Geometric Reasoning with Shapes Attributes Part 4 Classifying
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 hand 2 mind Join our community on ed. Web. net Building Understanding in Mathematics www. edweb. net/math
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Geometric Reasoning with Shapes & Attributes Classifying Plane Figures Sara Delano Moore, Ph. D. Director of Mathematics & Science ETA hand 2 mind 1 December 2015
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
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)
Building Shapes with Ang. Legs & Geoboards • Ask students to build a shape. • Compare your shape with your neighbor. • How are they the same? • How are they different?
What’s My Rule? Yes/True No/False
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
Attributes of Quadrilaterals • • Sides Angles Diagonals Symmetries
Parallel Lines What is the relationship between these line segments?
Parallel Lines in Quadrilaterals
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.
Attribute Chart No parallel sides 14 47 37 X X X At least one pair parallel sides 38 42 13 44 40 43 X X X X Two pairs parallel sides No congruent sides One pair congruent sides X Two pairs congruent sides Four congruent sides X No right angles One right angle Two right angles Four right angles X X X
Family Tree for Quadrilaterals
No Parallel Sides No parallel sides 14 47 37 X X X What kind of shapes? At least one pair parallel sides Irregular Quadrilaterals Two pairs parallel sides 14 No congruent sides One pair congruent sides Two pairs congruent sides One right angle Two right angles Four right angles Darts X 47 Four congruent sides No right angles Kites What other attributes? Concave / Convex 37
Family Tree for Quadrilaterals 37 47 14
At Least One Pair Parallel Sides 38 42 13 44 40 43 X X X X X No parallel sides At least one pair parallel sides Two pairs parallel sides 38 No congruent sides 44 One pair congruent sides Two pairs congruent sides X X Four congruent sides No right angles X X 42 40 X One right angle Two right angles Four right angles 13 X X X 43
Family Tree for Quadrilaterals 42 38
At Least One Pair Parallel Sides 38 42 13 44 40 43 X X X X X No parallel sides At least one pair parallel sides Two pairs parallel sides 38 No congruent sides 44 One pair congruent sides Two pairs congruent sides X X Four congruent sides No right angles X X 42 40 X One right angle Two right angles Four right angles 13 X X X 43
Family Tree for Quadrilaterals
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.
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
Join our community on ed. Web. net Building Understanding in Mathematics ü Invitations to upcoming webinars ü Webinar recordings and resources ü CE quizzes ü Online discussions Join the community www. edweb. net/math
Recognition for your participation today! Attending Live? Your CE Certificate will be emailed to you within 24 hours. CE Certificate provided by Viewing the Recording? Join the community at www. edweb. net/math Go to the Webinar Archives folder Take the CE Quiz to get a personalized CE Certificate
Join us for the next webinar Tuesday, January 19 th 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 hand 2 mind For an invitation to the next webinar join Building Understanding in Mathematics www. edweb. net/math
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