Park City Mathematics Institute
Middle School
Grade Level: 6-7
Subject: Ratios and Proportions
Topic: Unit rate and tools
Authors: Feynna Guerrero, Monica Valdez, Joanne Wells
Explore the new 6th grade tools (tape diagrams/double number lines) used to solve problems in Ratios and Proportions, and progress into 7th grade standards with rates involving fractional quantities.
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Grade Level: Middle Grades, 6-8
Subject: Middle School Mathematics
Topic: Functions Progression. From ratios to proportions to functions.
Authors: Ben Allen, Shelley Kryger, Nadine Williams
Teachers and grades can't work in isolation. This workshop will help bridge the cross-grade level gap, so teachers will know where their students came from and where they are going.

Building an understanding towards functions is critical. The relationships that functions represent is a key skill that students are expected to understand before entering high school. Teachers need to know what to emphasize as the focus at each grade level, and across grade levels, that lead to this important understanding.

In this activity, participants will work with one task about a teacher ordering baseball jerseys. However this one 8th grade task, adapted from the Mathematics Assessment Project, has been further modified. A second version addresses key proportion standards in 7th grade, and a third version addresses key ratio standards in 6th grade. By working with the same task that has been adapted to each grade level, participants can more clearly identify the progression of these topics throughout the middle grades towards functions.
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Grade Level: 6-8
Subject: Modeling in the CCSSM
Topic: How can we trace a mathematical task through the modeling cycle?
Authors: Diana Braham, Steven Koutsavlis, Aaron Orzech
This professional development session is designed to introduce participants to the Modeling Standard of the CCSSM and trace a mathematical task through the various components of the modeling cycle. Participants will explore the definition of modeling according to the CCSSM and will identify characteristics of what modeling does and does not look like in math classrooms. The guide then presents a sample seventh grade task and has participants respond to the task themselves, generating multiple mathematical representations. The session then compares these various representations, demonstrates how they can be manipulated to clarify solutions, and highlights how these processes are a central part of the modeling cycle. The guide employs the use of online tools such Desmos and Excel. Different examples of modeling tasks are then examined, along with counterexamples and opportunities for scaffolding. Finally, the guide outlines the broad range of applications that can be explored through mathematical modeling and shows how modeling connects to other Standards of Mathematical Practice in the CCSSM.
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Grade Level: Grade 8
Subject: Geometry
Topic: Transformations - Refection, translation, rotation, and dilation
Authors: Thea Curry, Barbara Lynch, Jessica Esquibel
This presentation was developed to help teachers implement transformations according to the CCSS and develop student understanding of congruence and similarity through rotations, reflections, translations, and dilations and describe their effects using coordinates. This unit centers on 8.G.2, 8.G.3, and 8.G.4 with a focus on hands-on activities and implementation of the math practice standards.
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Statistics and Probability
Grade Level: MS Grade 7
Subject: Middle Grades Statistics and Probability
Topic: Probability
Authors: Dillon, Fred and Sheridan, Mary Ann
Using Probability in the Middle School
The tasks in this session develop content knowledge of the Probability Standards in grade 7. Research on the learning of Statistics and Probability acknowledges the need for students to have hands-on experience with collecting data and becoming familiar with the underpinnings of probability. With that in mind, the activities in this session model the pedagogy of having students actively involved in their learning. We will focus specifically on developing an understanding of probability, using random samples and simulations, and Smaking inferences based on probability. Additionally, the session includes in context review of many of the standards from grade 6. There is a PowerPoint for a 90-minute professional development session that includes facilitator notes and handouts.
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© 2001 - 2013 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540

Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.