1. Formative Assessment Lessons grades 6 - 12 Mathematics Network Conference Santa Clara County Office of Education September 29, 2014 Suzanne Damm sdamm@santacruz.k12.ca.us Patricia Rogers patricia.rogers.math@gmail.com

2. Welcome to our session!

3. FALs  Formative Assessment Lessons  Classroom Challenges  Formative Re-engagement Lessons

4. Conceptual Understanding Problem Solving

5. ? Why? WHY? Why? Why?

6. Prior knowledge  What do you know?  Ways to discover it?

7. Key Differences  ‘Classroom Culture’  Productive struggle  Greater depth  Reflection

8. Organization of FALs  Pre-assessment  Student task  Post reflection

9. Let’s Try this One!  Representing and Combining Transformations

10. Pre-Assess  When?  Why?

11. What questions could you pose? a) Student confused the terms “horizontally” and “vertically”. b) Student ignores the center of rotation and rotates from a corner of the shaded triangle. c) Student used an inefficient combination of transformations.

12. Whole-class  Interactive Introduction (15 min.)

13. Translation P-13 Where will the L-shape be if it is translated by −2 horizontally and +1 vertically?

14. Reflection P-14 Where will the L-shape be if it is reflected over the line x = 2?

15. Rotation P-15 Where will the L-shape be if it is rotated through 180°around the origin?

16. Collaboration work (30 min.)  Student’s job  Card sort  Teacher’s job  Make notes of student approaches to the task  Support student reasoning

17. Matching Cards  Take turns to match two shape cards with a word card. Each time you do this, explain your thinking clearly and carefully.  Your partner should then either explain that reasoning again in his or her own words, or challenge the reasons you gave.  It is important that everyone in the group understands the placing of a word card between two shape cards.  Ultimately, you want to make as many links as possible.  Use all the shape card, and all the word the cards if possible. P-17

18. Whole-class discussion (15 min.)

19. Starting point (1, 4) P-19 Show me the new coordinates of the point (1, 4) after it is: Reflected over the x -axis Reflected over the y -axis Rotated through 180°about the origin. Reflected over the line y = x. Reflected over the line y = − x. Rotated through 90°clockwise about the origin. Rotated through 90°counterclockwise about the origin.

20. General starting point ( x, y ) P-20 Show me the new coordinates of the point ( x, y ) after it is: Reflected over the x -axis Reflected over the y -axis Rotated through 180°about the origin. Reflected over the line y = x. Reflected over the line y = − x. Rotated through 90°clockwise about the origin. Rotated through 90°counterclockwise about the origin.

21. Extending the discussion What is the single transformation that will produce the same result as: A rotation of 90 degrees clockwise around the origin, followed by a reflection in the y-axis? Show me two transformations that can be written as a single direction. Show me two tr4ansforamtions that cannot be written as a single direction. Can you change the starting point of the shape so that it can be written as a single direction?

22. Improving individual solutions to the pre-assessment task (10 min.)

23. Resources  Mathematics Assessment Project http://map.mathshell.org/  Inside Mathematics http://www.insidemathematics.org/  Georgia Department of Education https://www.georgiastandards.org/Commo n-Core/Pages/Math.aspx