This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.

This task requires students to think of dimes and pennies as fractions of dollars.

This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.

The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

With a simple demonstration activity, students are introduced to the concept of friction as a force that impedes motion when two surfaces are in contact. Then, in the Associated Activity (Sliding and Stuttering), they work in teams to use a spring scale to drag an object such as a ceramic coffee cup along a table top or the floor. The spring scale allows them to measure the frictional force that exists between the moving cup and the surface it slides on. By modifying the bottom surface of the cup, students can find out what kinds of surfaces generate more or less friction. They also discover that both static and kinetic friction are involved when an object initially at rest is caused to slide across a surface.

This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation.

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

This task requires students to recognize both "number of groups unknown" and "group size unknown" division problems in the context of a whole number divided by a unit fraction.

The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.

Students learn about the amazing adaptations of the ptarmigan to the alpine tundra. They focus one adaptation, the feathered feet of the ptarmigan, and ask whether the feathers serve to only keep the feet warm or to also provide the bird with floatation capability. They create model ptarmigan feet, with and without feathers, and test the hypothesis on the function of the feathers. Ultimately, students make a claim about whether the feathers provide floatation and support this claim with their testing evidence.

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).

This task is designed as a follow-up to the task F-LE Do Two Points Always Determine a Linear Function? Linear equations and linear functions are closely related, and there advantages and disadvantages to viewing a given problem through each of these points of view. This task is intended to show the depth of the standard F-LE.2 and its relationship to other important concepts of the middle school and high school curriculum, including ratio, algebra, and geometry.

This problem complements the problem ``Do two points always determine a linear function?''

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages. There are several ways (tables, graphing calculators, or statistical software) that students might calculate the required normal percentages. Depending on the method used, answers might vary somewhat from those shown in the solution.

Students explore the concept of optical character recognition (OCR) in a problem-solving environment. They research OCR and OCR techniques and then apply those methods to the design challenge by developing algorithms capable of correctly "reading" a number on a typical high school sports scoreboard. Students use the structure of the engineering design process to guide them to develop successful algorithms. In the associated activity, student groups implement, test and revise their algorithms. This software design lesson/activity set is designed to be part of a Java programming class.

The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.

Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct experiments to determine if the amount of area over which an object contacts a surface it is moving across affects the amount of friction encountered.