MS.PS2.A: Forces and Motion€¦ · DCI: Motion and Stability: Forces and Interactions MS.PS2.A: Forces and Motion The motion of an object is determined by the sum of the forces acting

DCI: Motion and Stability: Forces and Interactions

MS.PS2.A: Forces and MotionFor any pair of interacting objects, the force exerted by the firstobject on the second object is equal in strength to the force that thesecond object exerts on the first, but in the opposite direction(Newton’s third law). (MSPS21)


MS.PS2.A: Forces and MotionThe motion of an object is determined by the sum of the forcesacting on it; if the total force on the object is not zero, its motion willchange. The greater the mass of the object, the greater the forceneeded to achieve the same change in motion. For any given object,a larger force causes a larger change in motion. (MSPS22)


MS.PS2.A: Forces and MotionAll positions of objects and the directions of forces and motions mustbe described in an arbitrarily chosen reference frame and arbitrarilychosen units of size. In order to share information with other people,these choices must also be shared. (MSPS22)


MS.PS2.B: Types of InteractionsForces that act at a distance (electric, magnetic, and gravitational)can be explained by fields that extend through space and can bemapped by their effect on a test object (a charged object, or a ball,respectively). (MSPS25)


MS.PS2.B: Types of InteractionsElectric and magnetic (electromagnetic) forces can be attractive orrepulsive, and their sizes depend on the magnitudes of the charges,currents, or magnetic strengths involved and on the distancesbetween the interacting objects. (MSPS23)


MS.PS2.B: Types of InteractionsGravitational forces are always attractive. There is a gravitationalforce between any two masses, but it is very small except when oneor both of the objects have large mass—e.g., Earth and the sun. (MSPS24)

DCI: Energy

MS.PS3.A: Definitions of EnergyMotion energy is properly called kinetic energy; it is proportional tothe mass of the moving object and grows with the square of itsspeed. (MSPS31)

DCI: Energy

MS.PS3.A: Definitions of EnergyA system of objects may also contain stored (potential) energy,depending on their relative positions. (MSPS32)

DCI: Energy

MS.PS3.C: Relationship Between Energy andForcesWhen two objects interact, each one exerts a force on the other thatcan cause energy to be transferred to or from the object. (MSPS32)

DCI: Energy

MS.PS3.A: Definitions of EnergyTemperature is not a measure of energy; the relationship betweenthe temperature and the total energy of a system depends on thetypes, states, and amounts of matter present. (MSPS33)

DCI: Energy

MS.PS3.B: Conservation of Energy and EnergyTransferEnergy is spontaneously transferred out of hotter regions or objectsand into colder ones. (MSPS33)

DCI: Engineering Design

MS.ETS1.A: Defining and Delimiting EngineeringProblemsThe more precisely a design task’s criteria and constraints can bedefined, the more likely it is that the designed solution will besuccessful. Specification of constraints includes consideration ofscientific principles and other relevant knowledge that is likely to limitpossible solutions. (MSPS33)

DCI: Engineering Design

MS.ETS1.B: Developing Possible SolutionsA solution needs to be tested, and then modified on the basis of thetest results in order to improve it. There are systematic processes forevaluating solutions with respect to how well they meet criteria andconstraints of a problem. (MSPS33)

DCI: Energy

MS.PS3.A: Definitions of EnergyTemperature is not a measure of energy; the relationship betweenthe temperature and the total energy of a system depends on thetypes, states, and amounts of matter present. (MSPS34)

DCI: Energy

MS.PS3.B: Conservation of Energy and EnergyTransferThe amount of energy transfer needed to change the temperature ofa matter sample by a given amount depends on the nature of thematter, the size of the sample, and the environment. (MSPS34)

DCI: Energy

MS.PS3.B: Conservation of Energy and EnergyTransferWhen the motion energy of an object changes, there is inevitablysome other change in energy at the same time. (MSPS35)

DCI: Earth's Systems

MS.ESS2.A: Earth Materials and SystemsThe planet’s systems interact over scales that range frommicroscopic to global in size, and they operate over fractions of asecond to billions of years. These interactions have shaped Earth’shistory and will determine its future. (MSESS22)


MS.ESS2.C: The Roles of Water in Earth’sSurface ProcessesWater’s movements—both on the land and underground—causeweathering and erosion, which change the land’s surface featuresand create underground formations. (MSESS22)


MS.ESS2.C: The Roles of Water in Earth’sSurface ProcessesWater continually cycles among land, ocean, and atmosphere viatranspiration, evaporation, condensation and crystallization, andprecipitation, as well as downhill flows on land. (MSESS24)


MS.ESS2.C: The Roles of Water in Earth’sSurface ProcessesGlobal movements of water and its changes in form are propelled bysunlight and gravity. (MSESS24)


MS.ESS2.C: The Roles of Water in Earth’sSurface ProcessesThe complex patterns of the changes and the movement of water inthe atmosphere, determined by winds, landforms, and oceantemperatures and currents, are major determinants of local weatherpatterns. (MSESS25)


MS.ESS2.D: Weather and ClimateBecause these patterns are so complex, weather can only bepredicted probabilistically. (MSESS25)


MS.ESS2.C: The Roles of Water in Earth’sSurface ProcessesVariations in density due to variations in temperature and salinitydrive a global pattern of interconnected ocean currents. (MSESS26)


MS.ESS2.D: Weather and ClimateWeather and climate are influenced by interactions involvingsunlight, the ocean, the atmosphere, ice, landforms, and livingthings. These interactions vary with latitude, altitude, and local andregional geography, all of which can affect oceanic and atmosphericflow patterns. (MSESS26)


MS.ESS2.D: Weather and ClimateThe ocean exerts a major influence on weather and climate byabsorbing energy from the sun, releasing it over time, and globallyredistributing it through ocean currents. (MSESS26)

DCI: Earth's Place in the Universe

MS.ESS1.A: The Universe and Its StarsPatterns of the apparent motion of the sun, the moon, and stars inthe sky can be observed, described, predicted, and explained withmodels. (MSESS11)


MS.ESS1.B: Earth and the Solar SystemThis model of the solar system can explain eclipses of the sun andthe moon. Earth’s spin axis is fixed in direction over the shorttermbut tilted relative to its orbit around the sun. The seasons are a resultof that tilt and are caused by the differential intensity of sunlight ondifferent areas of Earth across the year. (MSESS11)


MS.ESS1.A: The Universe and Its StarsEarth and its solar system are part of the Milky Way galaxy, which isone of many galaxies in the universe. (MSESS12)


MS.ESS1.B: Earth and the Solar SystemThe solar system consists of the sun and a collection of objects,including planets, their moons, and asteroids that are held in orbitaround the sun by its gravitational pull on them. (MSESS12)


MS.ESS1.B: Earth and the Solar SystemThe solar system appears to have formed from a disk of dust andgas, drawn together by gravity. (MSESS12)


MS.ESS1.B: Earth and the Solar SystemThe solar system consists of the sun and a collection of objects,including planets, their moons, and asteroids that are held in orbitaround the sun by its gravitational pull on them. (MSESS13)

Performance Expectation

MSPS21: Apply Newton’s Third Law to design a solution toa problem involving the motion of two colliding objects. *Clarification Statement: Examples of practical problems could include theimpact of collisions between two cars, between a car and stationaryobjects, and between a meteor and a space vehicle. Assessment Boundary: Assessment is limited to vertical or horizontalinteractions in one dimension.* This performance expectation integrates traditional science content withengineering through a practice or disciplinary code idea.


MSPS22: Plan an investigation to provide evidence thatthe change in an object’s motion depends on the sum of theforces on the object and the mass of the object.Clarification Statement: Emphasis is on balanced (Newton’s First Law)and unbalanced forces in a system, qualitative comparisons of forces,mass and changes in motion (Newton’s Second Law), frame of reference,and specification of units. Assessment Boundary: Assessment is limited to forces and changes inmotion in onedimension in an inertial reference frame and to change inone variable at a time. Assessment does not include the use oftrigonometry.


MSPS23: Ask questions about data to determine thefactors that affect the strength of electric and magneticforces.Clarification Statement: Examples of devices that use electric andmagnetic forces could include electromagnets, electric motors, orgenerators. Examples of data could include the effect of the number ofturns of wire on the strength of an electromagnet, or the effect of increasingthe number or strength of magnets on the speed of an electric motor. Assessment Boundary: Assessment about questions that requirequantitative answers is limited to proportional reasoning and algebraicthinking.


MSPS24: Construct and present arguments usingevidence to support the claim that gravitational interactionsare attractive and depend on the masses of interactingobjects.Clarification Statement: Examples of evidence for arguments couldinclude data generated from simulations or digital tools; and chartsdisplaying mass, strength of interaction, distance from the Sun, and orbitalperiods of objects within the solar system. Assessment Boundary: Assessment does not include Newton’s Law ofGravitation or Kepler’s Laws.


MSPS25: Conduct an investigation and evaluate theexperimental design to provide evidence that fields existbetween objects exerting forces on each other even thoughthe objects are not in contact.Clarification Statement: Examples of this phenomenon could include theinteractions of magnets, electricallycharged strips of tape, and electricallycharged pith balls. Examples of investigations could include firsthandexperiences or simulations. Assessment Boundary: Assessment is limited to electric and magneticfields, and limited to qualitative evidence for the existence of fields.


MSPS31: Construct and interpret graphical displays ofdata to describe the relationships of kinetic energy to themass of an object and to the speed of an object.Clarification Statement: Emphasis is on descriptive relationships betweenkinetic energy and mass separately from kinetic energy and speed.Examples could include riding a bicycle at different speeds, rolling differentsizes of rocks downhill, and getting hit by a wiffle ball versus a tennis ball. Assessment Boundary: none


MSPS32: Develop a model to describe that when thearrangement of objects interacting at a distance changes,different amounts of potential energy are stored in thesystem.Clarification Statement: Emphasis is on relative amounts of potentialenergy, not on calculations of potential energy. Examples of objects withinsystems interacting at varying distances could include: the Earth and eithera roller coaster cart at varying positions on a hill or objects at varyingheights on shelves, changing the direction/orientation of a magnet, and aballoon with static electrical charge being brought closer to a classmate’shair. Examples of models could include representations, diagrams,pictures, and written descriptions of systems. Assessment Boundary: Assessment is limited to two objects and electric,magnetic, and gravitational interactions.


MSPS33: Apply scientific principles to design, construct,and test a device that either minimizes or maximizesthermal energy transfer.*Clarification Statement: Examples of devices could include an insulatedbox, a solar cooker, and a Styrofoam cup. Assessment Boundary: Assessment does not include calculating the totalamount of thermal energy transferred.* This performance expectation integrates traditional science content withengineering through a practice or disciplinary code idea.


MSPS34: Plan an investigation to determine therelationships among the energy transferred, the type ofmatter, the mass, and the change in the average kineticenergy of the particles as measured by the temperature ofthe sample.Clarification Statement: Examples of experiments could includecomparing final water temperatures after different masses of ice melted inthe same volume of water with the same initial temperature, thetemperature change of samples of different materials with the same massas they cool or heat in the environment, or the same material with differentmasses when a specific amount of energy is added. Assessment Boundary: Assessment does not include calculating the totalamount of thermal energy transferred.


MSPS35: Construct, use, and present arguments tosupport the claim that when the kinetic energy of an objectchanges, energy is transferred to or from the object.Clarification Statement: Examples of empirical evidence used inarguments could include an inventory or other representation of the energybefore and after the transfer in the form of temperature changes or motionof object. Assessment Boundary: Assessment does not include calculations ofenergy.


MSESS22: Construct an explanation based on evidence forhow geoscience processes have changed Earth's surface atvarying time and spatial scales.Clarification Statement: Emphasis is on how processes change Earth’ssurface at time and spatial scales that can be large (such as slow platemotions or the uplift of large mountain ranges) or small (such as rapidlandslides or microscopic geochemical reactions), and how manygeoscience processes (such as earthquakes, volcanoes, and meteorimpacts) usually behave gradually but are punctuated by catastrophicevents. Examples of geoscience processes include surface weathering anddeposition by the movements of water, ice, and wind. Emphasis is ongeoscience processes that shape local geographic features, whereappropriate. Assessment Boundary: none


MSESS24: Develop a model to describe the cycling ofwater through Earth's systems driven by energy from thesun and the force of gravity.Clarification Statement: Emphasis is on the ways water changes its stateas it moves through the multiple pathways of the hydrologic cycle.Examples of models can be conceptual or physical. Assessment Boundary: A quantitative understanding of the latent heatsof vaporization and fusion is not assessed.


MSESS25: Collect data to provide evidence for how themotions and complex interactions of air masses results inchanges in weather conditions.Clarification Statement: Emphasis is on how air masses flow fromregions of high pressure to low pressure, causing weather (defined bytemperature, pressure, humidity, precipitation, and wind) at a fixed locationto change over time, and how sudden changes in weather can result whendifferent air masses collide. Emphasis is on how weather can be predictedwithin probabilistic ranges. Examples of data can be provided to students(such as weather maps, diagrams, and visualizations) or obtained throughlaboratory experiments (such as with condensation). Assessment Boundary: Assessment does not include recalling thenames of cloud types or weather symbols used on weather maps or thereported diagrams from weather stations.


MSESS26: Develop and use a model to describe howunequal heating and rotation of the Earth cause patterns ofatmospheric and oceanic circulation that determine regionalclimates.Clarification Statement: Emphasis is on how patterns vary by latitude,altitude, and geographic land distribution. Emphasis of atmosphericcirculation is on the sunlightdriven latitudinal banding, the Coriolis effect,and resulting prevailing winds; emphasis of ocean circulation is on thetransfer of heat by the global ocean convection cycle, which is constrainedby the Coriolis effect and the outlines of continents. Examples of modelscan be diagrams, maps and globes, or digital representations Assessment Boundary: Assessment does not include the dynamics ofthe Coriolis effect.


MSESS11: Develop and use a model of the Earthsunmoon system to describe the cyclic patterns of lunarphases, eclipses of the sun and moon, and seasons.Clarification Statement: Examples of models can be physical, graphical,or conceptual. Assessment Boundary: none


MSESS12: Develop and use a model to describe the role ofgravity in the motions within galaxies and the solar system.Clarification Statement: Emphasis for the model is on gravity as the forcethat holds together the solar system and Milky Way galaxy and controlsorbital motions within them. Examples of models can be physical (such asthe analogy of distance along a football field or computer visualizations ofelliptical orbits) or conceptual (such as mathematical proportions relative tothe size of familiar objects such as students' school or state). Assessment Boundary: Assessment does not include Kepler’s Laws oforbital motion or the apparent retrograde motion of the planets as viewedfrom Earth.


MSESS13: Analyze and interpret data to determine scaleproperties of objects in the solar system.Clarification Statement: Emphasis is on the analysis of data from Earthbased instruments, spacebased telescopes, and spacecraft to determinesimilarities and differences among solar system objects. Examples of scaleproperties include the sizes of an object’s layers (such as crust andatmosphere), surface features (such as volcanoes), and orbital radius.Examples of data include statistical information, drawings andphotographs, and models. Assessment Boundary: Assessment does not include recalling factsabout properties of the planets and other solar system bodies.

Science and Engineering Practices

Asking Questions and Defining Problems

Asking questions and defining problems in grades 6–8 builds from gradesK–5 experiences and progresses to specifying relationships betweenvariables and clarifying arguments and models.

Ask questions that can be investigated within the scope of theclassroom, outdoor environment, and museums and other publicfacilities with available resources and, when appropriate, frame ahypothesis based on observations and scientific principles. (MSPS23)


Planning and Carrying Out Investigations

Planning and carrying out investigations to answer questions or testsolutions to problems in 6–8 builds on K–5 experiences and progresses toinclude investigations that use multiple variables and provide evidence tosupport explanations or design solutions.

Plan an investigation individually and collaboratively, and in thedesign: identify independent and dependent variables and controls,what tools are needed to do the gathering, how measurements willbe recorded, and how many data are needed to support a claim. (MSPS22)




Conduct an investigation and evaluate the experimental design toproduce data to serve as the basis for evidence that can meet thegoals of the investigation. (MSPS25)


Constructing Explanations and DesigningSolutionsConstructing explanations and designing solutions in 6–8 builds on K–5experiences and progresses to include constructing explanations anddesigning solutions supported by multiple sources of evidence consistentwith scientific ideas, principles, and theories.

Apply scientific ideas or principles to design an object, tool, processor system. (MSPS21)


Engaging in Argument from EvidenceEngaging in argument from evidence in 6–8 builds on K–5 experiences andprogresses to constructing a convincing argument that supports or refutesclaims for either explanations or solutions about the natural and designedworld(s).

Construct and present oral and written arguments supported byempirical evidence and scientific reasoning to support or refute anexplanation or a model for a phenomenon or a solution to a problem.(MSPS24)


Analyzing and Interpreting DataAnalyzing data in 6–8 builds on K–5 experiences and progresses toextending quantitative analysis to investigations, distinguishing betweencorrelation and causation, and basic statistical techniques of data and erroranalysis.

Construct and interpret graphical displays of data to identify linearand nonlinear relationships. (MSPS31)


Developing and Using Models

Modeling in 6–8 builds on K–5 experiences and progresses to developing,using, and revising models to describe, test, and predict more abstractphenomena and design systems.

Develop a model to describe unobservable mechanisms. (MSPS32)


Constructing Explanations and Designing

Solutions

Constructing explanations and designing solutions in 6–8 builds on K–5experiences and progresses to include constructing explanations anddesigning solutions supported by multiple sources of evidence consistentwith scientific ideas, principles, and theories.

Apply scientific ideas or principles to design, construct, and test adesign of an object, tool, process or system. (MSPS33)




Plan an investigation individually and collaboratively, and in thedesign: identify independent and dependent variables and controls,what tools are needed to do the gathering, how measurements willbe recorded, and how many data are needed to support a claim. (MSPS34)


Engaging in Argument from EvidenceEngaging in argument from evidence in 6–8 builds on K–5 experiences andprogresses to constructing a convincing argument that supports or refutesclaims for either explanations or solutions about the natural and designedworld(s).

Construct, use, and present oral and written arguments supported byempirical evidence and scientific reasoning to support or refute anexplanation or a model for a phenomenon. (MSPS35)


Constructing Explanations and DesigningSolutionsConstructing explanations and designing solutions in 6–8 builds on K–5experiences and progresses to include constructing explanations anddesigning solutions supported by multiple sources of evidence consistentwith scientific ideas, principles, and theories.

Construct a scientific explanation based on valid and reliableevidence obtained from sources (including the students’ ownexperiments) and the assumption that theories and laws thatdescribe the natural world operate today as they did in the past andwill continue to do so in the future. (MSESS22)


Developing and Using ModelsModeling in 6–8 builds on K–5 experiences and progresses to developing,using, and revising models to describe, test, and predict more abstractphenomena and design systems.

Develop a model to describe unobservable mechanisms. (MSESS24)




Collect data about the performance of a proposed object, tool,process, or system under a range of conditions. (MSESS25)




Develop and use a model to describe phenomena. (MSESS26)






Developing and Using ModelsModeling in 6–8 builds on K–5 experiences and progresses to developing,using, and revising models to describe, test, and predict more abstractphenomena and design systems.



Analyzing and Interpreting DataAnalyzing data in 6–8 builds on K–5 experiences and progresses toextending quantitative analysis to investigations, distinguishing betweencorrelation and causation, and basic statistical techniques of data and erroranalysis.

Analyze and interpret data to determine similarities and differencesin findings. (MSESS13)

Crosscutting Concepts

Cause and EffectCause and effect relationships may be used to predict phenomena innatural or designed systems. (MSPS23), (MSPS25)


Systems and System ModelsModels can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy and matterflows within systems. (MSPS21), (MSPS24)


Stability and ChangeExplanations of stability and change in natural or designed systemscan be constructed by examining the changes over time and forcesat different scales. (MSPS22)


Scale, Proportion, and QuantityProportional relationships (e.g. speed as the ratio of distancetraveled to time taken) among different types of quantities provideinformation about the magnitude of properties and processes. (MSPS31)


Systems and System ModelsModels can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy and matterflows within systems. (MSPS32)


Energy and MatterThe transfer of energy can be tracked as energy flows through adesigned or natural system. (MSPS33)


Scale, Proportion, and QuantityProportional relationships (e.g. speed as the ratio of distancetraveled to time taken) among different types of quantities provideinformation about the magnitude of properties and processes. (MSPS34)


Energy and MatterEnergy may take different forms (e.g. energy in fields, thermalenergy, energy of motion). (MSPS35)


Scale, Proportion, and QuantityTime, space, and energy phenomena can be observed at variousscales using models to study systems that are too large or too small.(MSESS22)


Energy and MatterWithin a natural or designed system, the transfer of energy drivesthe motion and/or cycling of matter. (MSESS24)


Cause and EffectCause and effect relationships may be used to predict phenomena innatural or designed systems. (MSESS25)


Systems and System ModelsModels can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy, matter, andinformation flows within systems. (MSESS26)


PatternsPatterns can be used to identify causeandeffect relationships. (MSESS11)


Systems and System ModelsModels can be used to represent systems and their interactions. (MSESS12)


Scale, Proportion, and QuantityTime, space, and energy phenomena can be observed at variousscales using models to study systems that are too large or too small.(MSESS13)

Connections to Nature of Science

Science Knowledge Is Based on EmpiricalEvidenceScience knowledge is based upon logical and conceptualconnections between evidence and explanations. (MSPS22), (MSPS24)

Connections to Engineering, Technology, and Applications of Science

Influence of Science, Engineering, andTechnology on Society and the Natural WorldThe uses of technologies and any limitations on their use are drivenby individual or societal needs, desires, and values; by the findingsof scientific research; and by differences in such factors as climate,natural resources, and economic conditions. (MSPS21)


Science Knowledge Is Based on EmpiricalEvidenceScience knowledge is based upon logical and conceptualconnections between evidence and explanations. (MSPS34)


Science Knowledge Is Based on EmpiricalEvidenceScience knowledge is based upon logical and conceptualconnections between evidence and explanations. (MSPS35)


Scientific Knowledge Assumes an Order and

Consistency in Natural Systems

Science assumes that objects and events in natural systems occur inconsistent patterns that are understandable through measurementand observation. (MSESS11)


Scientific Knowledge Assumes an Order and

Consistency in Natural Systems

Science assumes that objects and events in natural systems occur inconsistent patterns that are understandable through measurementand observation. (MSESS12)


Interdependence of Science, Engineering, and

Technology

Engineering advances have led to important discoveries in virtuallyevery field of science and scientific discoveries have led to thedevelopment of entire industries and engineered systems. (MSESS13)

Common Core State Standards for ELA/Literacy

Reading in Science

RST.68.1 Key Ideas and Details

Cite specific textual evidence to support analysis of science andtechnical texts. (MSPS21), (MSPS23)


Reading in Science

RST.68.3 Key Ideas and Details

Follow precisely a multistep procedure when carrying outexperiments, taking measurements, or performing technical tasks.(MSPS21), (MSPS22), (MSPS25)


Writing in Science

WHST.68.1 Text Types and Purposes

Cite specific textual evidence to support analysis of science andtechnical texts. (MSPS22)


Writing in Science

WHST.68.7 Research to Build and Present

Knowledge

Conduct short research projects to answer a question (including aselfgenerated question), drawing on several sources and generatingadditional related, focused questions that allow for multiple avenuesof exploration. (MSPS21), (MSPS25)

Common Core State Standards for Mathematics

Card Type name6.EE.A.2 undefinedWrite, read, and evaluate expressions in which letters stand for numbers.(MSPS21), (MSPS22)


The Number System6.NS.C.5 Apply and extend previous understandings ofnumbers to the system of rational numbers.Understand that positive and negative numbers are used together todescribe quantities having opposite directions or values (e.g., temperatureabove/below zero, elevation above/below sea level, credits/debits,positive/negative electric charge); use positive and negative numbers torepresent quantities in realworld contexts, explaining the meaning of 0 ineach situation. (MSPS21)


Expressions & Equations7.EE.B.3 Solve reallife and mathematical problems usingnumerical and algebraic expressions and equations.Solve multistep reallife and mathematical problems posed with positiveand negative rational numbers in any form (whole numbers, fractions, anddecimals), using tools strategically. Apply properties of operations tocalculate with numbers in any form; convert between forms as appropriate;and assess the reasonableness of answers using mental computation andestimation strategies. (MSPS21), (MSPS22)


Expressions & Equations7.EE.B.4 Solve reallife and mathematical problems usingnumerical and algebraic expressions and equations.Use variables to represent quantities in a realworld or mathematicalproblem, and construct simple equations and inequalities to solve problemsby reasoning about the quantities. (MSPS21), (MSPS22)


Mathematical PracticesMP.2 Reason abstractly and quantitativelyMathematically proficient students make sense of quantities and theirrelationships in problem situations. They bring two complementary abilitiesto bear on problems involving quantitative relationships: the ability todecontextualize—to abstract a given situation and represent it symbolicallyand manipulate the representing symbols as if they have a life of their own,without necessarily attending to their referents—and the ability tocontextualize, to pause as needed during the manipulation process in orderto probe into the referents for the symbols involved. Quantitative reasoningentails habits of creating a coherent representation of the problem at hand;considering the units involved; attending to the meaning of quantities, notjust how to compute them; and knowing and flexibly using differentproperties of operations and objects. (MSPS21), (MSPS22), (MSPS23)

Documents

MS.PS2.A: Forces and Motion€¦ · DCI: Motion and Stability: Forces and Interactions MS.PS2.A: Forces and Motion The motion of an object is determined by the sum of the forces acting