K-6 Geometry Progression In Practice Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Objectives To explore the K-5 Geometry Standards for Mathematics To experience a math activity that focuses on deeper understanding of the classification of shapes. http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g_k6_2012_06_27.pdf Today we are focusing on the Geometry Progression which can be found at http://ime.math.arizona.edu/progressions/ The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

The Geometry, Measurement and Data Standard from K-5 build into the middle school and high school geometry standards. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Illinois Mathematics Project

Geometry Learning Progression 2-D and 3-D Shapes Precise Terminology Compose and Decompose Properties and Attributes Sides and Angles Geometry Learning Progression K 1 2 http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g_k6_2012_06_27.pdf Today we are focusing on the Geometry Progression which can be found at http://ime.math.arizona.edu/progressions/ The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. I would like you to read through the overview on pages 2-5 and jot down a few ideas to share with a partner

Geometry Learning Progression Area Definitions Fractions Parallel, Perpendicular, Right, Acute, Obtuse angles, Line segments, Ray, Symmetry Volume Coordinate System Categorize Shapes Geometry Learning Progression 3 4 5

Read Geometry Progressions Overview Page 2-5 Introduce Think-Ink- Pair-Share strategy. Think about what they read. Note important ideas. Share ideas with a partner Share ideas with the whole group. http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g_k6_2012_06_27.pdf Today we are focusing on the Geometry Progression which can be found at http://ime.math.arizona.edu/progressions/ The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. I would like you to read through the overview on pages 2-5 and jot down a few ideas to share with a partner Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Introduce Think-Ink- Pair-Share strategy. Think about what they read. Note important ideas. Share ideas with a partner Share ideas with the whole group. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Introduce Think-Ink- Pair-Share strategy. Think about what they read. Note important ideas. Share ideas with a partner Share ideas with the whole group. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Introduce Think-Ink- Pair-Share strategy. Think about what they read. Note important ideas. Share ideas with a partner Share ideas with the whole group. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Goals for K-6 Geometry Shapes, components, properties and categorization based on properties Compose and decompose shapes Spatial relationships and structuring Bring out these important ideas Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Students recognize shapes. A rectangle “looks like a door”. Visual Students recognize shapes. A rectangle “looks like a door”. Descriptive Students perceive properties of shapes. A rectangle has four sides, all of its sides are straight, opposite sides have equal length. Analytic Students characterize shapes by their properties. A rectangle has opposite sides of equal length and four right angles. Abstract Students understand that a rectangle is a parallelogram because it has all the properties of parallelograms. Discuss this table From page 3 At the analytic level students recognize and characterize shapes by their properties. A student might think of a square as a figure that has four equal sides and four right angles. Different components of shapes are the focus at different grades, for instance second graders measure lengths and fourth graders measure angles. Initially, students cannot reliably distinguish between examples and non-examples of categories of shapes, such as triangles, rectangles, and squares. They are not thinking of properties of defining attributes of shapes. With experience, they progress to the next level of thinking. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

“From Kindergarten on, students experience all of the properties of shapes that they will study in Grades K–7, recognizing and working with these properties in increasingly sophisticated ways.” K-6 Geometry Progressions They increase their knowledge of a variety of shapes, including circles, triangles, squares, rectangles, and special cases of other shapes such as regular hexagons and trapezoids. For instance: K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. From Kindergarten on, students experience all of the properties of shapes that they will study in Grades K–7, recognizing and working with these properties in increasingly sophisticated ways. The Standards describe particular aspects Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Let’s do some math! Start with one post-it note. Fold the note in half on the diagonal. Cut along the fold. What new shapes have we created? Explore the shapes you can make with two triangles. What can we do to facilitate the development of geometric thinking? We need to engage students in geometric thinking focusing on the geometry standards at their grade level. Today we will experience a lesson that does just that. Ask participants “What shape is a post-it note?” Have participants do the activity on the slide Discuss Post a piece of Chart Paper Label it “Geometry Words” add to the chart as vocabulary is discussed. Add Square, Triangle, Diagonal… Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Guess My Rule These follow my rule These don’t follow my rule Tell the participants that we will be putting triangles together to make new shapes. However, we are going to follow a rule…Ask them to guess the rule. Rule: Sides that touch must be the same length and match up exactly. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

The Four Triangle Problem Cut another post-it on the diagonal. Use 4 triangles to compose a shape that follows my rule and tape it together. Is your shape the same or different from your teammates shapes? How do you know? What makes a shape unique? NOTE: Identical shapes could be different colors or in different positions. Rule: Sides that touch must be the same length and match exactly Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Shape Search With your team find all possible unique shapes using four triangles. Consider only congruence – not color or position. Tape each composite shape together. Persevere until you have found them all… how many do you think there are? Tell the participants that they will be working with their table teams to find all of the possible closed shapes that they can make with 4 triangles. They need to follow the rule. You can ask them to predict how many shapes they might find. Visit all groups and help them to keep looking for shapes There are 14 non-congruent shapes Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Shape Sort What attributes could you use to sort the shapes? Sort the shapes using this attribute. Display the results of your sort on a piece of chart paper. Be ready to share your sort. Participants can make posters of their sorts, then present their posters and discuss reason for sorts. Facilitator should highlight different strategies for sorting and ask for justification. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Connect to Geometry Progression Look at a grade level progression. How could you use the Four Triangle Problem at the grade level you teach? K.G. 2, 3, 6 Same or different shapes, identifying shapes 1.G. 1.G.2 2.G.1 sorting 3.G.1 sort different quadrilaterals 4.G.2,3 having attributes – parallel sides, perpendicular sides, lines of symmetry 5.G.3, angles Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

Connect to Geometry Standards Align this to a grade-level content standard. Align this to at least one practice standard. K.G. 2, 3, 6 Same or different shapes, identifying shapes 1.G. 1.G.2 2.G.1 sorting 3.G.1 sort different quadrilaterals 4.G.2,3 having attributes – parallel sides, perpendicular sides, lines of symmetry 5.G.3, angles Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

“It is important to vary the examples in many ways so that students do not learn limited concepts that they must later unlearn.” K-6 Geometry Progressions Like learning that a rectangle only looks one way or that the square is not a rectangle

Reflection How has the geometry domain changed since previous standards? How will this effect your teaching and planning? What resources/tools do you need to be able to implement the geometry domain in your classroom?

The Four Triangle Problem was written by Cheryl Rectanus and can be found in the book Math By All Means Geometry Grades 3 – 4 A Marilyn Burns Replacement Unit Copyright 1994 by Math Solutions Publications http://www.amazon.com/Geometry-Grades-3-4-Math-Means/dp/0941355101