1. Mary Lou Metz Indiana University of PA mlmetz@iup.edu
PCTM Geometry Workshop PCTM 66th Annual Conference Harrisburg, PA August 2, 2017
Mary Lou Metz
Indiana University of PA

2. Goal of this workshop:
This workshop will address geometry concepts outlined in the PA Core Standards for grades 3-5 with a focus on developing these geometric ideas conceptually.

3. PA Core Geometry Standards
CC2.3.3.A.1 Identify, compare, and classify shapes and
their attributes.
M03.C-G.1 Reason with shapes and their attributes.
CC A.2 Classify two‐dimensional figures by properties of their lines and angles.
M04.C-G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
CC A.2
Classify two‐dimensional figures into categories based on an understanding of their properties.
M05.C-G.2 Classify two-dimensional figures into categories based on their properties.

4. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Objectives
Sort quadrilaterals on the basis of specific attributes
Use Venn diagrams to classify quadrilaterals
Determine common attributes of a set of quadrilaterals
Materials
Plastic hoops/Venn Diagrams
Quadrilateral pieces
Ring labels

5. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Task 1: Select the labels “At least one right angle” and “No right angles.” Sort the shapes and place them in the appropriate area of the Venn diagram.

7. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Task 2: Select the labels “All sides the same length” and “At least one acute angle.” Sort the shapes and place them in the appropriate area of the Venn diagram.

9. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Task 3: Select the labels “At least one set of parallel sides” and “ At least one obtuse angle.” Sort the shapes and place them in the appropriate area of the Venn diagram.

11. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Task 4: Select the labels “At least two pairs of adjacent sides congruent” and “ All pairs of opposite sides congruent.” Sort the shapes and place them in the appropriate area of the Venn diagram.

13. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Task 5: Select the labels “All sides the same length”, “At least one obtuse angle”, and “At least one right angle.” Sort the shapes and place them in the appropriate area of the Venn diagram.

15. Activity 1 – “Roping in Quadrilaterals” from Navigating Through Geometry 3-5
Task 6: Select the labels “At least two pairs of adjacent sides equal”, “All pairs of opposite angles equal”, and “All adjacent angles equal.” Sort the shapes and place them in the appropriate area of the Venn diagram.

17. Activity 2 – “Properties of Special Quadrilaterals”
Objectives
Determine properties of special quadrilaterals
Use paper folding to determine congruence and symmetry
Materials
Parallelogram shapes
Patty paper
Properties of Special Quadrilaterals sheet

18. Activity 2 – “Properties of Special Quadrilaterals”
Task 1:
Trace all parallelograms onto patty paper. Use the index card to draw straight lines.
Using folding, measuring, etc. determine which properties are true for ALL parallelograms.
Mark the appropriate properties on the “Properties of Special Quadrilaterals” sheet.

19. Property Parallelogram Rhombus Rectangle Square
Opposite sides the same length
All sides the same length
Opposite angles the same measure
All angles the same measure
Diagonals bisect each other
Diagonals the same length
Diagonals perpendicular
Has at least one line of symmetry

20. Activity 2 – “Properties of Special Quadrilaterals”
Task 2:
Select all rhombii from your set of parallelograms.
Using folding, measuring, etc. determine which properties are true for ALL rhombii.
Mark the appropriate properties on the “Properties of Special Quadrilaterals” sheet.

21. Property Parallelogram Rhombus Rectangle Square
Opposite sides the same length
All sides the same length
Opposite angles the same measure
All angles the same measure
Diagonals bisect each other
Diagonals the same length
Diagonals perpendicular
Has at least one line of symmetry

22. Activity 2 – “Properties of Special Quadrilaterals”
Task 3:
Select all rectangles from your set of parallelograms.
Using folding, measuring, etc. determine which properties are true for ALL rectangles.
Mark the appropriate properties on the “Properties of Special Quadrilaterals” sheet.

23. Property Parallelogram Rhombus Rectangle Square
Opposite sides the same length
All sides the same length
Opposite angles the same measure
All angles the same measure
Diagonals bisect each other
Diagonals the same length
Diagonals perpendicular
Has at least one line of symmetry

24. Activity 2 – “Properties of Special Quadrilaterals”
Task 4:
Select all squares from your set of parallelograms.
Using folding, measuring, etc. determine which properties are true for ALL squares.
Mark the appropriate properties on the “Properties of Special Quadrilaterals” sheet.

25. Property Parallelogram Rhombus Rectangle Square
Opposite sides the same length
All sides the same length
Opposite angles the same measure
All angles the same measure
Diagonals bisect each other
Diagonals the same length
Diagonals perpendicular
Has at least one line of symmetry

26. Activity 3 – Properties of Parallelograms
Objective
Determine properties of special quadrilaterals using technology
Materials
Geogebra

27. Activity 3 – Properties of Parallelograms
Objective
Go to the following website:
Explore each of the special parallelograms by moving the vertices. Record on the sheet which properties are always true for each parallelogram.