The Mathematics Design Collaborative (MDC) brings to mathematics teaching and learning high-quality instructional tools and professional support services that play a pivotal role in helping the Bill & Melinda Gates Foundation realize its ambitious goal of having 80% of low-income and minority students ready for college by 2025.

### Introduction: Professional Learning Modules for the MDC

This Introductory Guide is intended to communicate the particular interpretation of formative assessment that underpins the Shell Centerâ€™s lessons.

### Course Outlines and Professional Learning Workshop Guides for a Selection of Classroom Challenges for Grades 6 Through Algebra 2

These course outlines are provided to help teachers place the Classroom Challenges in their math courses. The Course Outlines illustrate how the mathematics of the California Core State Standards (CCSS) flows from Grade 6 to Algebra 2 in rigorous, focused, and coherent units of study. Classroom Challenges are allocated to various units within a Course Outline. For more information on the Classroom Challenges, please see the Math Assessment Project's website.

The workshop guides are developed as a resource for workshop facilitators preparing to rollout Professional Learning around the Classroom Challenges. Professional Learning workshop guides have been developed for a selection of the Classroom Challenges allocated to Grades 6 through Algebra 2. These guides link supplemental materials such as Student Work, Criteria for Feedback, Growth Analysis Spreadsheets, and videos (if videos are available).

#### Grade 6 Course Outline

#### Grade 7 Course Outline

- Developing a Sense of Scale
- Estimations and Approximations: The Money Munchers
- Evaluating Statements About Probability
- Increasing and Decreasing Quantities by a Percent
- Proportion and Non-Proportion Situations
- Steps to Solving Equations
- Using Positive and Negative Numbers in Context

#### Grade 8 Course Outline

- Classifying Solutions to Systems of Equations
- Estimating Length Using Scientific Notation
- Interpreting Distance-Time Graphs
- Lines and Linear Equations
- Modeling: Making Matchsticks
- Repeating Decimals
- Solving Linear Equations in One Variable

#### Summary of Course Outlines for Middle School

#### Algebra 1 Course Outline

- Comparing Investments
- Defining Regions Using Inequalities
- Forming Quadratics
- Functions and Everyday Situations
- Interpreting Algebraic Expressions
- Modeling: Having Kittens
- Optimization Problems: Boomerangs
- Rational and Irrational Numbers 1
- Solving Linear Equations in Two Variables
- Sorting Equations and Identities

#### Geometry Course Outline

- 2D Representations of 3D Objects
- Applying Angle Theorems
- Calculating Volumes of Compound Objects
- Equations of Circles 1
- Evaluating Statements About Enlargements (2D & 3D)
- Evaluating Statements About Length and Area
- Finding Equations of Parallel and Perpendicular Lines
- Proofs of Pythagorean Theorem
- Representing and Combining Transformations

#### Algebra 2 Course Outline

- Ferris Wheel
- Modeling Conditional Probabilities 1: Lucky Dip
- Modeling Conditional Probabilities 2: A Fair Game
- Rational and Irrational Numbers 2
- Representing Polynomials

#### Summary of Course Outlines for High School

### Video Library

This first set of videos shows US teachers enacting a selection of the Classroom Challenges in their classrooms. The footage for each lesson has been edited into useful chunks that preserve the chronology of the lesson. While many of the videos show lesson openings and closings, the highlight of many of these short chunks is students working collaboratively and productively to resolve the common issues revealed by the pre-assessments.**Classroom Challenges Video Library**

This second set of videos, also based on the enactment of the Classroom Challenges, presents more tightly edited vignettes that integrate student and teacher interviews with classroom footage to present themes or issues related to the implementation of these effective teaching tools.**Student & Teacher Interviews Video Library**