## Math Sessions

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Mary Beth Richey, Mary Plumb
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. Judith Covington
A pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. The plane cannot be tiled with regular pentagons. However, are there any convex pentagons that can tile the plane? This session explores various pentagons and their tiling abilities. Gene Abrams
A Mad Veterinarian has created three animal transmogrifying machines… While grappling with the posed questions, players will explore a set of problems, figuring out how and if the machines can complete a given transformation. Connections can be made to invariants, abstract algebra, graph theory, and Leavitt path algebra. Caitlin Colburn, Mary Losito, Math Circles of Inquiry
Developed as part of the Math Circles of Inquiry project, this session is aimed at grades 7 or 8, but may be useful for high school algebra. It consists of worksheets and series of videos meant to get students to develop an understanding of solving linear equations, using the real world example of distributing M&Ms into jars. Craig Collins, Cynthia Kramer, Elizabeth Donovan
How many different ways are there to make change for a dollar? As mathematicians we often search for patterns in a problem. However, for this problem, there is no simple, predictable pattern to build to an answer, encouraging participants to reach outside their comfort zones and ponder alternative strategies in order to make progress. Elizabeth Livorsi, Maureen Aguglia, Sara MacKenzie
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 their reasoning. The activity is designed to have students then fluently add, subtract, multiply, and divide these rational numbers and justify the placement of their solutions on the number line. Jennifer K. Mann Austin
This activity packed session starts with a fun Pythagorean Puzzle Proof. Then, Knot Theory is explored while experimenting with the Mobius Band, Knots and Links; Untangling Ropes and Rings, and acting out the Human Knot Experiment. These explorations are further connected to the coiling and knotting of DNA molecules. David Patrick
Mathematicians have long been fascinated by prime numbers and a great deal of number theory revolves around the study of primes. Develop a deeper understanding of these intriguing numbers by exploring the questions presented in this session. Christopher Woodward
Pick’s Theorem is the relationship between the area of a polygon, the number of geoboard nails (or lattice points) inside the polygon, and the number of nails on the boundary. Participants will try to identify the formula and explain strategies for justifying it. After listing the number of ways of making change for twenty cents using pennies, nickels and dimes, can you find a connection between this activity and Pick’s formula? Heather Danforth-Clayson
While exploring the relationship between fractions and decimals, participants will have the opportunity to practice operations with fractions, notice and explain patterns, review understandings of place value and number sense, and justify their reasoning. 