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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

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Welcome to our session!

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FALs Formative Assessment Lessons Classroom Challenges Formative Re-engagement Lessons

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Conceptual Understanding Problem Solving

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? Why? WHY? Why? Why?

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Prior knowledge What do you know? Ways to discover it?

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Key Differences ‘Classroom Culture’ Productive struggle Greater depth Reflection

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Organization of FALs Pre-assessment Student task Post reflection

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Let’s Try this One! Representing and Combining Transformations

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Pre-Assess When? Why?

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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.

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Whole-class Interactive Introduction (15 min.)

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

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

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

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

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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

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Whole-class discussion (15 min.)

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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.

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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.

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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?

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

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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

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