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ACT IX Cohort Facilitator: Sohael Abidi October 3 rd, 2008 Day # 1

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Act Cohorts - Key Focuses Student & Teacher roles during lesson Facilitating Discussion: effective questioning - Engaging; Refocusing; Clarifying The Backward design of a lesson Assessment ‘For’ Learning; Assessment ‘As’ PD Embedding the Process Standards in lessons Mental Math Strategy Development Student & Teacher reflection on learning The Three Part Lesson Model Refer to ‘Today’s Mathematics Classroom Grades 7 – 9’ handout

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‘ACT’ Through Enduring Questions What is the math behind this activity? What are you assuming students need to know to do this activity? What process standards do you see in this lesson? How can this activity be accessible to all students? How will you know when your students have learned the math? What will you do with your assessment information? When would you do this activity?

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‘Three-Part’ Format for Problem-Based Lessons BEFORE DURING AFTER ▪ Get students mentally prepared for task ▪ Be sure the task is understood ▪ Clearly establish expectations ▪ Let go; listen carefully ▪ provide hints but not solutions ▪ Observe and assess ▪ Students discover the mathematics ▪ Engaging, redirecting, clarifying questions ▪ Allow enough time ▪ Share solutions and strategies ▪ Accept solutions without judgment ▪ Students justify and evaluate results and methods

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Process Standards How Students Acquire and Learn Math Knowledge Problem Solving – (build new math knowledge; using variety of strategies; monitoring and reflect on processes) Reasoning & Proof – (making math conjectures; develop and evaluate arguments/proofs; select and utilize various forms of reasoning and proof) Communication – (organize and consolidate thinking; clear and coherent; evaluate thinking strategies of others; use math language to express mathematical ideas) Connections – (recognize and utilize connections among math ideas; understand the interconnectedness of ideas; apply mathematics to external contexts)

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Process Standards How Students Acquire and Learn Math Knowledge Representations – (create and use to organize, record, and communicate ideas; use representations to model and interpret math phenomena; apply and select mathematical representations to solve problems)

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Representations Pictures Oral Language Written SymbolsManipulatives Real-World Situations Elementary and Middle School Mathematics: Teaching Developmentally by John A. Van de Walle

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Activity: The Human Number Line Obtain a number card from the facilitator Form a number line, from least to greatest Their should be NO TALKING! Once in line, you may discuss and explain your strategy that helped you make your decision.

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Human Number Line: Answer Least 0.01, 1/9, 0.2, ¼, 27%, 2/7, 1/3, 2/5, 0.45, ½, 53%, 4/7, 2/3, 5/7, 4/5, 0.82, 5/6, 9/10 3/3 Greatest

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Debriefing Discussion: Share our strategies Difficulties? What was one thing that you learned from the people beside you? How do we make this accessible to all learners? Reflect on the ‘Enduring Questions’ for each classroom activity…

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‘ACT’ Through Enduring Questions Human Number Line What is the math behind this activity? What are you assuming students need to know to do this activity? What process standards do you see in this lesson? How can this activity be accessible to all students? How will you know when your students have learned the math? What will you do with your assessment information? When would you do this activity? We will revisit these ‘core questions’ throughout the cohort

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Introducing a Mental Math Strategy Comparing & Ordering Real Numbers Warm-up – Pattern Blocks & Fraction Factory The Before: - If this is the whole, find ½. Find 1/6, ¼, 2/3, 9/12 - If this is the whole, find 2/6, ½, 2,3

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Warm-up Continued: If this is 2/3 of the whole, find the whole. Display each of the following fractions using pattern blocks or Fraction Factory: 1/3, 5/6, 5/12, 2/4

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Ordering Real Numbers (During) Indicate whether each of the following fractions are closer to either 0 or 1. (jot your answer down) Ready??

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Ordering Real Numbers

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0.78

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Ordering Real Numbers 0.3

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Ordering Real Numbers

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0.52

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Ordering Real Numbers

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The “After” What were some strategies used to make your decisions of ‘closer to 0 or 1?’ Share difficulties & discoveries Could we have used a ‘reference point’ along the number line? (benchmark) How would this have helped? Let’s model this using Fraction Factory or Pattern Blocks… (using ½ as our benchmark) How could we differentiate this activity? (Section #2 – Teacher Resource)

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Lesson #1: “How Close is Close?” (10 by 10 Grids / Faction Factory) With a partner, list 4 fractions between 1/9 & 8/9. Share your responses with your table members. Discuss methods as a group

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Lesson #1: “How Close is Close?” (10 by 10 Grids / Faction Factory) With a partner, list 4 fractions between ½ & 9/10. Share your responses with your table members. Discuss methods as a group

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Lesson: “How Close is Close?” (10 by 10 Grids / Faction Factory) Activity: Select two fractions that you believe are really close. The Task: Find 10 fractions that are between the two that you chose. Use any method you want, but you must be able to explain the method to your partner. Partner sharing session.

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Discussion Did your group make any discoveries? Share strategies of our group Can you make a conjecture regarding ordering fractions ? In what way has this activity changed your understanding of fractions?

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Lesson #1 - Debrief Refer back to the ‘Enduring Questions’ (slide 11) What were the 3-parts of this previous lesson (before, during, & after)? How Close is Close? – Lesson Plan Handout – discuss (designing a lesson backwards) - Big ideas, process standards, assessment Student Understanding - Handout

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Reinforcing a Mental Math Strategy What are some MM strategies we have discussed so far? Activity: - State whether the following real numbers are closer to ½ or 1. Ready??

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Reinforcing a Mental Math Strategy

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Okay, now… Place these values from least to greatest on a number line. (Fraction Factory available) 5/6, 2/3, 0.63, 12/24, 0.75, 6/8, 10/16

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Discussion/Debrief What were some strategies used for determining closer to ½ or 1? What were some strategies used for the number line placement activity? What might we see that could indicate the level of student thinking or understanding? What types of questions would lend to promoting student thought and exploration?

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LUNCH

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Back to The ‘Enduring Questions’ Closer to ½ or 1? Did any answers change from the introductory activity? (i.e.: closer to 0 or 1?) What is the math behind this activity? What are you assuming students need to know to do this activity? What process standards do you see in this lesson? How can this activity be accessible to all students? How will you know when your students have learned the math? What will you do with your assessment information? When would you do this activity?

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Mental Math Focus Handout select pgs. Of MM Booklet Please read select pgs. from grade 9 MM Booklet. “Introducing, reinforcing, & assessing” MM In groups, share ways in which you reinforce and assess MM. Assign one recorder for each group. Share strategies with the entire group.

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Things to remember… The idea of the “3 second response” expectation Variety of forms of assessment: observations; oral responses; explanations of strategies Assessment “For” vs. “Of” learning Importance of visuals when helping students understand a MM strategies: Alge-tiles; fraction factory; pattern blocks etc.

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Getting Back 49 units 2 36 units 2 45 units 2 ? ? Where/When would this activity be useful? Student Thinking?

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Lesson #2 “One integer is double another. The sum of their squares is 45. What are the integers?” Debrief Strategies

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“The Town Hall” (See Handout) A town council set up their town map in such way that the Town Hall was at the center (0, 0). This was then overlaid by a four-quadrant grid so that all locations were determined using positive and negative coordinates. The Hospital is located at (-5, -4), and the community swimming pool is located at (1, 4). One grid unit represents 1 km of actual distance. (a) How far are the hospital and the pool from city hall? (b) How far is the hospital from the pool? (Discuss your solution and procedure with a partner)

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Discussion/Debrief Strategies? (volunteers?) Areas of struggles? What about the Absolute Value and Principal Square root? Restrictions on Distance?

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Lesson #2 - Debrief Possible ‘Follow-Up’ ideas that will Reinforce student learning? See Portfolio Assignment Refer to the ‘Enduring Questions.” What outcome(s) did this activity cover? What are the three parts in the ‘3-Part Lesson Model?’ – What were they in the previous lesson?

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Mental Math – Reinforcement of a Strategy Ordering Real Numbers Let’s recall some strategies used to place numbers in order on a number line. Activity: Place the following numbers on #line using our Mental Math strategies. Do this activity alone, first. Then discuss with a partner.

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22/7, 6/7, 7/8, -3/4, 2/3, 0.62, ∏, -0.58

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Discussion What was the focus of conversations? Difficulties of placing certain numbers? Share solutions and strategies (volunteers?) Brainstorm: what types of assessment would be appropriate for this MM section? (Question levels; Question Types; pg.94 T.R) Portfolio Idea: Have students write about the strategies that are helpful to them, and when they apply.

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Manipulative Activity – Fraction Factory Refer to Handouts 5 – Minutes to Play! Demo and practice – work on sheets Addition, Subtraction, Multiplication, Division

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Q & A Participant questions Homework Sub-claim Forms

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