clark
Lesson Plan: #1
CED 530
Section: 800, Wednesday 4:30-7:30
Date: April 4, 2008
Mathematical Task:
1.Understanding Geometric Perspective
2.Learning to visualize what objects look like from different perspectives
3.Integrating different views of an object to form a mental model of the whole object
Grade Level: 7
Approximate Number of Students: 2
Curriculum Source: Investigations: Seeing Solids and Silhouettes, and New York Mathematics: Applications and Concepts
Materials and Sources: Overhead projector, interlocking cubes, transparency of student sheet 10, student sheet 10, 11, 12, 13, & 14
NYS Mathematics Performance Indicator(s):
State the Content Strand:
State 1-3 relevant Content Performance Indicators using bullets.
- 7.G.3 Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)
Process Indicators:
State 4-6 relevant Process Indicators illustrating a variety of processes using bullets.
- 7.PS.11 Work in collaboration with others to solve problems
- 7.CM.4 Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models and symbols in written and verbal form
- 7.CM.10 Use appropriate language, representation, and terminology when describing objects, relationships, mathematical solutions, and rationale
- 7. CN.9 Recognize and apply mathematics to other disciplines, areas of interest, and societal issues
- 7.R.9 Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects)
1
Performance Objective:
After exploring silhouettes of cube buildings with the teacher using interlocking cubes and an overhead projector, the students will be able to look at pictures of cube buildings, draw their silhouettes on grid paper from three different perspectives (front, right side, and top),and then reverse this process by constructing cube buildings from given silhouettes.
Part of Lesson
1. Launch/Anticipatory Set/Before
State prior knowledge needed, then explain how you will access prior knowledge and draw the students into this particular lesson. Also explain how you will launch the “problem” the students will solve during the explore. Some problems need more extensive launches than others.
Teacher and Student Actions
Teacher Actions:
5 Minutes-Quick Pace
1. Holding a two-dimensional picture of a cube and a three-dimensional (interlocking cube) I will ask the students various questions about the two objects in order to activate prior knowledge about two and three dimensional concepts.
Discuss with your partner what this picture and this cube have in common? How are they alike? Different?
Did you come up with the mathematical names for the differences?
Why is one two-dimensional, and the other three-dimensional?
2. Pointing out the front view of the cube (what they are seeing) place the cube on the overhead projector with the front view facing upward directly under the mirror. Turning it on, students will see the 2-D representation or silhouette of the front view of the cube.
Can anyone tell the class something about silhouettes? What is a silhouette? How is it produced? (A silhouette is a flat, dark shape that is produced when an object blocks light. We only see the outline of the object. It is like a shadow).
Has anyone ever had the silhouette of their head outlined?
1
3. This two-dimensional representation of the solid object doesn't allow you to see it from any other perspective other than the front view.
What do I mean by perspective?
Can an object have different perspectives? Explain that to me.
How many perspectives can it have? Why do you say that? Show me how.
What is another way of saying perspective? (point of view)
Can perspective or point of view be used in a way other than the mathematical sense? How? (Persons point of view or perspective on an opinion or subject)
4. For the purposes of this lesson, our points of view of cube buildings will be seen from (point them out leaving the cube stable and moving around it) the front, right side, and top of the object.
5.5 Min PRE-TEST At this point give each student the top half of student sheet 12 and have them draw the three silhouettes of the cube building that is on the sheet. Explain that this is just a way of determining their understanding so far of 2-D and 3-D perspective. Collect and quickly look to see if building was drawn using the correct perspectives and that they have drawn the recessed cubes too.
6. Continue on with lesson by: 10 minutes
a. Distributing to each student sheet 10 and 15 interlocking cubes.
b. Have students make the cube building that is shown on the sheet.
c. Next show them the transparency of student sheet 10, explain that these silhouettes are drawn on grids, and each square is one cube. The first was seen by looking at the front of the building and the third by looking at the right side of the same building.
d. Using one of the cube building models place it on the overhead with the front facing up directly under the mirror. Check the silhouette on the screen to make sure it matches the grid drawing. Repeat for right side.
e. With their buildings positioned as shown on the sheet have students draw the top view.
1
f. While the students are drawing observe to see if they are drawing from a perspective other than from the front looking on top. Look for the four possible positions of the silhouette in the students work.
g. Draw these on the board and ask students how these four silhouettes are different and how they are the same. Point out that in order to avoid confusion we usually draw the top silhouette as seen from the front side.
Point out that in order to avoid confusion we usually draw the top silhouette as seen from the front side.
Student Actions: Collaborating with each other, answering questions, listening, working.
2. Explore/During
Describe what the teacher will do and how the students will be engaged in the lesson/activity.
Teacher Actions: 10 minutes
1. Distribute Student Sheet 11.
2. Have students use cubes to make each building
3. Have students draw them. Students can compare and communicate amongst themselves during the exploration.
4. Teacher is observing, assessing, and guiding the exploration process to see if students understand perspective by moving around the building rather than moving the building. I am looking to see if they understand the difference between the 2-D and 3-D view of cubes by their drawing or not drawing the recessed cubes.
Student Actions: Constructing cube buildings, drawing, and collaborating.
1
3. Summary/Closure/After
Describe how you will summarize the lesson. This is a most important part of a problem solving lesson where the students share their strategies. The teacher should facilitate the discussion and the students should be actively engaged.
Teacher Actions: Facilitate discussion through questioning
Do you think you have constructed the cube building acurately? Why?
For Building 2 have someone tell you how they visualized the front silhouette of this building.
Teacher draws it on the board.
Did anybody draw a different silhouette? If yes, teacher draws that one, and helps students to determine which one is correct.
Continue on with this for the next two views (top, right side).
Look for and reinforce the that the recessed cubes will show up on a silhouette, and because they are looking at the 3-D view to draw, they still need to realize that the 2-D view needs to have them included.
Look for drawings coming from other perspectives that are not top front or right sided views.
Did you learn anything new by doing this activity?
How do you think understanding perspective can help your daily life? (art, architecture, forensics, etc.)
Student Actions: Actively engaged
4. Assessment
Clearly describe how the teacher will know if the students met the objective. Assessment should be embedded within the activities. The assessment may include a separate independent component.
Students will be given a Pre-test to determine whether or not they can visualize and transfer the views of a 3-D cube building onto a 2-D grid.
During exploration the teacher is observing, assessing, and guiding the exploration process to see if students understand perspective by moving around the building rather than moving the building. I am looking to see if they understand the difference between the 2-D and 3-D view of cubes by the drawing or not drawing the recessed cubes.
If students did well on the pre-test, I will give them a different post test using student sheet 13 which is like the pre-test only it has a different cube building. Otherwise I will use sheet 12 again. 1
5. Modification for Advanced Learners Briefly describe here. DO NOT state that advanced learners will help others. You need a meaningful activity/extension of the lesson.
For those who need advanced work Student Sheet 14 requires students to build a cube building using the three views. It does not have a picture of the building; therefore, requires students to combine information from the three different views and synthesize it to form one comprehensive view of the object.
Another option would be to draw silhouettes of three further views (leftside, back, and bottom) of any of the buildings on sheets 10-13 on one-centimeter graph paper. The are to label each drqwing according to the view it shows.
6. Modifications for two types of disabilities-state the name of the disability here. You may include a modification for ELL.Briefly describe here. DO NOT state that learning disabled students will receive help from advanced learners.
Student with LD will be allowed to construct building with cubes prior to drawing it on the pre-test and post-test if needed.
Student with ADHD will have the option of constructing the drawings on the student work sheets or may use the following website to construct the 2-D representation.
The National Library of Virtual Manipulatives has an activity with pattern blocks that will allow students to construct cube buildings virtually. This website will bring them to the home page. From this point choose grade 6-8 in the Geometry block, follow that down and click on pattern blocks.
1