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.

In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality.  Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions.  Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to “the whole” serves as a foundation for students.  Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations.  Material in early lessons is designed to reinforce students’ understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students use visual models and equations, building on their earlier work with these.  As the lessons and topics progress and students solve multi-step percent problems algebraically with numbers that are not as compatible, teachers may let students use calculators so that their computational work does not become a distraction.

**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**

Students are presented with a guide to rain garden construction in an activity that culminates the unit and pulls together what they have learned and prepared in materials during the three previous associated activities. They learn about the four vertical zones that make up a typical rain garden with the purpose to cultivate natural infiltration of stormwater. Student groups create personal rain gardens planted with native species that can be installed on the school campus, within the surrounding community, or at students' homes to provide a green infrastructure and low-impact development technology solution for areas with poor drainage that often flood during storm events.

Students apply the concepts of conduction, convection and radiation as they work in teams to solve two challenges. One problem requires that they maintain the warm temperature of one soda can filled with water at approximately human body temperature, and the other problem is to cause an identical soda can of warm water to cool as much as possible during the same 30-minute time period. Students design their engineering solutions using only common everyday materials, and test their devices by recording the water temperatures in their two soda cans every five minutes.

Through multi-trial experiments, students are able to see and measure something that is otherwise invisible to them seeing plants breathe. Student groups are given two small plants of native species and materials to enclose them after watering with colored water. After being enclosed for 5, 10 and 15 minutes, teams collect and measure the condensed water from the plants' "breathing," and then calculate the rates at which the plants breathe. A plant's breath is known as transpiration, which is the flow of water from the ground where it is taken up by roots (plant uptake) and then lost through the leaves. Students plot volume/time data for three different native plant species, determine and compare their transpiration rates to see which had the highest reaction rate and consider how a plant's unique characteristics (leaf surface area, transpiration rate) might figure into engineers' designs for neighborhood stormwater management plans.

With the assistance of a few teacher demonstrations (online animation, using a radiometer and rubbing hands), students review the concept of heat transfer through convection, conduction and radiation. Then they apply an understanding of these ideas as they use wireless temperature probes to investigate the heating capacity of different materials sand and water under heat lamps (or outside in full sunshine). The experiment models how radiant energy drives convection within the atmosphere and oceans, thus producing winds and weather conditions, while giving students the hands-on opportunity to understand the value of remote-sensing capabilities designed by engineers. Students collect and record temperature data on how fast sand and water heat and cool. Then they create multi-line graphs to display and compare their data, and discuss the need for efficient and reliable engineer-designed tools like wireless sensors in real-world applications.

Students use everyday building materials sand, pea gravel, cement and water to create and test pervious pavement. They learn what materials make up a traditional, impervious concrete mix and how pervious pavement mixes differ. Groups are challenged to create their own pervious pavement mixes, experimenting with material ratios to evaluate how infiltration rates change with different mix combinations.

As a weighted plastic egg is dropped into a tub of flour, students see the effect that different heights and masses of the same object have on the overall energy of that object while observing a classic example of potential (stored) energy transferred to kinetic energy (motion). The plastic egg's mass is altered by adding pennies inside it. Because the egg's shape remains constant, and only the mass and height are varied, students can directly visualize how these factors influence the amounts of energy that the eggs carry for each experiment, verified by measurement of the resulting impact craters. Students learn the equations for kinetic and potential energy and then make predictions about the depths of the resulting craters for drops of different masses and heights. They collect and graph their data, comparing it to their predictions, and verifying the relationships described by the equations. This classroom demonstration is also suitable as a small group activity.

This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not.

Students work in engineering teams to optimize cleaner energy solutions for cooking and heating in rural China. They choose between various options for heating, cooking, hot water, and lights and other electricity, balancing between the cost and health effects of different energy choices.

The purpose of this task is to engage students in Standard for Mathematical Practice 4, Model with mathematics and as such, the question as it is worded cannot be answered without making some assumptions. For example, if the items that are purchased do not have the same value, then the price reduction depends on the cost of the items.

There is a non-mathematical fact that students must know about mixtures in order to answer this question. When salt is dissolved in water, the salt disperses evenly through the mixture, so any sample from the mixture that has the same volume will have the same amount of salt.

This problem can be solved in more than one way. The choice in solution method may reflect the comfort and mathematical sophistication of the student.

This is a multi-step problem since it requires more than two steps no matter how it is solved. The problem is not scaffolded for the student, but each step is straightforward and should follow from the previous with a careful reading of the problem.

Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.

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.

Students reinforce an antenna tower made from foam insulation so that it can withstand a 480 N-cm bending moment (torque) and a 280 N-cm twisting moment (torque) with minimal deflection. During one class period, students discuss the problem, run the initial bending and torsion tests and graph the results. During the following class periods, students design, construct and test sturdier towers, and graph the results.