Geometry Trajectory –Putting It All Together Each concept builds on the previous idea and students should explore and construct concepts in such a sequence VAN DE WALLE VAN DE Level 0 *Kindergarten Level Visualization The object of thought (focus) is individual shapes. – Students are operating on specific examples of the shapes they see. – Orientation may even change what a student observes. – The goal is to see likenesses and differences. Level 1 Analysis The object of thought is classes of shapes. – Students consider all shapes in a class instead of an individual example. – What makes a shape “a shape”? The outcome is discovering properties of shapes. – Focus on properties. – Apply ideas to entire classes of figures. Level 2 Information Deduction The objects of thought are the properties. – Students understand that properties are related. – One set of properties may relate to another property. – Students can understand logical reasoning about the properties. The outcomes are relationships properties. Level 3 Deduction The objects of thought are the relationships the properties. The products of thought are the deductive axiomatic systems. Level 4 Rigor The objects of thought are the deductive axiomatic systems. The products of thought are comparisons and contrasts among different axiomatic systems of geometry. Adapted from the van Hiele Levels of Geometric Thought and taken from van de Walle & Lovin Teaching Student-entered Mathematics (k-3) The Big Picture in Kindergarten
Formative Assessment Lesson (FAL) Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications. These lessons enable teachers and students to monitor in more detail their progress towards the targets of the standards. *3-Act Task A Three-Act Task is a whole-group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three. More information along with guidelines for 3-Act Tasks may be found in the Guide to Three-Act Tasks on georgiastandards.org and the K-5 CCGPS Mathematics Wiki. Task Name Standards Task Type/ Grouping Strategy Content Addressed *Shapes in Our World MCC.K.G.1-6 MCC.KMD.3 3-Act Task Whole Group Recognize, name, analyze, compare, compose, and classify shapes What Shape is This? MCC.K.G.1 Constructing Task Large group/Small group Recognize and name shapes on a Shape Hunt MCC.K.G.1-3 Constructing Task Large group/Small group Recognize and name shapes Attributes Rule! MCC.K.G.4 MCC.KMD.3 Constructing Task Whole Group/Small Group/Individual Recognize, name, and compare shapes Exploration of Shapes MCC.K.G.1-3 Practice Task Large group/Small group Observe shapes in the environment (flat/solid) Listen and Do! MCC.K.G.1-2 Scaffolding Task Partner Spatial relationships Recognize and name shapes Copy Cat MCC.K.G.1 Practice Task Individual/Small Group Spatial relationships Recognize and name shapes Where’s Abe? MCC.K.G.1-2 Practice Task Partner/Small Group Spatial relationships Recognize and name shapes Sort MCC.K.G.1-3 MCC.K.MD.1 Practice Task Whole Group/ Small Group/Partner Recognize, name, and compare shapes
Touch It, Count It, Chart It MCC.K.G.1-4 Constructing Task Group Recognize, name, and compare shapes What’s in the Bag? (Flat or Solid) MCC.K.G.2-5 MCC.K.MD.1 Practice Task Whole Group/ Small Group/ Partner Recognize, name, and compare shapes Observe shapes in the environment Identify and Sort Shapes MCC.K.G.1-4 FAL Recognize, name and compare shapes Observe shapes in the environment Pattern Pictures MCC.K.G.2,3,4,6 Constructing Task Small Group/ Partner Name, compare and compose larger shapes from smaller shapes Geoboard Museum MCC.K.G.4-6 Practice Task Individual/ Small Group Compose and compare shapes Build A Marshmallow Shape MCC.K.G.3-6 Constructing Task Large Group/ Small Group Recognize, name, compare and compose shapes Tangram Challenge MCC.K.G.5-6 Performance Task Whole Group/ Individual Recognize, name, and compare shapes Compose larger shapes from simple shapes Shapes All Around MCC.K.G.1-6 MCC.K.MD.1 Culminating Task Small Group/ Individual Recognize, compose and compare shapes Each task is suggested but not required; teachers should choose the most appropriate tasks based on the needs of their students. For more information on these tasks in this unit please refer to the unit webinar found at *3 ACT TASK: Shapes In Our APPROXIMATE TIME: ONE CLASS SESSION In this lesson, students will identify shapes found in their environment revealed through a photograph. STANDARDS FOR MATHEMATICAL CONTENT
Children: Yes, we see a circle. Going on a shape hunt, Here we go. Going on a Flat Shape Hunt Circle what you square rectangle circle triangle hexagon Draw the shape: My shape was a :____________________ Circle what you found: square rectangle circle triangle hexagon Draw the shape: My shape was a :____________________ Circle what you found: square rectangle circle triangle hexagon Circle what you found: square rectangle circle triangle hexagon