Based on what they have already learned about friction, students formulate hypotheses concerning the effects of weight and contact area on the amount of friction between two surfaces. In the Associated Activities (Does Weight Matter? and Does Area Matter?), students design and conduct simple experiments to test their hypotheses, using procedures similar to those used in the previous lesson (Discovering Friction). An analysis of their data will reveal the importance of weight to normal friction (the friction that occurs as a result of surface roughness) and the importance of surface area to the friction that occurs between smooth surfaces due to molecular attraction. Based on their data, students will also be able to calculate coefficients of friction for the materials tested, and compare these to published values for various materials.

This problem uses the same numbers and asks essentially the same mathematical questions as "6.NS Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.

Students drop water from different heights to demonstrate the conversion of water's potential energy to kinetic energy. They see how varying the height from which water is dropped affects the splash size. They follow good experiment protocol, take measurements, calculate averages and graph results. In seeing how falling water can be used to do work, they also learn how this energy transformation figures into the engineering design and construction of hydroelectric power plants, dams and reservoirs.

The CyberSquad tests which broom can travel the furthest in five seconds in this video from Cyberchase.

Students have the opportunity to create and interpret data from simple daily questions.

The CyberSquad solves the problem of giving equal parts of two apples to Cerberus, the three headed dog of Greek mythology, in this video from Cyberchase.

Students develop and solidify their understanding of the concept of "perimeter" as they engage in a portion of the civil engineering task of land surveying. Specifically, they measure and calculate the perimeter of a fenced in area of "farmland," and see that this length is equivalent to the minimum required length of a fence to enclose it. Doing this for variously shaped areas confirms that the perimeter is the minimal length of fence required to enclose those shapes. Then students use the technology of a LEGO MINDSTORMS(TM) NXT robot to automate this task. After measuring the perimeter (and thus required fence length) of the "farmland," students see the NXT robot travel around this length, just as a surveyor might travel around an area during the course of surveying land or measuring for fence materials. While practicing their problem solving and measurement skills, students learn and reinforce their scientific and geometric vocabulary.

This lesson unit is intended to help teachers assess how well students are able to: model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions; and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.

This task allows students to relate addition and subtraction problems to money in a context that introduces the concept of scarcity.

In this video segment from Cyberchase, through addition and regrouping in base sixty, Matt helps Digit figure out what time his CyberSoufflŰ__ŒŰÖ will be done.

The CyberSquad reviews their budget for the second day of their film shoot in this video from Cyberchase.

In this video segment from Cyberchase, the CyberSquad compares their budget with their actual spending from day three of their film shoot.

In this Cyberchase video segment, the CyberSquad figures out how to incorporate a new scene into their film while staying within their budget.

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

This task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator.

This task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator.

This lesson unit is intended to help teachers assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to: find, from their equations, lines that are parallel and perpendicular; and identify and use intercepts. It also aims to encourage discussion on some common misconceptions about equations of lines.