## 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.
Anne Ho
We adapt “Parable of the Polygons” (Vi Hart and Nicky Case), an online simulation on diversity and segregation, into an appropriate MTC session. The session is interactive, and offers multiple layers of content depending on the age and comfort level of students with conversations on social issues.
Japheth Wood, Paul Ellis, Samuel Coskey
Are there more fractions than counting numbers? Surprisingly, an investigation into binary notation can help us answer this question! This session explores the binary number system. Participants will investigate Hyperbinary numbers, create a Fraction Tree, and discover connections between them.
Alicia Pakusch, Rachel Pellegrino
You want this year’s dance to be LIT! The dance committee has a goal of fundraising \$3,500 through ticket sales. How many tickets do they need to sell? Developed as part of the Math Circles of Inquiry project, this module presents an engaging problem which will allow students to investigate how to graph and solve a system of inequalities.
Caitlin Colburn, Mary Losito
Developed as part of the Math Circles of Inquiry project, this session is a good introduction to the 8th grade or Algebra Math curriculum using inquiry based instruction. Every time the Supreme Court justices get together, everyone shakes hands with each other. How many total handshakes will take place at one gathering?
Hanna Bennett, Nina White
Can you find all possible semiregular tilings of the plane? A tiling of the plane covers the (infinite) plane, without gaps or overlaps, using congruent copies of one or more shapes. A semiregular tiling is a tiling of the plane with certain constraints: two or more regular polygons are used, polygons meet edge-to-edge, and the pattern of polygons around every vertex is the same.
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?