3/17/14 ASDN Mathematics webinar #4 March 2014 What has happened since we were last together? Shrink the Change Brilliantly: Teach the focus areas of mathema-cal content within your grade band with precision Integrate standards of mathema-cal prac-ce into every lesson Provide quality performance tasks within your lessons 1 3/17/14 Shape the path 1.  Study the focus areas of mathema-cal content within your grade band with colleagues 2.  Integrate standards of mathema-cal prac-ce into one lesson a week 3.  Locate developed quality performance tasks The Why: Shift Three Rigor In major topics, pursue conceptual understanding, procedural skill and fluency, and applicaHon •  The Alaska MathemaHcs Standards require a balance of: –  Solid conceptual understanding –  Procedural skill and fluency –  ApplicaHon of skills in problem solving situaHons •  This requires equal intensity in Hme, acHviHes, and resources in pursuit of all three Problem Solving Plan video 2 3/17/14 Problem Solving Plan Ques-ons to Consider: •  How can students be encouraged to internalize the steps of the plan? •  Could you imagine giving students flexibility when working with the plan? •  Why/why not? •  What kinds of problems would be best solved with this plan? Looking at Tasks: Depth of Knowledge and Mathematical Practices, two lenses •  What is the depth of knowledge of these tasks? •  Which mathemaHcal pracHces do they promote? 3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 3 3/17/14 5.NF.C.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions Problem Solving Students can solve a range of complex well-­‐posed problems in pure and applied mathemaHcs, making producHve use of knowledge and problem solving strategies. A.  Apply mathemaHcs to solve well-­‐posed problems arising in everyday life, society, and the workplace B.  Select and use tools strategically C.  Interpret results in the context of the situaHon D.  IdenHfy important quanHHes in a pracHcal situaHon and map their relaHonships. Depth of Knowledge 4 3/17/14 Using rich tasks in the classroom… Let’s take a look… Solving a real problem Ques-ons to Consider: •  Why does Ms. Park go back to 3rd grade content standards? •  How does she ramp up to teaching 6th grade content? •  When Ms. Park says that you create your pracHce by knowing the content first, what does this mean? •  How does Ms. Park ask students to reflect on their learning? Why is this reflecHon important? 5 3/17/14 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b How did this activity support the big ideas of unit fractions? •  Determining what represents “whole” •  Reasoning about the size of a unit fracHon based on the meaning of a unit fracHon •  If the whole is represented by a region in the plane (area model) it is possible for idenHcal fracHons to be represented by different shapes? Environment for Rich Tasks •  Learners not passive recipients of mathematical
knowledge
•  Learners are active participants in creating
understanding and challenge and reflect on their own
and others understandings
•  Instructors provide support and assistance through
questioning and supports as needed
6 3/17/14 What makes a rich task? 1. 
Is the task interesHng to students? 2. 
Does the task involve meaningful mathemaHcs? 3. 
Does the task provide an opportunity for students to apply and extend mathemaHcs? 4. 
Is the task challenging to all students? 5. 
Does the task support the use of mulHple strategies and entry points? 6. 
Will students’conversaHon and collaboraHon about the task reveal informaHon about students’mathemaHcs understanding? Adapted from: Common Core Mathema,cs in a PLC at Work 3-­‐5 Larson,, et al Task Analysis Protocol Sheet Illustrativemathematics.org • 
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Performance tasks Videos of MathemaHcal PracHces Facilitated Professional Development Modules Three Year Planning Document 7 3/17/14 UPS Video 8