1. Orchestrating Discourse by Reengaging with Complex Tasks Ashley McCullough and Russell Geisner Promenade Elementary School, Alvord Unified School District

2. Choosing a Task:  MARS Tasks  Math Assessment Resource Service  Silicon Valley Mathematics Initiative (MAC)  Older ones available online  Search by grade level  1997 Standards aligned  Inside Mathematics  Newer ones aligned with CCSS available to SVMI member districts (secure) Good Entry Point Equal Access High Ceiling Productive Struggle for All Multiple Linked Tasks Complex Task

3. Tips for Timing the Task for Optimal Discourse Give the task before instruction has occurred Students work independently (SMP #1) No erasing Making tools available (SMP #5) All approaches are valuable Beginning of a Unit Builds Background Knowledge Encourages Discourse Discourages Regurgitation Becomes an Anchor for the Unit Build on Prior Understanding SMP #3 Construct viable arguments and critique the reasoning of others.

4. Two Fifth Grade Examples (Kind of): Hexagons Candies  Unit on 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.  Could also be used with:  6.EE.B.6 Use variables to represent numbers and write expressions when solving a real- world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  4. OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.  Unit on 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.  Could also be used with:  5.NF.B.6 Solve real word problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.  4.NF.A.1 Explain why Fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.

5. Analyzing Student Work Where did class’s understanding break down? Common Misconceptions Shared Knowledge Clear/Unclear Explanations Standout Strategies: Correct and Incorrect

6. Establishing a Learning Objective Learning Goal Students’ Knowledge Standard and SMPs Common Misconceptions

7. Our Goals Last Time Around: Hexagons Candies  Differentiate between a “within terms” pattern and a “without terms” pattern.  Discuss efficiency of each type of pattern.  Write an expression or “rule” for table.  Differentiate between a ratio and a part of a whole fraction.  Use equivalent fractions and ratios to answer solve problems.  Persevere in solving problems. (SMP #1)

8. Selecting Student Samples:  Categorize student strategies into groups:  Students who directly modeled the problem.  Students who used counting strategies.  Students who used equations. (SMP #7)  “Direct Modeling strategies are replaced by more abstract Counting strategies, which in turn are replaced with Number Fact strategies.” Children’s Mathematics p. 34  Consider connections that can be made between the strategies.  Samples should serve as a ramp for the students, taking them from where they were to where you want them to be.

9. Student Samples- What order? Productive Struggle SMP #3-Construct Viable Arguments and Critique the Reasoning of Others Incorrect First Equal Access to All Students Students have an end point about which to talk. Correct First

10. Facilitating the Discussion Getting Started Give students time to remember what strategies they used. Quickly review questions from the task on which students were successful. Show Student Sample #1 and give students quiet time to analyze it. Give Pair/Share time. Class needs to come to a consensus. What is the right answer? Students decide what is right or wrong. Go To Questions What did this student know? Not know? Is this answer correct or incorrect? Why? How are these strategies similar? Different? Can you fix this answer? How are the numbers from the problem represented in the model or equation? Are these answers the same? Equivalent? Would this strategy work all the time? Tips Duct Tape! Ask questions and repeat student answers only. Be flexible! Lots of Pair/Share Listen during Pair/Share and give a “heads-up”. Ask students to repeat/paraphrase. Follow up CFU Be flexible!