Elementary Sessions
Fractions, Essential Questions, and the Common Core Benjamin Geiger and Glen Sherman, Cambridge Public Schools
The Common Core standards present a significant shift in what students are expected to understand about fractions, and when and how deeply they are supposed to understand it. But how do we teach toward and measure depth of understanding? One approach is the use of Essential Questions and "backward" design: developing openended questions that serve as anchors through a unit and inform the creation of engaging lessons and challenging tasks. We'll look at some examples of this process and at some tasks that require students to demonstrate conceptual understanding on a variety of levels, and we'll consider how what we learn from student responses to such tasks can deepen our own understanding and support the development of further Essential Questions.
The Development of Division Concepts in Grades 36
Katherine Marin, Westwood Public Schools
This workshop examines the progression of division concepts throughout the CCSSM and will develop participants’ understanding of the visual models outlined in the division standards in grades 36. We will work with visual models including: pictorial models, bar models, number lines, arrays, and area models and discuss the affordances, limitations, and applications of the different models.
Essentials for Developing Early Numeracy (PreK2)
Jill Milton, Norwood Public Schools
During this session we will work with materials to help ensure that your early childhood classroom lessons are designed to provide students with opportunities for counting, building fluency with small numbers and developing the concepts of onetoone correspondence. Through the use of five and ten frames, dot cards and conversation we can ensure that students are engaging in experiences that support the development of early numeracy concepts. We will discuss visual and spatial arrangements along with the latest buzz word in early childhood mathematics, subitizing. These fundamental skills lead the way to ensuring students are successful with composing and decomposing numbers to ten and beyond. Are you teaching PreK mathematicians? Or providing remediation to a struggling second grader? Either or both? Please join me for an informationpacked session to learn practical strategies.
Is there high cognitive demand in the questions I ask? (Elementary)
Jennifer Shore, Newton Public Schools
The advent of the “Common Core Standards for Mathematical Practice” have created a need to examine the questions we ask students. In order for students to engage in meaningful mathematics, teachers need to start with highlevel, cognitively complex math tasks.
Using the work of Stein, Smith, Henningsen and Silver (2009) in Implementing StandardsBased Mathematics Instruction as a guide, we will explore and categorize questions posed in a K5 class during math instruction. We will measure the level of student engagement and thinking required by instructional tasks, consider how and why tasks differ and analyze how these differences can impact opportunities for student learning.

Middle School Sessions
PARCC Potpourri: Design, Cognitive Complexity, and Going Beyond the Single Standard
Darren Burris, Boston Collegiate Charter School PARCC has several documents that define what it is, how it works, and what it means for teachers and students. This presentation intends to provide the links between the claims of the assessment, the evidence collected by to support those claims, the tasks that are intended to elicit that evidence, and how student performance will be communicated to all stakeholders. This will lead to a more focused discussion of the cognitive complexity framework used in task design and scoring within the PARCC assessment. The hope is that understanding this assessment will lead to a new reading of the standards and what this means for classroom practice.
Is there high cognitive demand in the questions I ask (Middle School) Sherri Flecca, Newton Public Schools The advent of the “Common Core Standards for Mathematical Practice” have created a need to examine the questions we ask students. In order for students to engage in meaningful mathematics, teachers need to start with highlevel, cognitively complex math tasks.
Using the work of Stein, Smith, Henningsen and Silver (2009) in Implementing StandardsBased Mathematics Instruction as a guide, we will explore and categorize questions posed in a typical middle school math class. We will measure the level of student engagement and thinking required by instructional tasks, consider how and why tasks differ and analyze how these differences can impact opportunities for student learning.
Making Rational Numbers More Meaningful Peg Kenney, Boston College
Revisit rational numbers through the lens of the Common Core State Standards. Explore unit fractions, the relations <. =, >, the number line, operations, and probing questions. Perhaps you'll uncover some unexpected results!
Diagramming Problems in 58 Math Ellen Metzger, Lincoln Public Schools
A good diagram shows quantities and relationships visually. Participants will get acquainted with different types of diagrams that can be helpful to students (and teachers!) in solve problems and communicating about them. We will look at bar models, double number lines, area models, and possibly others in the context of rate problems, multiplication and division of fractions, and problems involving percents. Participants will be encouraged to create their own diagrams.

High School Sessions
How to flip without flopping: getting the most out of a flipped classroom Ross Benson, Cambridge High School
As more and more technology comes in to the mathematics classroom, teachers need to make sure that it is being used to help and not hinder the education process. A flipped classroom, where students watch lecture videos for homework and then spend class time on problems and activities, can lead to better differentiated instruction and a more efficient use of time in the classroom. I will lead a discussion about what has worked well in the three years since I flipped and what has not. Be on the lookout for an email with a link to the lecture part of this presentation so that we can spend most of the time on discussion and Q & A.
Rethinking Mathematics Education In the New Era Don Cameron, The Brooks School
The factorylike method of mathematics education we have employed for over 100 years worked well when the learned skills lasted a lifetime. But with the age of technology that has thrust upon us skills that become obsolete almost as quickly as they are introduced, has come the need to shift our focus from teaching to learning; from instruction to inquiry; from competitiveness to cooperation. The implementation of the Common Core Standards represents a significant step towards rethinking mathematics education. This presentation will share some useful technology techniques and pedagogical strategies that support the Common Core Standards while guiding us not only in becoming better teachers but also in helping our students to become better learners.
Do you See What I See? Lisa Lopes and Talitha Oliveri, Hopedale High School
In this workshop, participants will explore problembased learning activities that are aligned with the Common Core State Standards. Participants will work in small groups on finding equations to match patterns and learn some fun ways to get students actively involved in the problem solving process.
What We Can Learn from the “Lowly” Trapezoid
Steve Yurek, Leslie University
It’s just one property away from being a JAQ, but the trapezoid has a few secrets that make it a rich and interesting subject. There’s so much more to learn than just its perimeter and area.
JAQ: Just Another Quadrilateral
