Developing appropriate vocabulary and providing technology tools is key to getting the study of Geometry on track.
View Progressions in Geometry
See the standards throughout the grades: http://www.corestandards.org/Math/Content/G/
G1.a. Identify angle relationships: supplementary, complementary, vertical, adjacent, alternate interior, alternate exterior. Use a ruler and protractor, as well as dynamic graphing tools (such as Geometer’s Sketchpad or Geogebra), to construct figures with given conditions.
G1.b. Find missing angles in arrangements of intersecting lines with parallel lines and transversal or in n-gons.
G1.d. Use deductive reasoning to verify angle relationships; for example, determine that vertical angles are congruent; that the angles of a triangle total 180 degrees.
G2.a. List specific characteristics of squares, rectangles, rhombi, different types of triangles by using appropriate language including perpendicular, parallel, right, obtuse, and acute angles, congruent segments and angles.
G2.c. Explore how collections of attributes are related to categories of shapes. Sometimes, removing one attribute from a collection of attributes does not change the set of shapes the attributes apply to and sometimes it does.
G2.d Identify shared attributes of shapes in different categories (squares, rectangles, rhombi) and that the shared attributes can define a larger category (quadrilaterals).
G2.e. Demonstrate the relationships among categories via Venn diagrams.
G2.f. Using triangle congruence properties and deductive reasoning, derive some properties of isosceles triangles, parallelograms and trapezoids (e.g. opposite sides of a parallelogram are congruent; diagonals of a rectangle are congruent).
Dynamic graphing tools allow students to explore what stays the same and what changes when geometric objects are manipulated
Definitions are much more meaningful if students first explore characteristics and categorizations of shapes before learning definitions.
Slides for Chapter 10 in Mathematics for Elementary Teachers with Activities, 5th edition by Sybilla Beckmann.)
G1.a-d Online dynamic geometry tool: Link to GeoGebra
G1.a-d Games to become more familiar with dynamic geometry tools: Euclidea and Euclid
G2.a-e Manipulative Polygons + Power Pack - Have students use triangles, quadrilaterals, circles, and other shapes to design, sort, measure, and compare polygons. Students can explore topics such as congruency, angles, and symmetry in this exciting classroom resource.
G2.a-e Offline activity Black Line Master for Assorted Shapes - BLM 41-47 from John Van de Walle
G2.a Online activity Quadrilateral Exploration in GeoGebra - Each shapemaker will only make the type of shape named. Through exploration, students can derive definitions of quadrilaterals. *See note about trapezoids below.
G2.a Online activity Shape Classification Game - This interactive mathematics resource from Learn Alberta explores the properties of triangles, quadrilaterals and regular polygons and allows students to classify shapes based on their properties. The resource includes print activities, solutions, learning strategies, and a shape guessing game.
G2.a Online activities Hexagons and Quadrilaterals: Desmos polygraph activities. Students work in pairs to identify a shape based on its characteristics.
G2.d Offline activity Describing and Defining Quadrilaterals - Formative assessment activity from Shell Center
G2.d Offline activity Describing and Defining Triangles - Formative assessment activity from Shell Center
G2 Videos of students talking about geometric shapes from Christy Graybeal