My favorite lesson is based on a problem my geometry students encounter. When we study similar triangles, students use indirect measurement to determine the height of an object.

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### Michael Weiss

One of the central components of high school algebra is the study of quadratic functions and equations. The Common Core State Standards (CCSSI 2010) for Mathematics states that students should learn to solve quadratic equations through a variety of methods (CCSSM A-REI.4b) and use the information learned from those methods to sketch the graphs of quadratic (and other polynomial) functions (CCSSM A-APR.3). More specifically, students learn to graph a quadratic function by doing some combination of the following:

- Locating its zeros (x-intercepts)
- Locating its y-intercept
- Locating its vertex and axis of symmetry
- Plotting additional points, as needed

### Yating Liu and Mary C. Enderson

Similar assumptions seem to give rise to conflicting answers when students approach probability questions differently.

### Kent Thele

Encourage investigation of the conic-section attributes of focus, eccentricity, directrix, and semi-latus rectum using polar coordinates and projective geometry.

### Miriam Gates, Tracy Cordner, Bowen Kerins, Al Cuoco, Eden Badertscher and Gail Burrill

With this professional development program, teachers work with colleagues and experience a manner of teaching that embeds habits of mind.

### James Metz, Lance Hemlow and Anita Schuloff

Explore the relationship between families of quadratic expressions factorable over the integers and Pythagorean triples.

### Craig Huhn

Lesson planning leads to a deeper consideration of what it means to study and learn mathematics.

### Ruth N. Urbina-Lilback

Two instructional principles–being open to students' input and building on misconceptions–can open the door for mathematics learning in community college.

### S. Asli Özgün-Koca

Student interviews inform us about their use of technology in multiple representations of linear functions.

### Benjamin Dickman

Problem solving may incorporate wild guessing, but tame guessing when the answer is already known helps develop mathematical intuition.