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 mlmetz@iup.edu

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.

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.2.3.4.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.2.3.5.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.

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

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.

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.

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.

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.

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.

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.

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

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.

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

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.

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

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.

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

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.

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

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

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. https://www.geogebra.org/m/yDskkJaq