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Cutting to the “Common Core” for Grades 6-8

2014 Winter Series590x

Join us in Orlando • February 14—15

** Register by February 7 ** 

The Interactive Institute for Grades 6-8 Educators 

Cutting to the “Common Core” In Mathematics in Grades 6—8 is designed to increase your knowledge of mathematics content related to the Common Core domains for the middle grades. 

This institute is part of the NCTM Interactive Institute Winter Professional Development Series—Cutting to the “Common Core,” available for Pre-K-12 Teachers and School Leaders.

Learn more about NCTM's Interactive Institute   2014 Winter Institute 6-8180x 

Focus on Your Grade 

Who Should Attend  

What You'll Accomplish  


Schedule Overview



Program & Presentations   

Registration & Rates 

Hotel & Travel  

Focus on your Grade 

The experience will be suited to your interests—you’ll take part in sessions and be grouped with educators according to the grade level you select for your strand of focus. 


  • Grade 6
  • Grade 7
  • Grade 8


 Who Should Attend  

  • Teachers Grades 6-8
  • Preservice teachers
  • Math specialists and coaches
  • Math supervisors
  • Lead teachers
  • Curriculum coordinators


What You'll Accomplish—Defined Outcomes  

Participants will—

  • understand the progression of the mathematics content in the Common Core State Standards within and across grade bands;
  • increase their knowledge of mathematics content related to the Common Core domains for grades 6-8;
  • identify instructional strategies that develop students’ habits of mind as espoused in the Standards for Mathematical Practice;
  • participate in activities that model formative assessment and appropriate pedagogy promoted in the Common Core State Standards.



  • Ratios and Proportional Relationships
  • The Number System
  • Expressions and Equations
  • Functions
  • Geometry
  • Statistics and Probability


Schedule Overview  

Friday, February 14 

(All content on this day will be addressed through the lens of the mathematical practices.)

8:00 a.m.–9:00 a.m. 

Materials Pickup

9:00 a.m.–10:15 a.m. 

Mathematical Practices Keynote (Diane Briars)

10:15 a.m.–10:30 a.m. 


10:30 a.m.–Noon 

Breakout Workshop 1 

Noon-1:00 p.m. 


1:00 p.m.-2:30 p.m. 

Breakout Workshop 2  

2:30 p.m.-2:45 p.m. 



Breakout Workshop 3  

Saturday, February 15 

(All content on this day will be addressed through the lens of assessment.) 

8:30 a.m.–9:45 a.m. 

Assessment Keynote (Presentations by Smarter Balanced and PARCC) 

9:45 a.m.–10:00 a.m. 


10:00 a.m.–11:30 a.m. 

Breakout Workshop 4  

11:30 a.m.–12:30 p.m. 


12:30 a.m.- 2:00 p.m. 

Breakout Workshop 5  

2:00 p.m.- 2:15 p.m. 


2:15 p.m.- 4:00 p.m. 

Breakout Workshop 6   


Keynote Presentations 

Diane Briars 

President-Elect, National Council of Teachers of Mathematics

Cutting to the Common Core for Grades 6–12: Focus on the Standards for Mathematical Practice  

The Standards for Mathematical Practice are an integral part of CCSSM with significant implications for mathematics teaching and learning. In this session, we will analyze these standards: What they are, why they are important, and what they look like “in action” in grade 6–12 classrooms.

Diane J. Briars is a mathematics education consultant and senior developer and research associate for the NSF-funded Intensified Algebra Project—a joint venture of the University of Illinois at Chicago, the University of Texas at Austin, and the technology company Agile Mind. Briars has served in many roles in NCTM over the years and has also had leadership roles with other national education organizations, including serving as president of the National Council of Supervisors of Mathematics (NCSM) and as a trustee of the College Board.

Doug Sovde 

PARCC Mathematics  

Director, PARCC Content and Instructional Supports   

Incorporating PARCC Tools into Your School Improvement Plan   

Learn about PARCC’s approach to assessing CCSSM using a variety of tools, and receive guidance and coaching in putting those tools to work in school classrooms.


 Shelbi Cole  Smarter Balanced Mathematics  

Director of Mathematics

Collaboration is the Key to Better Assessment

Learn how the Smarter Balanced Assessment Consortium has used the collective capacity of its member states to create a common vision for better mathematics assessment.



Fred Dillon150px  FRED DILLON
Baldwin Wallace University, Berea, OH
Jane Porath  JANE PORATH
Member, Board of Directors, National Council of Teachers of Mathematics 
Traverse City East Middle School, MI
Erik Tillema  ERIK TILLEMA
Indiana University – Purdue University, Indianapolis, IN


Program & Presentations 

Day 1 

Ratio, Proportion, and Function, (Parts 1 and 2)
Grades 6–8 
The major focus of mathematics in the middle grades is the ratio, proportion, and function strand. Experience the growth and development of this strand in grades 6–8 by engaging in a sequence of activities. Start with a hands-on activity that highlights different approaches to and representations for the important concepts of ratio. Continue with activities involving unit ratios, equivalent ratios, and methods of creating and solving proportions. Wrap up your work with an activity that highlights the connection between proportions and the key concept of function. The session will also model different formative assessments and important pedagogical moves for use in implementing the activities.

Grades 6-8
The culminating activity in this session is to establish a geometric proof of the Pythagorean theorem. To build to this work, examine two common methods for finding the areas of figures: (1) covering them with triangles and rectangles of known areas and (2) enclosing them in a rectangle or triangle of known area. As part of constructing the proof, engage in drawing geometric figures with rulers on grid paper, and discuss choosing an appropriate scale for drawings on grid paper. Also take part in a discussion of congruent figures made in the process of the proof and how to use transformations of these figures to demonstrate congruency.

Day 2  

Expressions and Equations: Connecting Number to Algebra
Grade 6
How does an expression differ from an equation? What are common errors that sixth graders make when dealing with expressions and equations? Examine rich activities that address these questions while helping students make connections between arithmetic and algebra. Explore how formulas fit with CCSSM for grade 6, and create and analyze methods of solving equations. Apply these ideas in considering important discourse moves and formative assessments for use with these topics.

Measures of Center and Variability
Grade 6
CCSSM expects students to do their first serious work with statistics in sixth grade. Explore activities that can support your students in meeting CCSSM’s expectations in the areas of statistics and probability. Investigate ways to collect and use data to explore measures of center, the shapes of graphs, and the variability of data. Questioning techniques and other effective teaching practices, including possibilities for formative assessments, will be important parts of this session.

Modeling and Making Sense of Multiplication and Division of Fractions
Grade 6   
Examine several different representations of multiplication and division of fractions to see what CCSSM means by the “standard algorithm” in grade 6. Then explore ways to help students understand division of fractions through the use of manipulative materials and different approaches, such as measurement and partitive models. Finally, take part in an activity that you can give to your students to extend their work to the use of reciprocals. The session will also model different formative assessments and important pedagogical moves.

Modeling Real-World Situations with Expressions and Equations
Grade 7

Students often struggle to differentiate between algebra and arithmetic. Explore both arithmetic and algebraic solutions to similar problems, and investigate how students can begin to differentiate between the two. Also explore how students can develop general expressions from repeating patterns, and consider common approaches as well as common errors that students make when working with symbolic expressions and equations.

What’s the Difference? Examining Key Ideas Related to Operations with Integers
Grade 7 

Learn three key conceptual ideas about addition and subtraction with integers that will expand your students’ understanding of these operations, particularly subtraction. By examining problems in different contexts and samples of student work, learn strategies to help your students develop a better understanding of operations with integers.

How Likely Is It? Developing Probabilistic Reasoning
Grade 7

Take away strategies that you can use to identify and dispel common student misconceptions as well as support students as they learn to reason productively about probability by solving mathematical problems. Unpack vocabulary related to the probability standards in CCSSM, and consider sample problems that facilitate understanding of such ideas as compound events and experimental probability.

Building an Understanding of Irrational Number
Grade 8
CCSSM expects students to develop their understanding of rational and irrational numbers in grade 8. Explore rich tasks that you can readily implement in your classroom. Learn how to support your students in making geometric connections with concepts related to square roots and cube roots. The session will also focus on effective discourse and formative assessment.

Expressions and Equations: Student Modeling of Functions
Grade 8
As detailed in CCSSM, a major focus in grade 8 is the concept of linear functions. Explore activities that offer opportunities to work with power tables and systems of linear equations. What patterns do you notice? Why do those work? Would you expect your students to see and understand these patterns? What other methods could you—or your students—use to solve the problems? The session will also address connections among the tasks and opportunities for gathering data to inform instruction.

Exploring Real Issues with Statistics and Probability
Grade 8
Are women really catching up with men in terms of income? Are they closing the gap and moving toward income equality? Analyze relevant data, make inferences, and justify your conclusions as you engage in a statistical activity that you can implement in your classroom. The session will also focus on the processes in CCSSM’s Standards for Mathematical Practice, formative assessment, and the power of purposeful discourse. 



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