CCGPS Mathematics Unit-by-Unit Grade Level Webinar 3 rd Grade Unit 5: Geometry November 13, 2012 Session will be begin at 3:15 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

Please provide feedback at the end of today’s session.  Feedback helps us all to become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit to share your feedback. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– Elementary Mathematics Specialist

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Third Grade Unit 5: Geometry November 13, 2012 Turtle Toms– Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Welcome! Thank you for taking the time to join us in this discussion of Unit 5. At the end of today’s session you should have at least 3 takeaways:  What the research says about developing understanding.  Ideas to support student and teacher understanding.

The intent of this webinar is to bring awareness to:  the development of foundational geometry understanding.  the mathematics of Unit 5.  the underlying structure of a task. We will view task structure by looking at the culminating task for Unit 5 during this webinar.

What’s Unit 5 all about? Geometric properties Examples and non-examples of a variety of plane and solid figures Hierarchy of quadrilaterals Partitioning plane figures into equal areas- halves, thirds, fourths, sixths and eighths. Data collection and use

What should students bring from previous grades? Knowledge of triangles, quadrilaterals, pentagons, hexagons, cubes, cones, cylinders, spheres, rectangular prisms Familiarity with angle, face terminology Two-dimensions, three dimensions Defining attributes of various shapes Partitioning into halves, thirds, fourths Foundations of area Measurement with inches, feet, centimeters, meters Line plot, bar graph, picture graph

Levels of geometric thinking: Visual/syncretic- Students recognize shapes, e.g., a rectangle “looks like a door.” Descriptive- Students perceive properties of shapes, e.g., a rectangle has four sides, all its sides are straight, opposite sides have equal length. Analytic- Students characterize shapes by their properties, e.g., 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.

Students find that some combinations of properties signal certain classes of figures and some do not; thus the seeds of geometric implication are planted. However, only at the next level, abstraction, do students see relationships between classes of figures (e.g., understand that a square is a rectangle because it has all the properties of rectangles) Competence at this level a ff ords the learning of higher-level geometry, including deductive arguments and proof.

Thus, learning geometry cannot progress in the same way as learning number, where the size of the numbers is gradually increased and new kinds of numbers are considered later. In learning about shapes, it is important to vary the examples in many ways so that students do not learn limited concepts that they must later unlearn. ( 06/ccss_progression_g_k6_2012_06_27.pdf)

Geometric properties

What’s Unit 5 all about? Using and sorting examples and non-examples of a variety of plane and solid figures

Regular vs irregular polygons Regular- equal sides, equal angles Irregular- unequal sides and/or angles. Is a rectangle regular or irregular?

What’s Unit 5 all about? Hierarchy of quadrilaterals

Subset thinking:

Trapezoid? In the U.S., that the term “trapezoid” may have two different meanings. In their study, The Classification of Quadrilaterals (Information Age Publishing, 2008), Usiskin et al. call these the exclusive and inclusive definitions: T(E): a trapezoid is a quadrilateral with exactly one pair of parallel sides T(I): a trapezoid is a quadrilateral with at least one pair of parallel sides.

These different meanings result in different classifications at the analytic level. According to T(E), a parallelogram is not a trapezoid; according to T(I), a parallelogram is a trapezoid. Both definitions are legitimate. However, Usiskin et al. conclude, “The preponderance of advantages to the inclusive definition of trapezoid has caused all the articles we could find on the subject, and most college- bound geometry books, to favor the inclusive definition.” Based on the above, Georgia will use the inclusive definition. A trapezoid is a quadrilateral with at least one pair of parallel sides.

What’s Unit 5 all about? Partitioning plane figures into equal areas- halves, thirds, fourths, sixths and eighths.

What’s Unit 5 all about? Data collection and use Picture graph vs pictograph

What’s Unit 5 all about? Geometry progression: ( g_k6_2012_06_27.pdf)

Culminating Task: Geometry Choice Board What is the goal of this task? How can you structure the task so that it works for your classroom?

Culminating Task: Geometry Choice Board What is the goal of this task?

Choice Board What might you add? How might you increase student choice/entry points?

Culminating Task: Geometry Choice Board How can you structure the task so that it works for your classroom? Intro task- start with task and rubric. Edit either/both to better fit your students. Students work independently/you circulate and ask questions, take notes Set benchmarks along the way to keep students moving forward, help kids to organize their workflow

Culminating Task: Geometry Choice Board Refer students back to rubric all along the way to help kids to organize their thinking and improve their work. Choose strategically which student ideas offer opportunities for “mid-stream minilessons”. Question more than you answer. Listen more than you talk. If you are recording your thinking, you are modeling your expectation for them.

Culminating Task: grade-math?fd=1 grade-math?fd=1

Rubric How might the rubric be made more useful for your students? How might the rubric be made more useful for you?

Horizontal and vertical connections Strategies apply everywhere, in multiple contexts Integration of content areas ensures connections and relational thinking Multiple steps builds understanding and deeper thinking Work the culminating task collaboratively with colleagues so you know where your kids need to go, and what they might have difficulty with

Effective Feedback Sharing thinking

Culmination of the unit, not the grade.

Food for thought: “ I’ve learned a lot from watching good teachers. The most important thing I’ve learned: adopt the mantra “ Just the answer isn’t good enough.” I watched teachers transform passive students into thinkers because of this simple idea. This expectation, that a teacher sets at any point in the year, opens up doors to all of the SMP’s (not every one every day – but many every day). In those classes, because “ just the answer isn’t good enough,” kids made sense of the mathematics they were doing, reasoned to justify that their answer was correct, critiqued their work and others’, used tools and made models of the mathematics that was happening, used some measure of precision as they explained their thinking, and sometimes found structure (even a few teachers found this) in their own repeated reasoning.” From a math coach friend…

Thank You! Please visit to provide us with your feedback! Turtle Gunn Toms Program Specialist (K-5) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! Follow on Twitter! (yep, I’m tweeting math resources in a very informal manner)