In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

This task helps students understand the meaning of the equal sign and to use it appropriately.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

In this problem students must transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent.

The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.

The task is designed to show that random samples produce distributions of sample means that center at the population mean, and that the variation in the sample means will decrease noticeably as the sample size increases. Random sampling (like mixing names in a hat and drawing out a sample) is not a new idea to most students, although the terminology is likely to be new.

Tag Line: Building number sense one day at a time.

The site provides a number of estimation activities involving height, number of objects etc. The activities may include a photo or video to help students develop some reference to solve the activity. The answers are provided, but the idea is that students utilize their estimation skills to determine the appropriate answer.

The site also includes a blog, a relationship between some american common core standards and estimation activities, as well as information on clothesline math activities as well.

Simple machines are devices with few or no moving parts that make work easier, and which people have used to provide mechanical advantage for thousands of years. Students learn about the wedge, wheel and axle, lever, inclined plane, screw and pulley in the context of the construction of a pyramid, gaining insights into tools that have been used since ancient times and are still important today. Through numerous hands-on activities, students imagine themselves as ancient engineers building a pyramid. Student teams evaluate and select a construction site, design a pyramid, perform materials calculations, test a variety of cutting wedges on different materials, design a small-scale cart/lever transport system to convey building materials, experiment with the angle of inclination and pull force on an inclined plane, see how a pulley can change the direction of force, and learn the differences between fixed, movable and combined pulleys. While learning the steps of the engineering design process, students practice teamwork, creativity and problem solving.

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.

Students learn about energy, kinetic energy, potential energy, and energy transfer through a series of three lessons and three activities. They learn that energy can be neither created nor destroyed and that relationships exist between a moving object's mass and velocity. The associated activities give students hands-on experience with examples of potential-to-kinetic energy transfers. The activities also provide ways for students to apply the core concepts of energy through engineering practices such as building and testing prototypes to meet design criteria, planning and carrying out investigations, collecting and interpreting data, optimizing a system design, and collaborating with other research groups. The fundamental concepts presented in this unit serve as a good foundation for future lessons on energy technologies and electricity production.

Students are introduced to the concept of energy conversion, and how energy transfers from one form, place or object to another. They learn that energy transfers can take the form of force, electricity, light, heat and sound and are never without some energy "loss" during the process. Two real-world examples of engineered systems light bulbs and cars are examined in light of the law of conservation of energy to gain an understanding of their energy conversions and inefficiencies/losses. Students' eyes are opened to the examples of energy transfer going on around them every day. Includes two simple teacher demos using a tennis ball and ball bearings. A PowerPoint(TM) presentation and quizzes are provided.

Students learn about kinetic and potential energy, including various types of potential energy: chemical, gravitational, elastic and thermal energy. They identify everyday examples of these energy types, as well as the mechanism of corresponding energy transfers. They learn that energy can be neither created nor destroyed and that relationships exist between a moving object's mass and velocity. Further, the concept that energy can be neither created nor destroyed is reinforced, as students see the pervasiveness of energy transfer among its many different forms. A PowerPoint(TM) presentation and post-quiz are provided.

Students are introduced to the definition of energy and the concepts of kinetic energy, potential energy, and energy transfer. This lesson is a broad overview of concepts that are taught in more detail in subsequent lessons and activities in this curricular unit. A PowerPoint(TM) presentation and pre/post quizzes are provided.

Students learn the basics of the electromagnetic spectrum and how various types of electromagnetic waves are related in terms of wavelength and energy. In addition, they are introduced to the various types of waves that make up the electromagnetic spectrum including, radio waves, ultraviolet waves, visible light and infrared waves. These topics help inform students before they turn to designing solutions to an overarching engineering challenge question.

In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.