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For Use by DPS and Blueprint Only. Standards of Mathematical Practices 1 & 3 Math Fellow Training 2013

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SMP 1 & 3 Objectives: F/CWBAT explain why it is important for students to demonstrate proficiency in SMP 1 and 3, citing real world connections. F/CWBAT explain how the techniques Ratio and Wait Time can affect student achievement, citing the Framework for Fellow Effectiveness indicators for SMP 1 and 3.

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Do Now 1. Give a real world example from your life of a time when you had to, “make sense of a problem, and persevere in solving it.” 2. Give a real world example from your life of a time when you had to, “construct a viable argument and critique the reasoning of others.”

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SMP 1 Standards of Mathematical Practice 1: Make sense of problems and persevere in solving them Student Indicators Students ask probing questions to clarify conceptual understandings Students respond appropriately to problems, despite the difficulty level Students describe possible approaches to a solution Students identify connections to prior learning Students are able to identify specific steps they will take to accomplish weekly goals, as well as long-term SMI and TCAP goals Students persist in making multiple attempts to solve, and avoid asking for the solution Students check their answers using different methods Students monitor their progress and change strat egies when needed Students utilize reading comprehension strategies

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SMP 1 Standards of Mathematical Practice 1: Make sense of problems and persevere in solving them Framework for Fellow Effectiveness: Instructional Practice 1: Ask clarifying questions and extend student thinking Fellow Indicators Fellow asks “how and why” questions Fellow explains and emphasizes the understanding of a concept, before teaching a procedure or algorithms Fellow links lesson objective to prior learning Fellow links daily work to students’ lives, as a means to motivate and encourage perseverance Fellow gives students appropriate wait time Fellow does not allow students to opt out of a response Fellow scaffolds instruction effectively Fellow celebrates resilient problem solving efforts Fellow models, and empowers students to utilize, reading comprehension strategies

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SMP 1 Standards of Mathematical Practice 1: Make sense of problems and persevere in solving them Framework for Fellow Effectiveness: Instructional Practice 1: Ask clarifying questions and extend student thinking Evidence Implementations Strategies and Resources Student or Fellow work samples with written explanations and key academic language Example problems with multiple approaches for solving Current data trackers, utilized for self-monitoring by students Wait Time Teach Like a Champion pg. 134

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SMP 3 Standards of Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Student Indicators Students use assumptions, definitions, and previous results to explain or justify solutions Students use logic to articulate conjectures Students use examples and counterexamples in constructing viable arguments Students justify conclusions in a way that is understandable to teachers and peers Students compare two possible arguments for strengths and weaknesses Students use academic language appropriately Students write viable arguments in their work Students write precise and reasonable critiques of others’ work

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SMP 3 Standards of Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Framework for Fellow Effectiveness: Instructional Practice 3: Encourage student discourse Fellow Indicators Fellow asks “how and why” questions Fellow provides opportunities for students to analyze other students’ work to try to understand the thought process behind the work Fellow explains and emphasizes the understanding of a concept, before teaching a procedure or algorithms Fellow has students make and test conjectures to communicate their mathematical thinking Fellow encourages productive student discourse around viable arguments and critique of reasoning by: ○ Providing a positive, respectful environment: Error is normalized, all students have equal opportunity to share, students receive precise praise, questions are encouraged ○ Modeling productive discourse: Proper language usage, active listening skills, turn-taking, utilizing wait time, questioning, respectful disagreement ○ Scaffolding to support dialogue: Providing sentence starters for questioning and disagreement ○ Upholding high expectations ○ Emphasizing that reasoning is more important than the final answer

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SMP 3 Evidence Implementations Strategies and Resources Sentence starters and discussion points posted Student work demonstrating arguments that justify reasoning, with specific feedback from Fellow and/or peers Ratio Teach Like a Champion pg. 92 Standards of Mathematical Practice 3: Construct viable arguments and critique the reasoning of others Framework for Fellow Effectiveness: Instructional Practice 3: Encourage student discourse

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Video - Christina For Use by DPS and Blueprint Only. Christina Dehning 02 - http://vimeo.com/album/232324 0/video/62896858 http://vimeo.com/album/232324 0/video/62896858 Password = mindthegap (start time 10:00 – end time 12:00) Look for… SMP 1 & 3 indicators What are students doing? What is the Fellow doing? What other evidence do you see? I noticed examples of SMP1/3 when…”

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Ratio and Wait Time For Use by DPS and Blueprint Only. Ratio: The proportion of cognitive work your students do 1.Unbundle 2.Half-statement 3.What’s next? 4.Feign ignorance 5.Repeated examples 6.Rephrase or add on 7.Whys and Hows 8.Supporting evidence 9.Batch process 10.Discussion objectives WaitTime Strategically delaying a few seconds after answering a question Narration

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Video - Christina For Use by DPS and Blueprint Only. Christina Dehning 02 - http://vimeo.com/album/232324 0/video/62896858 http://vimeo.com/album/232324 0/video/62896858 Password = mindthegap (start time 10:00 – end time 12:00) Look for… Ratio &Wait Time techniques I noticed examples ratio when…”

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Exit Ticket 1. Explain how the techniques Ratio and Wait Time connect to student achievement, citing the Framework for Fellow Effectiveness indicators for SMP 1 and 3. 2. Explain why it is important for students to demonstrate proficiency in SMP 1 and 3, citing real world connections.

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