Algebra

Algebra Tasks and Materials

**Distance Formula/Pythagorean Theorem**
 * Equation of a Circle Investigation : A discovery approach to developing an equation of a circle using the distance formula and Pythagorean Theorem.


 * Shortest Distance to Dinner : An activity to get students excited about practicing the distance formula. It's specific to the camp my students attended, but you could customize it to be a place your students are familiar with or a fictitious place.


 * Pythagorean Theorem Geometric Proof : Leads students through a proof of the Pythagorean Theorem. I like this one!

**Equations**
 * Tile Patio Pattern Task: Complete PTR lesson plan of a patio tile pattern task. Gets at modeling a situation with algebraic equations and a better understanding of equivalence.


 * Triangles and Squares Pattern Task : Complete PTR lesson plan of pattern tasks involving triangles and squares. Students generalize a linear pattern.

**Exponents and Exponential Functions**
 * Exponential Function Investigation : Can we model the decay of the English language with an exponential function?


 * Half-life of M&Ms : There is no lesson plan for this one because I never actually used this problem. It is just an excel spreadsheet example of how you can talk about half life with an m&m experiment. Just take some m&ms and toss them onto a table. Eat all of the ones that have the m side up. Record how many remain. Repeat this until the m&ms are gone. I did this for fun and have attached my results. It's pretty cool :)


 * Scientific Notation

**Midpoint**
 * Midpoint Investigation : Exploratory approach to develop the midpoint formula with a few cool extension questions. When I used this with my students, they came up with two seemingly different formulas which led to a nice discussion about why the formulas were equivalent.

**Quadratic Equations**
 * Coefficient of x^2 : How does changing a affect the graph of the equation y = ax^2? (Worksheet and lesson plan included)


 * Vertex Form of Quadratic Equations: Task, lesson plan, and corresponding GeoGebra file for an exploration of the vertex form of quadratic equations.

**Slope**


 * Slope Investigation : Basic introduction to slope to get students thinking about it in terms of a ratio.

**Square Roots and Square Root Functions**
 * Graphing Square Root Functions : As exploratory as I could possibly make graphing square root functions. I tried.