Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
Follow The Annenberg Learner on LinkedIn Follow The Annenberg Learner on Facebook Follow Annenberg Learner on Twitter
MENU
Teaching Math Home   Sitemap
Session Home Page
 
RepresentationSession 05 OverviewTab atab btab ctab dtab eReference
Part A

Observing Student Representations
  Introduction | Building Viewpoints | Student Work Reflection #1 | More Building Viewpoints | Student Work Reflection #2 | Observe a Classroom | Classroom Practice | Your Journal

 
 

Now let's look at how a middle school student solved the following problem:


This is the floor plan (or top view) of a structure made from cubes. The numbers in the squares indicate the number of cubes in that stack. Construct this building on the Building Mat.


top view and building mat

Reflect on the problem and think about some questions you would ask this student. Then look at the questions listed below. For each question, think about an answer the student might provide, then select "Show Answer" to reveal a sample response.


As you read these questions and answers, analyze the student's representation. How does this representation help the student identify relationships among the different views of the building?


Teacher: Can you draw what you would see if you were in front of the structure, looking at it from eye level?

Show Answer
Student:
Yes:

bird's eye view

 

Teacher: That is what the building would look like if you were looking down at it from the sky -- what we call a "bird's eye view." If you, get down and look at the front view of the building, at your eye level, can you draw what you see then?

Show Answer
Student:
(observes the building from eye level) Oh, okay:

front view

 

Teacher: What would you see if you were in back of the structure, looking at it from your eye level? Can you draw that?

Show Answer
Student:
Yes:

back side view

 

Teacher: How is the view from the back different from the view from the front?

Show Answer
Student:
It is reversed.
 

Teacher: What would you see if you were on the right side of the structure, looking at it from your eye level? Can you draw that?

Show Answer
Student:
Yes:

right side view

 

Teacher: And now can you draw what you would see if you were on the left side of the structure, looking at it from your eye level?

Show Answer
Student:
Yes:

left side view

 

Teacher: How is the view from the right side different from the view from the left side?

Show Answer
Student:
It is reversed.
 

Teacher: Is there another name for this relationship?

Show Answer
Student:
It's a mirror image, or symmetrical.
 

Teacher: If you were under the building and looking straight up, what would you see?

Show Answer
Student:
It would be the same shape as from the top.

(Note: The orientation of the shape would depend on where the student was standing: at the front of the building, at the back, at an angle, etc.)


 

next  Reflect on the student work

    Teaching Math Home | Grades 6-8 | Representation | Site Map | © |  
   
Home | Video Catalog | About Us | Search | Contact Us | Site Map |
  • Follow The Annenberg Learner on Facebook


© Annenberg Foundation 2013. All rights reserved. Privacy Policy.