Park City Mathematics Institute Middle School Module Abstracts
Path to Functions
Subject: Mathematics
Title: Path to Functions
Authors: Devin Engledew, Jessica Reynolds, Anita Yu

The Common Core State Standards set the pathway for a progression of the concepts building to functions. This training emphasizes the connection between visual patterns and functions while also providing problem sets that can be used in grades 7, 8 and algebra instruction. Clear understanding of the progression empowers teachers to make more informed choices about their instruction. Teachers will exit this training with new ideas about how to leverage student prior knowledge, how to provide familiar access points to new material, and how to help students identify patterns within increasingly complex functions. In addition to these tools, teachers will be provided with a summary of function standards by grade level linked to example tasks and will develop a renewed appreciation for the design of the CCSS sequence.

Differentiation
Subject: Middle School Mathematics
Title: Rich Tasks That Naturally Differentiate
Authors: Ron Lodetti, Jennifer Mack, Kristen Smith

The CCSSM Math Practice #1 is for students to make sense of problems and persevere in solving them. That happens when a) the tasks are worth persevering to solve, and b) the students have the tools so that persevering can lead to success. Since we all teach in classrooms where students have a wide range of skills, experiences, and dispositions, the best tasks for working on MP1 are those that naturally 'differentiate.'

In this workshop we're going to explore how to choose or modify tasks so that struggling and advanced students can both get better at MP1. Participants will compare and contrast tasks and evaluate them based on their accessibility and rigor. This workshop will highlight two components of a rich task - a high floor and a low ceiling. By the end of the workshop participants will be able to evaluate the entry points, solution paths, and extensions of tasks.

Multiple Representations
Subject: Expressions and Equations in CCSSM
Representation in Expressions and Equations: Grades 6-8
Authors: Lauren Leischer, David Newhouse, Leah Parnes

This professional development session allows participants to explore multiple representations throughout the middle school Expressions and Equations domain in the Common Core State Standards. Participants will learn about the Lesh model, a model used to categorize representations and think about connections among multiple representations for one situation. Participants will develop methods of connecting representations by completing a middle school task and developing questions to help students. By connecting multiple representations, participants will specifically address Standards of Mathematical Practices 4 and 7 (4: Model with Mathematics and 7: Look for and make use of structure).
The task involves the familiar Tortoise and the Hare fairytale and asks participants to represent different parts of the task in multiple ways. The participants will experience the task in two parts that highlight the progression of the standards from 6th through 8th grade.

Fractions
Subject: Middle School Fractions
Title: Middle School Fractions
Authors: Caitlin Webster, Jennifer Outzs, Marcia Bonds

According to the 1988 NCTM Yearbook on Algebra, almost half of common Algebra mistakes were related to fraction misconceptions. It is essential to middle school students' success that their teachers have a solid understanding of the elementary school fraction progressions. This workshop will present tasks from the 3rd - 6th grade fraction strand to inform middle school teachers of some key standards within the progression. Participants will look at a 7th grade CCSSM task that incorporates students' prior knowledge of fractions to a ratio and proportion problem that involves complex fractions. Teachers will apply their understanding of the fraction progressions to solve the task and address potential student misconceptions.

Socio-Mathematical Norms
Grade Level: Middle School (6th - 8th)
Subject: Mathematical Practice 3
Title: Let's Talk Math Baby!
Authors: Rachell Ashley and Nadine Williams

This professional development session is designed to have participants identify norms that promote productive Math discussions, experience what that looks like, read about reasons students do not participate in these types of discussions, and decide on teacher moves that will establish norms in their classrooms that foster productive Math discussions.

Ratio & Proportional Relationships
Subject: Ratios and Proportionality
Title: Using Two Interpretations of Ratios to Develop Proportional Reasoning
Authors: Ryan Casey, Barbara Lynch, Mary Ann Sheridan

This professional development session is designed to introduce participants to the two perspectives on ratios: 1) a ratio as a composed unit and 2) a ratio as fixed number pairs as described in the Appendix of the Progression on Ratios and Proportional Relationships for the Common Core State Standards in Mathematics. Using two-color chips participants will explore and apply these two perspectives while looking for relationships in a Plant Growth Task. This module explores the progression of ratios needed for proportional reasoning. Connections will be made between a manipulative, its table, double number line, graph and the equation within the context of the task.

Technology
Subject: Using technology as a tool to teach
Title: Middle School Technology
Authors: Chase Arington, Cheryl Schafer

This presentation is designed to enable teachers to use technology as an instructional tool. It is not device specific, and therefore can be adapted to laptops, tablets, iPads, graphing calculators.... The focus will be on Math Practice Standards 5 (use tools strategically), 7 (make use of structure and patterns) and 8 (regularity in repeated reasoning/generalizing). Through the use of Desmos, teachers will explore proportional and linear relationships with sliders and will learn how to create such documents themselves. Teachers will see how being able to explore multiple examples in a short span of time allows for patterns to appear and generalizations to be made.