As part of a design challenge, students learn how to use a rotation sensor (located inside the casing of a LEGO® MINDSTORMS ® NXT motor) to measure how far a robot moves with each rotation. Through experimentation and measurement with the sensor, student pairs determine the relationship between the number of rotations of the robot's wheels and the distance traveled by the robot. Then they use this ratio to program LEGO robots to move precise distances in a contest of accuracy. The robot that gets closest to the goal without touching the toy figures at the finish line is the winning programming design. Students learn how rotational sensors measure distance, how mathematics can be used for real-world purposes, and about potential sources of error due to gearing when using rotation sensor readings for distance calculations. They also become familiar with the engineering design process as they engage in its steps, from understanding the problem to multiple test/improve iterations to successful design.

In order to solve this problem, students must assume that if you mix a cubic foot of sand with a cubic foot of cement, you will have 2 cubic feet of mix.

The purpose of this task is to provide students an opportunity to use mathematics addressed in different standards in the same problem.

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).

In this task students use ratio and rate reasoning to solve the real-world problem of a runners rate and distance.

In this task students use ratio and rate reasoning to solve the real-world problem of placing a security camara in a shop.

There is a 40% chance that the lower ⅓ of the of the Cascadia subduction zone will rupture in the next 50 years, generating a large earthquake and ensuing tsunami. In this project, students will work collaboratively to design and test a model of a vertical evacuation structure. They will evaluate the performance of their models and propose further modifications to improve their design. Students will then make a scale drawing and a model to apply math concepts of scale to designing and creating an ideal model of a vertical evacuation structure. Finally, students will present their findings and proposed final design to their peers and an adult audience. The entire process takes about 2 weeks, and was expanded to include more information and activities with earthquake/tsunami prediction and application of scale. The unit is a great fit for standards within Earth Science (specifically plate tectonics and human mitigation) as well as Engineering and Design standards.

Engineers design and implement many creative techniques for managing stormwater at its sources in order to improve and restore the hydrology and water quality of developed sites to pre-development conditions. Through the two lessons in this unit, students are introduced to green infrastructure (GI) and low-impact development (LID) technologies, including green roofs and vegetative walls, bioretention or rain gardens, bioswales, planter boxes, permeable pavement, urban tree canopies, rainwater harvesting, downspout disconnection, green streets and alleys, and green parking. Student teams take on the role of stormwater engineers through five associated activities. They first model the water cycle, and then measure transpiration rates and compare native plant species. They investigate the differences in infiltration rates and storage capacities between several types of planting media before designing their own media mixes to meet design criteria. Then they design and test their own pervious pavement mix combinations. In the culminating activity, teams bring together all the concepts as well as many of the materials from the previous activities in order to create and install personal rain gardens. The unit prepares the students and teachers to take on the design and installation of bigger rain garden projects to manage stormwater at their school campuses, homes and communities.

This problem is the fifth in a series of seven about ratios. In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates. The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.

This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex.

This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Every problem requires students to understand what ratios are and apply them in a context. The problems build in complexity and can be used to highlight the multiple ways that one can reason about a context involving ratios.

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

This problem, the third in a series of tasks set in the context of a class election, is more than just a problem of computing the number of votes each person receives. In fact, that isnŐt enough information to solve the problem. One must know how many votes it takes to make one half of the total number of votes. Although the numbers are easy to work with, there are enough steps and enough things to keep track of to lift the problem above routine.

This is the fourth in a series of tasks about ratios set in the context of a classroom election. What makes this problem interesting is that the number of voters is not given. This information isnŐt necessary, but at first glance some students may believe it is.