1. Exploring Polygons, Part 1
Core Mathematics Partnership
Building Mathematical Knowledge and
High-Leverage Instruction for Student Success
2:45 – 4:00
July 21, 2016

2. Learning Intention and Success Criteria
We are learning to…
- Understand and classify polygons.
We will be successful when we can…
- Define polygons.
- Classify polygons according to attributes.
2 minutes

3. Composing and decomposing geometric shapes
…the most important goals for elementary geometry according to three categories. K-6 Geometry Progressions
Geometric shapes, their components (e.g. sides, angles, faces), their properties, and their categorization based on those properties.
Composing and decomposing geometric shapes
Spatial relations and spatial thinking.
We need to transition to polygons.

4. What is a polygon?
We have to make a Frayer model.

5. Trio: Silent Sorting
Write 2 sticky notes: Polygons Not-A-Polygon WITHOUT TALKING… Select a card from the envelope. Place the figure under the appropriate category. Move on to the next person without talking. **Signal to indicate you are done.

6. Refining Your Definition
Study the sorted cards. Discuss cards you agree with and cards you disagree with. As a trio…refine your definition of a polygon and reorganize your cards (if needed). Be ready to share your definition and any cards that challenged your thinking.

7. A Polygon is… A polygon is a closed figure with line segments
as sides, and vertices.
- Grade 4 Shapes and Symmetry, Investigations v.2

8. Joe made two inventions for Science
Joe made two inventions for Science. He claims both of them are polygons. Is Joe correct? Why or Why not?
Invention A
Invention B

9. Review your Frayer model
Revise your definition. You can make a clean copy or add information/examples to your paper.

11. Thinking a little bit further…
Find shapes 21, 22, 23, 25
How are they the same? How are they different?
What would you name this category of shapes?

12. Polygon Capture: Pairs
Take the cards out of the envelope and lay the cards face down to make 2 piles:
Angles Sides
Spread the polygon shape cards on your table.
Take 1 card from each pile – read directions.
Capture all polygons that meet the criteria on
both cards.
Find the polygon capture game in your binder.

13. Polygon Capture: Pairs
Switch players.
Round 1: Remove Wild Card/ Steal Cards
Round 2: Add Wild Card/Steal Card

14. MP6 and MP7
What mathematics are students engaged in as they play Polygon Capture? How would Polygon Capture helping students develop MP6 and MP7? What adjustments might you make for students at your grade level?

15. Trapezoids! Who Knew?
“A quadrilateral with at least one pair of parallel sides.” OR “A quadrilateral with exactly one pair of parallel sides.” How does YOUR curriculum define trapezoids?
Both EngageNY and Investigations use the Inclusive definition of trapezoid:

16. Polygon Riddles

17. Polygon Riddles
Work in a trio: Scatter polygon card shapes face-up on desk. Person 1: Select a card. Read each clue one at a time. Pause between reads to allow duo to eliminate cards that do not fit the clue. Person 2 & 3: Work together to eliminate shape cards that do not fit the clues read. Switch roles. Play several times.

18. Sample Polygon Riddles
Clue A: My polygon is a quadrilateral. Clue B: My polygon has exactly two sides that are parallel. Clue C: My polygon has two right angles. Clue D: The longer parallel side is about twice as long as the shorter parallel side.

19. Clarifying van Hiele Levels
Visual Level
Recognize figures as total entities, but do not recognize properties.
Descriptive Level/Analytic
Identify properties of figures and see figures as a class of shapes defined by their properties.
Informal Deduction [Analytic]
Formulate generalizations about relationships among properties of shapes; Develop informal explanations.
The analytic level is in the Progressions (grey box p.3) There has been research done since they have done their initial research

20. Sample Polygon Riddles
Clue A: My polygon is a quadrilateral. Clue B: My polygon has exactly two sides that are parallel. Clue C: My polygon has two right angles. Clue D: The longer parallel side is about twice as long as the shorter parallel side.

21. Thinking a little bit further…
Study your Polygon Riddle cards
Look for a clue you can “drop” from each card.
Test it!

22. Clarifying van Hiele Levels
Visual Level
Recognize figures as total entities, but do not recognize properties.
Descriptive Level/Analytic
Identify properties of figures and see figures as a class of shapes defined by their properties.
Informal Deduction [Analytic]
Formulate generalizations about relationships among properties of shapes; Develop informal explanations.
The analytic level is in the Progressions (grey box p.3) There has been research done since they have done their initial research

23. Thinking about the van Hiele Levels
Consider our polygon activities through the lens of the van Hiele levels. What do you notice? What are you thinking? Open to page 78 in your “Essential Understandings” book and read the bottom half of the page.

24. One perspective on evaluating the van Hiele Levels
“… allows for the possibility that a student can develop two consecutive levels of reasoning at the same time, although what usually happens is that the acquisition of the lower level is more complete than the acquisition of the higher level. In fact, we observed that not all students used a single level of reasoning, but some of them used several levels at the same time, probably depending on the difficulty of the problem.” - Gutierrez, Jaime & Fortuny (1991), p. 250

25. One perspective on evaluating the van Hiele Levels
“… allows for the possibility that a student can develop two consecutive levels of reasoning at the same time, although what usually happens is that the acquisition of the lower level is more complete than the acquisition of the higher level. In fact, we observed that not all students used a single level of reasoning, but some of them used several levels at the same time, probably depending on the difficulty of the problem.” - Gutierrez, Jaime & Fortuny (1991), p. 250

26. Shall We Play a Game?

27. Quadrilateral Sorting Activity
Remove a card from the envelope.
Sort the quadrilateral shapes by the directions on the card.
Record the sort and discussion on the recording sheet.
Push all of the shapes back into a pile.
Pass the envelope to the left and repeat steps 1–4 with the next card.

29. CCSSM Geometry Standards
Reason with shapes and their attributes. 3.G.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

30. CCSSM Geometry Standards
Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

31. CCSSM Geometry Standards
Classify two-dimensional figures into categories based on their properties. 5.G.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. 5.G.4. Classify two-dimensional figures in a hierarchy based on properties.

32. Thinking a little bit further…
Read the section: Geometric shapes, components and properties – in the K-6 Geometry Progressions Pages
Also read page 18 and study the Venn diagram.
As you read….
How did the activity push you level of geometric reasoning in relation to the van Hiele levels?

34. True or False? A square is a special kind of rectangle.
It is a rectangle in which all four sides are the same length.
A parallelogram is a special kind of trapezoid.
It is a trapezoid with two pairs of parallel sides.
A rhombus is a special kind of parallelogram.
It is a parallelogram in which all four sides are the same length.

35. Learning Intention and Success Criteria
We are learning to…
- Understand and classify polygons.
We will be successful when we can…
- Define polygons.
- Classify polygons according to attributes.
2 minutes

36. Core Mathematics Partnership Project
Disclaimer
Core Mathematics Partnership Project
University of Wisconsin-Milwaukee,
This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors.
This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.