Students use estimation or other methods to place the decimal points in products and quotients. They review the algorithms for the four basic decimal operations and solve multistep word problems involving decimal operations.Key ConceptsThe algorithms for whole-number operations can be extended to decimal operations. Students learned the algorithms for decimal operations in Grade 5. By the end of Grade 6, they should be fluent with these operations.For decimal addition and subtraction, once the decimal points of the addends are aligned (which aligns like place values), the algorithms are the same as for whole numbers. The decimal point in the sum or difference goes directly below the decimal point in the numbers that were added or subtracted.For decimal multiplication and division, one method is to ignore the decimal points and apply the whole-number algorithms. Then use estimation or some other method to place the decimal point in the answer.Goals and Learning ObjectivesReview and practice the algorithms for all four decimal operations.Solve real-world problems involving decimal operations.

The purpose of this lesson is to help students understand the relationship between the mass and the weight of an object. Students will study the properties of common materials and why airplanes use specific materials.

The application of engineering principles is explored in the creation of mobiles. As students create their own mobiles, they take into consideration the forces of gravity and convection air currents. They learn how an understanding of balancing forces is important in both art and engineering design.

This supplemental resource provides problems and activities related to Numerical and Algebraic Operations & Analytical Thinking in Middle School Mathematics.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This lesson will allow students to explore an important role of environmental engineers: cleaning the environment. Students will learn details about the Exxon Valdez oil spill, which was one of the most publicized and studied environmental tragedies in history. In the accompanying activity, they will try many "engineered" strategies to clean up their own manufactured oil spill and learn the difficulties of dealing with oil released into our waters.

The purpose of this lesson is to introduce the students to the Sun. They explore various aspects of the Sun including its composition, its interior workings, and its relationship to the Earth.

On the topic of energy related to motion, this summary lesson is intended to tie together the concepts introduced in the previous four lessons and show how the concepts are interconnected in everyday applications. A hands-on activity demonstrates this idea and reinforces students' math skills in calculating energy, momentum and frictional forces.

Students use real-world data to evaluate whether solar power is a viable energy alternative for several cities in different parts of the U.S. Working in small groups, they examine maps and make calculations using NREL/US DOE data from the online Renewable Energy Living Lab. In this exercise, students analyze cost and availability for solar power, and come to conclusions about whether solar power is a good solution for four different locations.

Students learn the concept of angular momentum and its correlation to mass, velocity and radius. They experiment with rotation and an object's mass distribution. In an associated literacy activity, students use basic methods of comparative mythology to consider why spinning and weaving are common motifs in creation myths and folktales.

Students explore orbit transfers and, specifically, Hohmann transfers. They investigate the orbits of Earth and Mars by using cardboard and string. Students learn about the planets' orbits around the sun, and about a transfer orbit from one planet to the other. After the activity, students will know exactly what is meant by a delta-v maneuver!

This lesson discusses how each component of a spacecraft is specifically designed so that a rover can land safely in six minutes. Also, students will learn how common, everyday materials and technology, like nylon, polyester and airbags, are used in space-age technology.

Students culture cells in order to find out which type of surfactant (in this case, soap) is best at removing bacteria. Groups culture cells from unwashed hands and add regular bar soap, regular liquid soap, anti-bacterial soap, dishwasher soap, and hand sanitizer to the cultures. The cultures are allowed to grow for two days and then the students assess which type of soap design did the best job of removing bacteria cells from unwashed hands. Students extend their knowledge of engineering and surfactants for different environmental applications.

Students see how different levels of surface tension affect water's ability to move. Teams "race" water droplets down tracks made of different materials, making measurements, collecting data, making calculations, graphing results and comparing to their predictions and the properties of each surface, determining which surface exhibits the highest (or lowest) level of surface tension with water. They apply their results to make engineering recommendations for real-world applications.

Students strengthen their communicate skills about measurements by learning the meaning of base units and derived units, including speed one of the most common derived units (distance/time). Working in groups, students measure the time for LEGO MINDSTORMS(TM) NXT robots to move a certain distance. The robots are started and stopped via touch sensors and programmed to display the distance traveled. Using their collected data, students complete a worksheet to calculate the robots' (mean/average) speeds at given motor powers.

The airplanes unit begins with a lesson on how airplanes create lift, which involves a discussion of air pressure and how wings use Bernoulli's principle to change air pressure. Next, students explore the other three forces acting on airplanes thrust, weight and drag. Following these lessons, students learn how airplanes are controlled and use paper airplanes to demonstrate these principles. The final lessons addresses societal and technological impacts that airplanes have had on our world. Students learn about different kinds of airplanes and then design and build their own balsa wood airplanes based on what they have learned.

Students learn about the types of waves and how they change direction, as well as basic wave properties such as wavelength, frequency, amplitude and speed. During the presentation of lecture information on wave characteristics and properties, students take notes using a handout. Then they label wave parts on a worksheet diagram and draw their own waves with specified properties (crest, trough and wavelength). They also make observations about the waves they drew to determine which has the highest and the lowest frequency. With this knowledge, students better understand waves and are a step closer to understanding how humans see color.

The purpose of this activity is to demonstrate how drag affects falling objects. Students will make a variety of shapes out of paper and see how size and shape affects the speed with which their paper shapes fall.

Students learn about friction and drag two different forces that convert energy of motion to heat. Both forces can act on a moving object and decrease its velocity. Students learn examples of friction and drag, and suggest ways to reduce the impact of these forces. The equation that governs common frictional forces is introduced, and during a hands-on activity, students experimentally measure a coefficient of friction.

Expanding on the topic of objects in motion covering Newton's laws of motion, acceleration and velocity, which are taught starting in third grade, students are introduced to new concepts of speed, density, level of service (LOS) (quality of roadways), delay and congestion. Every day we are affected by congestion even if we do not step out of our homes. For example, the price we pay for goods increases due to increases in shipping costs caused by congestion delays. A congestion metric would help us to compare roadways and assess improvement methods. A common metric used to measure congestion is called level of service (LOS).