In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations.

Working in engineering project teams, students evaluate sites for the construction of a pyramid. They base their decision on site features as provided by a surveyor's report; distance from the quarry, river and palace; and other factors they deem important to the project based on their team's values and priorities.

This task suggests methods of introducing and continuing choral counting in the classroom.

Teachers (and then students) lead the class in chanting numbers from 1 to 120.

The purpose of this task is for students to find different pairs of numbers that sum to 7.

This task is primarily about volume and surface area, although it also gives students an early look at converting between measurements in scale models and the real objects they correspond to.

Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.

Students use the same method as in the activity from lesson 2 of this unit to explore the magnetism due to electric current instead of a permanent magnet. Students use a compass and circuit to trace the magnetic field lines induced by the electric current moving through the wire. Students develop an understanding of the effect of the electrical current on the compass needle through the induced magnetic field and understand the complexity of a three dimensional field system.

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.

Students use bearing measurements to triangulate and determine objects' locations. Working in teams of two or three, they must put on their investigative hats as they take bearing measurements to specified landmarks in their classroom (or other rooms in the school) from a "mystery location." With the extension activity, students are challenged with creating their own maps of the classroom or other school location and comparing them with their classmates' efforts.

Students observe and discuss a simple balloon model of an electrostatic precipitator to better understand how this pollutant recovery method functions in cleaning industrial air pollution.

Engineers design methods of removing particulate matter from industrial sources to minimize negative effects of air pollution. In this activity, students will undertake a similar engineering challenge as they design and build a filter to remove pepper from an air stream without blocking more than 50% of the air.

Posed with a paradigmatic engineering problem, students consider and explore mathematical algorithms and/or geometric concepts to devise possible solutions. The problem: How should a robotic vacuum move in order to best clean a floor of unknown shape and dimensions? They grapple with what could be a complex problem by brainstorming ideas, presenting the best idea for a solution and analyzing all presented solutions, and then are introduced to an elegant solution. Rather than elaborately calculating the most efficient route and keeping track of which tiles the robot has visited, a random number generator determines which direction the robot will take when it hits a barrier. Students are able to visually confirm how an unfamiliar programming concept (a random number generator) can make for a simple and efficient program that causes an NXT robot (that is suitably equipped) to clean a bare floor. Then students think of other uses for random numbers.

Following the steps of the engineering design process and acting as biomedical engineers, student teams use everyday materials to design and develop devices and approaches to unclog blood vessels. Through this open-ended design project, they learn about the circulatory system, biomedical engineering, and conditions that lead to heart attacks and strokes.

This course is designed to provide an understanding of how the human brain works in health and disease, and is intended for both the Brain and Cognitive Science major and the non-Brain and Cognitive Science major. Knowledge of how the human brain works is important for all citizens, and the lessons to be learned have enormous implications for public policy makers and educators. The course will cover the regional anatomy of the brain and provide an introduction to the cellular function of neurons, synapses and neurotransmitters. Commonly used drugs that alter brain function can be understood through a knowledge of neurotransmitters. Along similar lines, common diseases that illustrate normal brain function will be discussed. Experimental animal studies that reveal how the brain works will be reviewed. Throughout the seminar we will discuss clinical cases from Dr. Byrne's experience that illustrate brain function; in addition, articles from the scientific literature will be discussed at each class.

Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

Students analyze international oil consumption and production data. They make several graphs to organize the data and draw conclusions about the overall use of oil in the world.

In this task using a number line, students must partition the interval between 0 and 1 into eighths.