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### Pinwheel

6-8, 9-12

Each student creates parallelograms from square sheets of paper and connects them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and students discover a surprising result.### Vigenere Cipher

9-12

Following their introduction to the Caesar Cipher, students will now learn about the polyalphabetic Vigenere cipher. Text will be encoded and decoded using inverse operations.### Domain Representations

9-12

Students use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions.### Stacking Squares

9-12

This lesson prompts students to explore ways of arranging squares to represent equivalences involving square- and cube-roots. Students’ explanations and representations (with their various ways of finding these roots) form the basis for further work with radicals.### Rediscovering the Patterns in Pick’s Theorem

9-12

Students will use a geoboard, geoboard interactive, or Geometer’s Sketchpad^{®}to help them discover the pattern of Pick’s Theorem.

### Pick’s Theorem as a System of Equations

9-12

Students will gather three examples from a geoboard or other representation to generate a system of equations. The solution will provide the coefficients for Pick’s Theorem.### Rates of Change in Pick’s Theorem

9-12

Students will use a spreadsheet to investigate rates of change among various figures created on a geoboard. The coefficients of Pick’s Theorem are easily determined from these rates of change.### Hanging Chains

9-12

Both ends of a small chain will be attached to a board with a grid on it to (roughly) form a parabola. Students will choose three points along the curve and use them to identify an equation. Repeating the process, students will discover how the equation changes when the chain is shifted.### Movie Lines

9-12

This lesson allows students to apply their knowledge of linear equations and graphs in an authentic situation. Students plot data points corresponding to the cost of DVD rentals and interpret the results.### Tetrahedral Kites

6-8, 9-12

Each student constructs a tetrahedron and describes the linear, area and
volume measurements using non‑traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed.