The lesson introduces students to the steps of the water cycle and rivers. They think about the effects of communities, sidewalks and roads on the natural flow of rainwater. Students also learn about the role of engineering in community planning and protecting our natural resources.

This task uses the same situation to explore different concepts of probability theory.

In this number tracing activity students create a rainbow number line. This can be a colorful tool with a personal connection to the student that may be used as a reference. It can serve as a visual and motor reminder when reading and writing numbers because the student went through the tracing motion.

In this task students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given function is invertible.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables, and review the relationships between these concepts.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables and review the relationships between these concepts.

This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation.

The task is better suited for instruction than for assessment as it provides students with a non standard setting in which to interpret the meaning of functions. Students should carry out the process of flipping a coin and modeling this Random Walk in order to develop a sense of the process before analyzing it mathematically.

This task provides a context to calculate discrete probabilities and represent them on a bar graph. It could also be used to create a class activity where students gather, represent, and analyze data, running simulations of the random walk and recording and then displaying their results.

This task completes the line of reasoning of Random Walk III in a situation where the numbers become too large to calculate and so abstract reasoning is required in order to compare the different probabilities. It is intended for instructional purposes only with a goal of understanding how to calculate and compare the combinatorial symbols.

Student teams assign importance factors, called "desirability points," the rock properties found in the previous lesson/activity in order to mathematically determine the overall best rocks for building caverns within. They learn the real-world connections and relationships between the rock and the important engineering properties for designing and building caverns (or tunnels, mines, building foundations, etc.).

Play with the left and right hands in different ways, and explore ratio and proportion. Start on the Discover screen to find each challenge ratio by moving the hands. Then, on the Create screen, set your own challenge ratios. Once you've found a challenge ratio, try to move both hands while maintaining the challenge ratio through proportional reasoning.

This task makes for a good follow-up task on rational irrational numbers after that the students have been acquainted with some of the more basic properties. In addition to eliciting several different types of reasoning, the task requires students to rewrite radical expressions in which the radicand is divisible by a perfect square (N-RN.2).

In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours). No such distinction is made in the common core and hence, the two quantities in a ratio may or may not have a common unit. However, when there is a common unit, as in this problem, it is possible to add the two quantities and then find the ratio of each quantity with respect to the whole (often described as a part-whole relationship).

Students investigate the endothermic reaction involving citric acid, sodium bicarbonate and water to produce carbon dioxide, water and sodium citrate. In the presence of water [H2O], citric acid [C6H8O7] and sodium bicarbonate [NaHCO3] (also known as baking soda) react to form sodium citrate [Na3C6H5O7], water [H2O], and carbon dioxide [CO2]. Students test a stoichiometric version of the reaction followed by testing various perturbations on the stoichiometric version in which each reactant (citric acid, sodium bicarbonate, and water) is strategically doubled or halved to create a matrix of the effect on the reaction. By analyzing the test matrix data, they determine the optimum quantities to use in their own production companies to minimize material cost and maximize CO2 production. They use their test data to "scale-up" the system from a quart-sized ziplock bag to a reaction tank equal to the volume of their classroom. They collect data on reaction temperature and CO2 production.

In this activity, students are guided through a close reading of The Journal of Sean Sullivan: A Transcontinental Railroad Worker, a fictional book for young readers based on historical sources. Students will read a short excerpt from the beginning of the book and determine the meaning of key words. Working in groups, students will then read excerpts related to one of the following themes: working conditions of railroad builders; tension between immigrant groups; corruption of the railroad companies; conflict with Great Plains Indian tribes; and boomtowns. They will also complete an individual writing task on their theme. Finally, students will consider the positive and negative effects of the railroad on the country as a whole, as well as on specific groups of Americans.

Students are asked to design simple yet accurate timing devices using limited supplies. The challenge is to create a device that measures out a time period of exactly three minutes in order to enable a hypothetical prison escape. Student groups brainstorm ideas using the different materials provided. They observe and explain the effects of conservation of energy.

Students observe an in-classroom visual representation of a volcanic eruption. The water-powered volcano demonstration is made in advance, using sand, hoses and a waterballoon, representing the main components of all volcanoes. During the activity, students observe, measure and sketch the volcano, seeing how its behavior provides engineers with indicators used to predict an eruption.

This task helps students understand that when you multiply by a number you always get a bigger number.

The three tasks in this set are not examples of tasks asking students to compute using the standard algorithms for multiplication and division because most people know what those kinds of problems look like. Instead, these tasks show what kinds of reasoning and estimation strategies students need to develop in order to support their algorithmic computations.