The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines.

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever AXB is a right angle.

Fire is one of the leading causes of accidental deaths. It is important for everyone to take every preventative measure and precaution possible to be ready to deal with a fire emergency.
More than half of all fatal fires occur between 10 p.m. and 6 a.m. when everyone in the home is usually asleep. Smoke alarms are necessary to alert you to fires when you sleep. Will smoke alarms allow enough time to evacuate safely?

The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year.

Total solar eclipses are quite rare, so much so that they make the news when they do occur. This task explores some of the reasons why.

This lesson unit is intended to help educators assess how well students are able to solve quadratics in one variable.

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

The purpose of this task is twofold. First, it prompts students to notice and explain a connection between the factored form of a polynomial and the location of its zeroes when graphed. Second, it highlights a complication that results from a seemingly innocent move that students might be tempted to make: "dividing both sides by x."

This lesson unit is intended to help educators assess how well students are able to recognize the differences between equations and identities, as well as substitute numbers into algebraic statements in order to test their validity in special cases.

A South Sea island chain has decided to transform one of their islands into a resort. This roughly circular island, about 5 kilometers across, contains a mountain that covers the entire island. The mountain is approximately conical, is about 1000 meters high at the center, appears to be sandy, and has little vegetation on it. It has been proposed to lease some fire-fighting ships and wash the mountain into the harbor. It is desired to accomplish this as quickly as possible.

On July 21, 2011, the 135th and final US Space Shuttle landed in Florida after its 13-day mission into orbit, complete with a docking at the International Space Station (ISS). NASA will now have to rely on other nations or commercial endeavors to travel into space until a replacement vehicle is developed and constructed. Develop a comprehensive ten-year plan complete with costs, payloads, and flight schedules to maintain the ISS.

Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, we can derive the sine and cosine of special angles, in this case of π/4. This task can be done as a mini lecture soliciting responses from the students, or as a challenge problem for students to ponder and discuss.

The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

Your team is helping to plan the use of solar power to provide electricity to a 1600 square-foot home being built in a remote area. You need to plan for enough energy to support the energy requirements of the home at night and on a cloudy day. You have done some research and found that you can either pull energy from the grid (i.e. a power company) when your solar panels aren’t producing enough, or use an energy storage system. As the house is in a remote area, the cost of connecting to the grid is very expensive, so you decide to go off-the-grid and invest in energy storage.

This task is designed to help students understand statistics as a process for making inferences about population parameters based on a random sample from that population.

This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180.