Facilitator Guides – MathCircles.org

Puzzling Pairs

By:

Topic(s):

Combinatorics, Number Theory, Parity / Invariants, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Lesson Plan, References

Langford pairings are sequences in which a set of N pairs, {1, 1, 2, 2, …, N, N}, is arranged so that every pair, {k, k}, appears in the sequence with k numbers between the pair. Langford pairings have been actively studied by mathematicians since the 1960s for their applications...

Stomachion (Archimedes’ Box)

By:

August Raybould

Topic(s):

Geometry, Problem Solving / General

Supporting Resources:

Facilitator Guides, Featured in MCircular, Handouts, Lesson Plan, References

The Stomachion puzzle, attributed to the Ancient Greek scholar Archimedes and preserved within the Archimedes Palimpsest, is considered to be the oldest known mathematical puzzle. The puzzle contains 14 pieces in 12 distinct shapes that fit perfectly into a square. Since its discovery, the underlying structure of the puzzle has...

Grade Optimization

By:

Kenneth Levasseur

Topic(s):

Optimization

Supporting Resources:

Facilitator Guides, Handouts

At the beginning of each term we decide on the weights we assign to components of our courses. But there are other weights that we might consider to be just as reasonable -some students’ grades will increase with them but others’ may decrease. Why not give students the benefit of...

Mural Mathematics

By:

Topic(s):

Geometry, Mathematical Modeling, Social Justice Mathematics

Supporting Resources:

Facilitator Guides, Handouts, Photos & Videos

Students will explore existing equity themed murals to identify themes, and the mathematics necessary to plan/create a city mural. Students will utilize Google maps tools to begin connecting Mathematical representations to precisely interpret circle properties and apply them to the mural design.

Cup Stacking

By:

Topic(s):

Mathematical Games, Problem Solving / General

Supporting Resources:

Facilitator Guides, Handouts, Photos & Videos, References

Begin with a row of cups and end with all of the cups in a single stack. Rules: 1. Count the number of cups in a stack. That stack must jump that number of spaces. For example, 1 cup can only move 1 space; 2 cups have to move 2...

Making Connections Between Forms of Quadratic Equations

By:

Mary Beth Richey

Topic(s):

Geometry

Supporting Resources:

Facilitator Guides, Handouts, Virtual Tools

Developed as part of the Math Circles of Inquiry project, the goal of this module is to help students in Algebra II become fluent in the various forms of a parabola equation based on the information that they are given. Students sometimes fail to understand that there are multiple ways...

Percents

By:

Alexandra Edwards, Dyan Palmer

Topic(s):

Algebra / Arithmetic

Supporting Resources:

Facilitator Guides, Handouts

Developed as part of the Math Circles of Inquiry project, this module has students grapple with different representations of percents in various contexts in order to solve real life problems. Students need fluency in percentages for real world applications such as shopping, eating at restaurants, commission based careers, etc. Understanding...

Rational Numbers

By:

Elizabeth Livorsi, Maureen Aguglia, Sara MacKenzie

Topic(s):

Algebra / Arithmetic, Number Theory

Supporting Resources:

Facilitator Guides, Handouts

Developed as part of the Math Circles of Inquiry project, this module is an introductory activity for rational numbers, likely aligned with Grade 7. Students will be given five points on a number line and will be asked to estimate the values of each in a 3-part task and explain...

Trigonometric Ratios in Right Triangles

By:

Mary Beth Richey, Mary Plumb

Topic(s):

Geometry

Supporting Resources:

Facilitator Guides, Handouts, Lesson Plan

Developed as part of the Math Circles of Inquiry project, this five to six day activity is designed to help students understand trigonometric ratios, by building on their understanding of similar triangles and ratios of corresponding sides. The purpose of this module is for students to spend time and energy...

Systems of Linear Equations

By:

Alexandra Edwards, Dyan Palmer, Ryan Gantner

Topic(s):

Algebra / Arithmetic, Geometry

Supporting Resources:

Facilitator Guides, Handouts

Developed as part of the Math Circles of Inquiry project, this short module explores a graphical solution to a system of equations. Students answer questions about lemonade sales and physically stand on the coordinates of a giant grid in order to see that plotting two equations on the same set...

Supporting Material: Facilitator Guides