1. Understanding Angle Group 3 CCLM^2 Spring 2013 Leadership for the Common Core in Mathematics (CCLM^2) Project University of Wisconsin-Milwaukee, 2012–2013 This material was developed for the Leadership for the Common Core in Mathematics project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. You may not use this work for commercial purposes. This project was supported through a grant from the Wisconsin ESEA Title II Improving Teacher Quality Program.

2. OPENING MUSIC ON ANGLES Source: http://www.youtube.com/watch?v=yptZt9hwrzU

3. UNDERSTANDING ANGLE Common Core Leadership in Mathematics Tuesday, January 29, 2013 Suzette Grube-Thur, Cecile Labecki, Patty Coleman, Liz Cutter

4. UNDERSTANDING ANGLE Introductions Learning Intentions and Success Criteria What Makes an Angle? Exploring Angle Measurement Examining the Conceptual Development of Angles and Angle Measurement Invitation

5. LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to… - Define and measure angles. - Understand student expectations of angle identification and measurement as defined by one standard in grade 4. We will be successful when we can… - Explain the mathematical content and language of standard 4.MD.5a and provide examples of the mathematics and language.

6. On your index card, answer this question: What is an angle? Write a definition and draw a representation of your thinking. ~ 3 minutes ~ Share your thinking with your shoulder partner.

7. CCSSM DEFINITION: An angle is a geometric shape that is formed wherever two rays share a common endpoint.

8. Individually: -Read the standard -Highlight key words and key phrases -Use your worksheet to draw a representation for the standard ~ 5 minutes ~

10. AN ANGLE IS FORMED WHEREVER TWO RAYS SHARE A COMMON ENDPOINT  As you consider this definition, think of some activities you could use with students to develop an understanding of this concept. ~ 4 minutes to brainstorm ~

11. WHAT MISCONCEPTIONS MIGHT STUDENTS HAVE AS THEY APPROACH ANGLES? 3 minutes to brainstorm

12. EXPLORING ANGLE MEASUREMENT WITHIN A CIRCLE

13. HOW MIGHT YOU USE THIS FIGURE TO PROVE THAT THE MEASURE OF EACH ANGLE OF A SQUARE IS 90°? A Circle is 360° Since a circle can be drawn around any given point, we can find the measure of the angles in a polygon. 360/4 = 90 ~ 3 minutes ~

14. USE YOUR PATTERN BLOCKS TO DETERMINE THE DEGREE MEASURE OF THE SPECIFIED ANGLE. Share your thinking on chart paper. In your explanation make sure you are referencing the language from the standards. From this perspective how would students view angle size? Also, consider which math practices you may highlight in your focus when teaching this with students. ~ 10 minutes ~

15.  As you examine your grade level Standards, what connections do you find that help students prepare for or build upon understanding of angles and angle measurement in this fourth grade standard? ~ 6 minutes ~

16. LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to… - Define and measure angles. - Understand student expectations of angle identification and measurement as defined by one standard in grade 4. We will be successful when we can… - Explain the mathematical content and language of standard 4.MD.5a and provide examples of the mathematics and language.

17. INVITATION TO CONSIDER  As you return to your respective mathematical worlds, please consider how you will facilitate the development of the concept of angle.