Packaged Courses

BEAM’s packaged courses from our summer programs are available to the math enrichment community.

BEAM courses are created with mathematical beauty and utility in mind. Our classes are uniquely collaborative, student-centered, and promote rich mathematical understanding and exploration.

These courses are designed for students from historically excluded backgrounds who are ready for more challenging math. We hope these courses will be utilized by school districts and communities, individuals running math circles, BEAM teachers gaining inspiration from colleagues at different sites, and more.

See the outlines of BEAM’s packaged courses below.

If you’d like to inquire further about using one of our packaged courses, please email us at info@beammath.org.

Each course contains:

  • Lesson plans for 11 1-hour-long classes.

  • Problem sets that offer puzzles and problems that are extensions or classwork for each lesson.

  • Answer keys for each problem set.

  • Course overview with background information for educators on course goals, philosophy, and additional context and resources.

  • Suggestions for extensions and scaffolding, as well as best practices for how to use a second person (such as a teaching assistant) during the lesson.

Logical Reasoning Courses

Logical Reasoning courses introduce topics and skills including: deductive logic, case analysis, working methodically, and proof by contradiction. Students are first introduced to puzzles such as Sudoku or Ken-Ken, liar/truthteller puzzles, or "matching riddles." Having gained basic skills in these puzzles, they transition to using those skills on mathematical problems.

Puzzles ‘N Proofs

Author: Sam Hilkey

This course features…

  • An experience mirroring what mathematicians do. Students tackle challenging non-procedural problems, build logic and problem-solving skills, and gain exposure to formal proofs.

  • Constant student engagement in small-group work on fun and challenging problems, such as the “100 Coins Problem” and the “Broken Eggs Problem.”

This course is good for someone who…

  • Wants to facilitate students’ work on challenging, open-ended problems that typically do not have an immediate answer.

  • Teaches middle-school or high-school students in any setting.  Several problems are challenging enough for older students and can be used as stand-alone activities.

  • Is interested in teaching with group work structures from Building Thinking Classrooms, by Peter Liljedahl. Course plans provide clear descriptions on implementing practices such as visibly random groups, vertical non-permanent surfaces, and verbally introduced problems.

Puzzling, Yet Logical!

Author: Sarah Yoseph

This course features…

  • An introduction to logic and problem-solving skills through engaging puzzles such as KenKen, cryptarithms, and logic grids.

  • Consistent structures for students to record and reflect on their problem-solving tools and process.

  • A capstone activity in which students create their own puzzles and solve classmates’ creations.

This course is good for someone who…

  • Loves solving puzzles and wants to share this with their students.

  • May be newer to teaching or to middle-school students.  The course includes very specific, detailed plans and tips for successfully implementing activities.

Cryptarithms

Author: Sian Zelbo

This course features…

  • An in-depth overview of the topic of logical reasoning and descriptors of what logical reasoning skills look like in middle schoolers.

  • Classic math problems such as “The Brownie Problem / Square Squares.”

This course is good for someone who…

  • Seeks a course that blends pedagogical insight with elegant content. This course could fit academics with less experience teaching young people or math coaches.

  • Is curious about more problems outside of the course. The course author wrote “Camp Logic,” a book that contains additional logic puzzles and activities that educators can build on.

Applied Math Courses

Applied Math introduces students to different areas of work related to mathematics. Examples include programming, astronomy, mathematical biology (such as predator and prey models, or genetics), or estimation and Fermi problems.

Aviation

Author: Catherine Tung

This course is good for someone who…

  • Knows some physics, including principles of forces such as lift, thrust, weight, and drag.

  • Is excited about guiding students through building and testing engineering projects.

  • Can lead students through building, testing, and recording data about their prototypes.

This course features…

  • An engaging, hands-on introduction to principles of aviation.

  • Exciting engineering projects in every lesson: students build kites, balloons, gliders, and rockets.

  • Engagement with the scientific method, as students test and record data about their designs.

Games and Strategies

Author: Taylor Courtney Corcoran

This course is good for someone who…

  • Has more experience teaching adults than teaching teenagers; the lessons:

    • Have both abbreviated and scripted plans, and include clear directions for teachers.

    • Provide a developmentally appropriate introduction to logical argumentation.

    • Show an alternative to lecture-style instruction.

This course features…

  • Games students likely haven’t seen before!

  • Student engagement strategies and cues for educators.

  • Opportunities to connect content to other Discovery packaged courses: this course features concepts present in Voting Theory and Big Questions and Big Answers. 

Voting Theory

Author: Meghan VanderMale

This course is good for someone who…

  • Is ready to learn new material themselves.

  • Is an interdisciplinary topics teacher or Expeditionary Learning (EL) school teacher.

  • Has classroom management experience due to lessons with physical activities and requiring materials management.

This course features…

  • Totally new content for students! This course includes analysis of different voting systems and matching algorithms, and introduces students to polyominoes and a geometric understanding of compactness.

  • Topics directly connect to real life, particularly in years with federal elections.

  • Lessons that challenge traditional understandings of mathematics as static — “what makes things ‘fair?’” and “who gets to decide?” are questions that arise on multiple occasions.

Primes and Programming

Author: Anna Pierrehumbert

This course is good for someone who…

  • Has experience in Python. Experience in Python is necessary for teachers, and is helpful, but not necessary for TAs.

  • Is a K-12 teacher who either teaches Computer Science or is interested in starting a Computer Science class.

  • Is a programmer with limited classroom experience. The class’s student engagement modes would also support a programmer with limited experience managing a classroom.

This course features…

  • Innovative and clearly presented classroom structure and student engagement modes.

  • Programming combined with advanced mathematics: students use Python to learn about the Fundamental Theorem of Arithmetic and more.

Big Questions and Big Answers

Author: Peter Gao

This course is good for someone who…

  • Is interested in and comfortable moderating discussions on bias with students.

  • Is a middle school math teacher: the course contains questions that can be used in year-round instruction.

  • Is an academic with limited experience teaching middle schoolers: the course’s organization and student engagement strategies make it straightforward to use “out of the box”.

This course features…

  • Fermi question races, probability, and fairness concepts are explored via dice games and other topics.

  • An introduction to statistical concepts aligned with middle school Common Core Learning Standards.

  • Estimation as a vehicle for building number sense and introducing scientific notation.

Creative Problem Solving Courses

Creative Problem Solving exposes students to problems that require creativity, such as those in math contests (for example, from MATHCOUNTS). Most of these courses cover a specific topic area, like number theory (focusing on prime factorization), combinatorics (focusing on the multiplication principle), or geometry, although there is flexibility.

Words Meet Numbers: An Algebra Story

Author: Al Lucero

This course is good for someone who…

  • Is a classroom teacher looking to explore algebra from a new perspective. 

  • Is an academic with limited middle school teaching experience: the course’s organization and student engagement strategies make it straightforward to use “out of the box”.

This course features…

  • Lessons that are organized around a topic or relationship, rather than a skill. For example, rather than organizing problems around solving one-step equations using inverse operations, there is a lesson about using the formulas for the area of a circle in myriad ways. By putting equations in sequence like this, algebraic reasoning becomes a problem-solving tool.

  • High-energy activities such as mazes, team competitions, and stations.

Count Without Counting

Author: Javier Ronquillo Rivera

This course is good for someone who…

  • Can differentiate with ease and knows how to push students to different levels of engagement with problems. 

  • Understands how to foster productive struggle.

This course features…

  • Math problems that are considered “classics”, such as “the 1,000 locker problem”, as well as math enrichment topics such as the Pigeonhole Principle.

  • Lessons that are built around prioritizing student inquiry, with many lessons focused on one big problem that can be broken down into multiple stages.

  • An introduction to college-level concepts such as set theory and the notion of “bijection” in an age-appropriate way.

Exponents: The Superpowers of Numbers

Author: Meghan VanderMale

This course is good for someone who…

  • Has post-secondary experience with abstract algebra or an interest in exploring the topic alongside students.

  • Brings a strong and engaging mathematical presence to the classroom; the contents of this course are relatively abstract.

This course features...

  • A focus on prime factorization and an introduction to modular arithmetic.

  • Regular use of manipulatives to model factorization, motivating pattern recognition, and mathematical abstraction.

Math Fundamentals Courses

Math Fundamentals courses cover mathematics from school, while focusing on leading students to understand mathematics without relying on memorized procedures. Explore Math Fundamentals courses by clicking on any of the buttons below.

Exponents: The Superpowers of Numbers

Author: Meghan VanderMale

This course is good for someone who…

  • Has post-secondary experience with abstract algebra or an interest in exploring the topic alongside students.

  • Brings a strong and engaging mathematical presence to the classroom; the contents of this course are relatively abstract.

This course features...

  • A focus on prime factorization and an introduction to modular arithmetic.

  • Regular use of manipulatives to model factorization, motivating pattern recognition, and mathematical abstraction.

“Power”ful Numbers

Author: Lisa Garcia

This course is good for someone who…

  • Wants to engage students through a variety of engaging activity routines, including “Notice and Wonder,” “Which One Doesn’t Belong?” and “Row Games.” 

  • Is a middle-school or high-school classroom teacher.  The course plans develop laws of exponents through a problem-based, conceptual approach that can also be implemented successfully in school-year classes.

This course features…

  • A problem-solving approach to perfect squares, exponents, and laws of exponents.

  • A focus on conceptual understanding rather than rote computations.

  • Engaging puzzles and games related to exponents.

Fractions

Author: Michael Pershan

This course is good for someone who…

  • Is new to teaching middle schoolers. This course includes developmentally appropriate opportunities to build conceptual understanding around foundational skills. 

  • Is interested in or providing remediation to older students. The course invites students to strategize and utilize deep thinking using fractions, as an alternative to revisiting the content.

This course features…

  • Fun games, mental math exercises, and visual puzzles

  • A second look at fractions, with opportunities for students to do deep sense making

  • Sneak previews to advanced mathematical topics like limits and fractals

  • Student work samples and photos taken after implementing activities in BEAM classrooms

Other Courses

Math for Pirates

Author: Joe Quinn, contributions from Lara Du

This course features…

  • An introduction to proof by induction and logical operators.

  • Suggestions on how to support mathematical thinking and how to structure the classroom.

Note: The game of Nim, which appears in this course, also appears in Games and Strategies.

This course is good for someone who…

  • Is knowledgeable on the topics of formal mathematical proof-writing and symbolic logic; the course introduces concepts that are rarely explored in K-12 math classes.

  • Is an academic with less experience with middle schoolers: the course provides detailed teaching supports.

Counselor Pedagogy

Authors: An Nguyen and Lynn Cartwright-Punnett

This course development was also supported by past Pedagogy faculty members: David Price, Melody Jaros, Michael Pershan, Javier Ronquillo Rivera, Evelyn Owhor, Sam Hilkey, Lisa Garcia, and Giselle George.

Counselors are often described as the heart of BEAM programs: their near-peer relationship with students in the academic and social settings of BEAM is integral to the program’s community. The Counselor Pedagogy course was designed to support counselors where they are and build their toolkit, whether just to help students through summer at BEAM or to prepare the counselor for a future career in teaching.