1. Geometric Reasoning with Shapes & Attributes
Part 4: Classifying Plane Figures
Tuesday, December 1, 2015
Presented by Sara Delano Moore, Ph.D.
Director of Mathematics and Science at ETA hand2mind
Join our community on edWeb.net
Building Understanding in Mathematics

2. Building Understanding in Mathematics
Join our community on edWeb.net
Building Understanding in Mathematics
Invitations to upcoming webinars
Webinar recordings and resources
CE quizzes
Online discussions
Join the community

3. Recognition for your participation today!
Attending Live?
Your CE Certificate will be
ed to you within 24 hours.
Viewing the Recording?
Join the community at
Go to the Webinar Archives folder
Take the CE Quiz to get a personalized CE Certificate
CE Certificate provided by

4. Webinar Tips
For better audio/video, close other applications (like Skype) that use bandwidth.
If you are having any audio or video issues, try refreshing your browser.
Maximize your screen for a larger view by using the link in the upper right corner.
Tweet with #edwebchat

5. Geometric Reasoning with Shapes & Attributes
Classifying Plane Figures
Sara Delano Moore, Ph.D.
Director of Mathematics & Science
ETA hand2mind
1 December 2015

6. Geometric Reasoning with Shapes & Attributes
September 15: Laying a Strong Foundation
October 13: Identifying Critical Attributes
November 10: Properties of Lines and Angles
December 1: Classifying Plane Figures

7. Levels of Geometric Understanding
Level 0: Visualization
“It looks like …”
Focus only on the shapes available at the time
Level 1: Analysis
“Laundry list” of properties
Understanding of classes of shapes with common properties
Level 2: Informal Deduction
Identify informal relationships among properties
Identify necessary and sufficient properties
Level 3: Deduction
Create proofs about properties
Level 4: Rigor
Reason about different axiomatic systems (e.g., spherical geometry)

8. Building Shapes with AngLegs & Geoboards
Ask students to build a shape.
Compare your shape with your neighbor.
How are they the same?
How are they different?

9. What’s My Rule?
Yes/True
No/False

10. Lists of Attributes
Give students a collection of shapes in one category (different groups can have different categories)
Each group makes a list of all the attributes common to any shape in their category.
Attribute Categories: Sides, Angles, Diagonals, Symmetries
Students need tools – index card, ruler, tracing paper, mirror/Mira, etc

11. Attributes of Quadrilaterals
Sides
Angles
Diagonals
Symmetries

12. Parallel Lines
What is the relationship between these line segments?

13. Parallel Lines in Quadrilaterals

14. Classification based on lines
Does the shape have exactly one pair of parallel sides? No
Yes
Trapezoids
Parallelograms
Sorting shapes already determined
to have at least one pair of parallel sides.

15. Attribute Chart 14 47 37 38 42 13 44 40 43 X No parallel sides
At least one pair parallel sides
Two pairs parallel sides
No congruent sides
One pair congruent sides
Two pairs congruent sides
Four congruent sides
No right angles
One right angle
Two right angles
Four right angles

16. Family Tree for Quadrilaterals

17. No Parallel Sides What kind of shapes? What other attributes? 14 47 37X
At least one pair parallel sides
Two pairs parallel sides
No congruent sides
One pair congruent sides
Two pairs congruent sides
Four congruent sides
No right angles
One right angle
Two right angles
Four right angles
What kind of shapes? 14
Irregular Quadrilaterals
Kites
Darts 47
What other attributes? 37
Concave / Convex

18. Family Tree for Quadrilaterals37 47 14

19. At Least One Pair Parallel Sides38 42 13 44 40 43
No parallel sides
At least one pair parallel sides X
Two pairs parallel sides
No congruent sides
One pair congruent sides
Two pairs congruent sides
Four congruent sides
No right angles
One right angle
Two right angles
Four right angles 44 38 42 40 13 43

20. Family Tree for Quadrilaterals42 38

21. At Least One Pair Parallel Sides38 42 13 44 40 43
No parallel sides
At least one pair parallel sides X
Two pairs parallel sides
No congruent sides
One pair congruent sides
Two pairs congruent sides
Four congruent sides
No right angles
One right angle
Two right angles
Four right angles 44 38 42 40 13 43

22. Family Tree for Quadrilaterals

23. Grade 5 Geometry
Classify two-dimensional figures into categories based on their properties.
3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
4. Classify two-dimensional figures in a hierarchy based on properties.

24. Geometric Reasoning with Shapes & Attributes
September 15: Laying a Strong Foundation
October 13: Identifying Critical Attributes
November 10: Properties of Lines and Angles
December 1: Classifying Plane Figures

26. Building Understanding in Mathematics
Join our community on edWeb.net
Building Understanding in Mathematics
Invitations to upcoming webinars
Webinar recordings and resources
CE quizzes
Online discussions
Join the community

27. Recognition for your participation today!
Attending Live?
Your CE Certificate will be
ed to you within 24 hours.
Viewing the Recording?
Join the community at
Go to the Webinar Archives folder
Take the CE Quiz to get a personalized CE Certificate
CE Certificate provided by

28. Building Understanding in Mathematics www.edweb.net/math
Join us for the next webinar
Tuesday, January 19th at 4 pm (Eastern Time)
Number Sense Essentials: Using Counters, Rekenreks and Ten Frames to Develop Number Sense Through Counting
Presented by
Sara Delano Moore, Ph.D.
Director of Mathematics and Science at ETA hand2mind
For an invitation to the next webinar join
Building Understanding in Mathematics

29. Thank you!