This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.

This task is intended for instructional (rather than assessment) purposes, providing an opportunity to discuss technology as it relates to irrational numbers and calculations in general. The task gives a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

This lab demonstrates Ohm's law as students set up simple circuits each composed of a battery, lamp and resistor. Students calculate the current flowing through the circuits they create by solving linear equations. After solving for the current, I, for each set resistance value, students plot the three points on a Cartesian plane and note the line that is formed. They also see the direct correlation between the amount of current flowing through the lamp and its brightness.

The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.

The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.

This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

Students are introduced to the concept of energy cycles by learning about the carbon cycle. They will learn how carbon atoms travel through the geological (ancient) carbon cycle and the biological/physical carbon cycle. Students will consider how human activities have disturbed the carbon cycle by emitting carbon dioxide into the atmosphere. They will discuss how engineers and scientists are working to reduce carbon dioxide emissions. Lastly, students will consider how they can help the world through simple energy conservation measures.

This task lets students explore the concept of independence of events. There are two alternative ways of solving the problem.

In this task, students can see that if the price level increases and peopleŐs incomes do not increase, they arenŐt able to purchase as many goods and services; in other words, their purchasing power decreases.

Students learn how the aerodynamics and rolling resistance of a car affect its energy efficiency through designing and constructing model cars out of simple materials. As the little cars are raced down a tilted track (powered by gravity) and propelled off a ramp, students come to understand the need to maximize the energy efficiency of their cars. The most energy-efficient cars roll down the track the fastest and the most aerodynamic cars jump the farthest. Students also work with variables and plot how a car's speed changes with the track angle.

Students observe Pascal's law, Archimedes' principle and the ideal gas law as a Cartesian diver moves within a closed system. The Cartesian diver is neutrally buoyant and begins to sink when an external pressure is applied to the closed system. A basic explanation and proof of this process is provided in this activity, and supplementary ideas for more extensive demonstrations and independent group activities are presented.

Working in teams of three, students perform quantitative observational experiments on the motion of LEGO MINDSTORMS(TM) NXT robotic vehicles powered by the stored potential energy of rubber bands. They experiment with different vehicle modifications (such as wheel type, payload, rubber band type and lubrication) and monitor the effects on vehicle performance. The main point of the activity, however, is for students to understand that through the manipulation of mechanics, a rubber band can be used in a rather non-traditional configuration to power a vehicle. In addition, this activity reinforces the idea that elastic energy can be stored as potential energy.

Students observe the relationship between the angle of a catapult (a force measurement) and the flight of a cotton ball. They learn how Newton's second law of motion works by seeing directly that F = ma. When they pull the metal "arm" back further, thus applying a greater force to the cotton ball, it causes the cotton ball to travel faster and farther. Students also learn that objects of greater mass require more force to result in the same distance traveled by a lighter object.

In this video segment from Cyberchase, the CyberSquad and Digit construct a physical profile of the person who kidnapped Choocroca, a giant cybercrocodile.