ms.ps1.a: structure and properties of matter · dci: matter and its interactions ms.ps1.a:...

DCI: Matter and Its Interactions

MS.PS1.A: Structure and Properties of MatterSubstances are made from different types of atoms, which combinewith one another in various ways. Atoms form molecules that rangein size from two to thousands of atoms. (MSPS11)


MS.PS1.A: Structure and Properties of MatterEach pure substance has characteristic physical and chemicalproperties (for any bulk quantity under given conditions) that can beused to identify it. (MSPS12), (MSPS13)


MS.PS1.A: Structure and Properties of MatterGases and liquids are made of molecules or inert atoms that aremoving about relative to each other. (MSPS14)


MS.PS1.A: Structure and Properties of MatterIn a liquid, the molecules are constantly in contact with others; in agas, they are widely spaced except when they happen to collide. In asolid, atoms are closely spaced and may vibrate in position but donot change relative locations. (MSPS14)


MS.PS1.A: Structure and Properties of MatterSolids may be formed from molecules, or they may be extendedstructures with repeating subunits (e.g., crystals). (MSPS11)


MS.PS1.A: Structure and Properties of MatterThe changes of state that occur with variations in temperature orpressure can be described and predicted using these models ofmatter. (MSPS14)


MS.PS1.B: Chemical ReactionsSubstances react chemically in characteristic ways. In a chemicalprocess, the atoms that make up the original substances areregrouped into different molecules, and these new substances havedifferent properties from those of the reactants. (MSPS12), (MSPS13),(MSPS15)


MS.PS1.B: Chemical ReactionsThe total number of each type of atom is conserved, and thus themass does not change. (MSPS15)


MS.PS1.B: Chemical ReactionsSome chemical reactions release energy, others store energy. (MSPS16)

DCI: Energy

MS.PS3.A: Definitions of EnergyThe term “heat” as used in everyday language refers both to thermalenergy (the motion of atoms or molecules within a substance) andthe transfer of that thermal energy from one object to another. Inscience, heat is used only for this second meaning; it refers to theenergy transferred due to the temperature difference between twoobjects. (MSPS14)

DCI: Energy

MS.PS3.A: Definitions of EnergyThe temperature of a system is proportional to the average internalkinetic energy and potential energy per atom or molecule (whicheveris the appropriate building block for the system’s material). Thedetails of that relationship depend on the type of atom or moleculeand the interactions among the atoms in the material. Temperature isnot a direct measure of a system's total thermal energy. The totalthermal energy (sometimes called the total internal energy) of asystem depends jointly on the temperature, the total number ofatoms in the system, and the state of the material. (MSPS14)

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. (MSPS16)


MS.ETS1.C: Optimizing the Design Solution

Although one design may not perform the best across all tests,identifying the characteristics of the design that performed the best ineach test can provide useful information for the redesign process that is, some of the characteristics may be incorporated into the newdesign. (MSPS16)


MS.ETS1.C: Optimizing the Design Solution

The iterative process of testing the most promising solutions andmodifying what is proposed on the basis of the test results leads togreater refinement and ultimately to an optimal solution. (MSPS16)

DCI: Energy

MS.PS3.D: Energy in Chemical Processes and

Everyday Life

The chemical reaction by which plants produce complex foodmolecules (sugars) requires an energy input (i.e., from sunlight) tooccur. In this reaction, carbon dioxide and water combine to formcarbonbased organic molecules and release oxygen. (MSLS16)

DCI: From Molecules to Organisms: Structures and Processes

MS.LS1.C: Organization for Matter and Energy

Flow in Organisms

Plants, algae (including phytoplankton), and many microorganismsuse the energy from light to make sugars (food) from carbon dioxidefrom the atmosphere and water through the process ofphotosynthesis, which also releases oxygen. These sugars can beused immediately or stored for growth or later use. (MSLS16)

DCI: Energy

MS.PS3.D: Energy in Chemical Processes and

Everyday Life

Cellular respiration in plants and animals involve chemical reactionswith oxygen that release stored energy. In these processes, complexmolecules containing carbon react with oxygen to produce carbondioxide and other materials. (MSLS17)

DCI: From Molecules to Organisms: Structures and Processes

MS.LS1.C: Organization for Matter and Energy

Flow in Organisms

Within individual organisms, food moves through a series ofchemical reactions in which it is broken down and rearranged to formnew molecules, to support growth, or to release energy. (MSLS17)

DCI: Ecosystems: Interactions, Energy, and Dynamics

MS.LS2.A: Interdependent Relationships inEcosystemsOrganisms, and populations of organisms, are dependent on their

environmental interactions both with other living things and with

nonliving factors. (MSLS21)


MS.LS2.A: Interdependent Relationships inEcosystemsIn any ecosystem, organisms and populations with similar

requirements for food, water, oxygen, or other resources may

compete with each other for limited resources, access to which

consequently constrains their growth and reproduction. (MSLS21)


MS.LS2.A: Interdependent Relationships inEcosystemsGrowth of organisms and population increases are limited by access

to resources. (MSLS21)


MS.LS2.A: Interdependent Relationships in

Ecosystems

Similarly, predatory interactions may reduce the number of

organisms or eliminate whole populations of organisms. Mutually

beneficial interactions, in contrast, may become so interdependent

that each organism requires the other for survival. Although the

species involved in these competitive, predatory, and mutually

beneficial interactions vary across ecosystems, the patterns of

interactions of organisms with their environments, both living and

nonliving, are shared. (MSLS22)

DCI: Earth and Human Activity

MS.ESS3.C: Human Impacts on Earth Systems

Human activities have significantly altered the biosphere, sometimes

damaging or destroying natural habitats and causing the extinction of

other species. But changes to Earth’s environments can have

different impacts (negative and positive) for different living things.

(MSESS33)



Typically as human populations and percapita consumption of

natural resources increase, so do the negative impacts on Earth

unless the activities and technologies involved are engineered

otherwise. (MSESS33)



Typically as human populations and percapita consumption ofnatural resources increase, so do the negative impacts on Earthunless the activities and technologies involved are engineeredotherwise. (MSESS34)

DCI: Earth's Systems

MS.ESS2.A: Earth Materials and Systems

All Earth processes are the result of energy flowing and mattercycling within and among the planet’s systems. This energy isderived from the sun and Earth’s hot interior. The energy that flowsand matter that cycles produce chemical and physical changes inEarth’s materials and living organisms. (MSESS21)


MS.ESS2.A: Earth Materials and Systems

The 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)

Performance Expectation

MSPS11: Develop models to describe the atomiccomposition of simple molecules and extended structures.Clarification Statement: Emphasis is on developing models of moleculesthat vary in complexity. Examples of simple molecules could includeammonia and methanol. Examples of extended structures could includesodium chloride or diamonds. Examples of molecularlevel models couldinclude drawings, 3D ball and stick structures, or computer representationsshowing different molecules with different types of atoms. Assessment Boundary: Assessment does not include valence electronsand bonding energy, discussing the ionic nature of subunits of complexstructures, or a complete description of all individual atoms in a complexmolecule or extended structure is not required.


MSPS12: Analyze and interpret data on the properties ofsubstances before and after the substances interact todetermine if a chemical reaction has occurred.Clarification Statement: Examples of reactions could include burningsugar or steel wool, fat reacting with sodium hydroxide, and mixing zincwith hydrogen chloride. Assessment Boundary: Assessment is limited to analysis of the followingproperties: density, melting point, boiling point, solubility, flammability, andodor.


MSPS13: Gather and make sense of information todescribe that synthetic materials come from naturalresources and impact society.Clarification Statement: Emphasis is on natural resources that undergo achemical process to form the syntheic material. Examples of new materialscould include new medicine, foods, and alternative fuels. Assessment Boundary: Assessment is limited to qualitative information.


MSPS14: Develop a model that predicts and describeschanges in particle motion, temperature, and state of a puresubstance when thermal energy is added or removed.Clarification Statement: Emphasis is on qualitative molecularlevelmodels of solids, liquids, and gases to show that adding or removingthermal energy increases or decreases kinetic energy of the particles untila change of state occurs. Examples of models could include drawing anddiagrams. Examples of particles could include molecules or inert atoms.Examples of pure substances could include water, carbon dioxide, andhelium. Assessment Boundary: none


MSPS15: Develop and use a model to describe how thetotal number of atoms does not change in a chemicalreaction and thus mass is conserved.Clarification Statement: Emphasis is on law of conservation of matter andon physical models or drawings, including digital forms, that representatoms. Assessment Boundary: Assessment does not include the use of atomicmasses, balancing symbolic equations, or intermolecular forces.


MSPS16: Undertake a design project to construct, test,and modify a device that either releases or absorbs thermalenergy by chemical processes.*Clarification Statement: Emphasis is on the design, controlling thetransfer of energy to the environment, and modification of a device usingfactors such as type and concentration of a substance. Examples ofdesigns could involve chemical reactions such as dissolving ammoniumchloride or calcium chloride. Assessment Boundary: Assessment is limited to the criteria of amount,time, and temperature of substance in testing the device.* This performance expectation integrates traditional science content withengineering through a practice or disciplinary code idea.


MSLS16: Construct a scientific explanation based onevidence for the role of photosynthesis in the cycling ofmatter and flow of energy into and out of organisms.Clarification Statement: Emphasis is on tracing movement of matter andflow of energy. Assessment Boundary: Assessment does not include the biochemicalmechanisms of photosynthesis.


MSLS17: Develop a model to describe how food isrearranged through chemical reactions forming newmolecules that support growth and/or release energy as thismatter moves through an organism.Clarification Statement: Emphasis is on describing that molecules arebroken apart and put back together and that in this process, energy isreleased. Assessment Boundary: Assessment does not include details of thechemical reactions for photosynthesis or respiration.


MSLS21: Analyze and interpret data to provide evidencefor the effects of resource availability on organisms andpopulations of organisms in an ecosystem.Clarification Statement: Emphasis is on cause and effect relationshipsbetween resources and growth of individual organisms and the numbers oforganisms in ecosystems during periods of abundant and scarceresources. Assessment Boundary: none


MSLS22: Construct an explanation that predicts patternsof interactions among organisms across multipleecosystems.Clarification Statement: Emphasis is on predicting consistent patterns ofinteractions in different ecosystems in terms of the relationships amongand between organisms and abiotic components of ecosystems. Examplesof types of interactions could include competitive, predatory, and mutuallybeneficial. Assessment Boundary: none


MSESS33: Apply scientific principles to design a methodfor monitoring and minimizing a human impact on theenvironment.*Clarification Statement: Examples of the design process includeexamining human environmental impacts, assessing the kinds of solutionsthat are feasible, and designing and evaluating solutions that could reducethat impact. Examples of human impacts can include water usage (such asthe withdrawal of water from streams and aquifers or the construction ofdams and levees), land usage (such as urban development, agriculture, orthe removal of wetlands), and pollution (such as of the air, water, or land). Assessment Boundary: none* This performance expectation integrates traditional science content withengineering through a practice or disciplinary code idea.


MSESS34: Construct an argument supported by evidencefor how increases in human population and percapitaconsumption of natural resources impact Earth's systems.Clarification Statement: Examples of evidence include gradeappropriatedatabases on human populations and the rates of consumption of food andnatural resources (such as freshwater, mineral, and energy). Examples ofimpacts can include changes to the appearance, composition, andstructure of Earth’s systems as well as the rates at which they change. Theconsequences of increases in human populations and consumption ofnatural resources are described by science, but science does not make thedecisions for the actions society takes. Assessment Boundary: none


MSESS21: Develop a model to describe the cycling ofEarth's materials and the flow of energy that drives thisprocess.Clarification Statement: Emphasis is on the processes of melting,crystallization, weathering, deformation, and sedimentation, which acttogether to form minerals and rocks through the cycling of Earth’smaterials. Assessment Boundary: Assessment does not include the identificationand naming of minerals.


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.

Science and Engineering Practices

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 predict and/or describe phenomena. (MSPS11),(MSPS14)



Develop a model to describe unobservable mechanisms. (MSPS15)


Analyzing and Interpreting Data

Analyzing data in 6–8 builds on K–5 experiences and progresses to

extending quantitative analysis to investigations, distinguishing between

correlation and causation, and basic statistical techniques of data and error

analysis.

Analyze and interpret data to determine similarities and differencesin findings. (MSPS12)


Constructing Explanations and Designing

Solutions

Constructing explanations and designing solutions in 6–8 builds on K–5

experiences and progresses to include constructing explanations and

designing solutions supported by multiple sources of evidence consistent

with scientific ideas, principles, and theories.

Undertake a design project, engaging in the design cycle, toconstruct and/or implement a solution that meets specific designcriteria and constraints. (MSPS16)


Obtaining, Evaluating, and Communicating

Information

Obtaining, evaluating, and communicating information in 6–8 builds on K–5

experiences and progresses to evaluating the merit and validity of ideas and

methods.

Gather, read, and synthesize information from multiple appropriatesources and assess the credibility, accuracy, and possible bias ofeach publication and methods used, and describe how they aresupported or not supported by evidence. (MSPS13)


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. (MSLS16)



Develop a model to describe unobservable mechanisms. (MSLS17)


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 provide evidence for phenomena. (MSLS21)



Construct an explanation that includes qualitative or quantitativerelationships between variables that predict phenomena. (MSLS22)



Apply scientific ideas or principles to design an object, tool, processor system. (MSESS33)


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 an oral and written argument supported by empiricalevidence and scientific reasoning to support or refute an explanationor a model for a phenomenon or a solution to a problem. (MSESS34)



Develop and use a model to describe phenomena. (MSESS21)



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)



Develop a model to describe unobservable mechanisms. (MSESS24)


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.

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


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 and use a model to describe phenomena. (MSESS26)

Crosscutting Concepts

Patterns

Macroscopic patterns are related to the nature of microscopic andatomiclevel structure. (MSPS12)


Cause and EffectCause and effect relationships may be used to predict phenomena innatural or designed systems. (MSPS14)


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.(MSPS11)


Energy and MatterMatter is conserved because atoms are conserved in physical andchemical processes. (MSPS15)


Energy and MatterThe transfer of energy can be tracked as energy flows through adesigned or natural system. (MSPS16)


Structure and FunctionStructures can be designed to serve particular functions by takinginto account properties of different materials, and how materials canbe shaped and used. (MSPS13)


Energy and MatterWithin a natural system, the transfer of energy drives the motionand/or cycling of matter. (MSLS16)


Energy and MatterMatter is conserved because atoms are conserved in physical andchemical processes. (MSLS17)


Cause and EffectCause and effect relationships may be used to predict phenomena innatural or designed systems. (MSLS21)


PatternsPatterns can be used to identify causeandeffect relationships. (MSLS22)


Cause and EffectRelationships can be classified as causal or correlational, andcorrelation does not necessarily imply causation. (MSESS33)


Cause and EffectCause and effect relationships may be used to predict phenomena innatural or designed systems. (MSESS34)


Stability and ChangeExplanations of stability and change in natural or designed systemscan be constructed by examining the changes over time andprocesses at different scales, including the atomic scale. (MSESS21)


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)

Connections to Nature of Science

Science Knowledge Is Based on EmpiricalEvidenceScience knowledge is based upon logical and conceptualconnections between evidence and explanations. (MSPS12)

Connections to Nature of Science

Science Models, Laws, Mechanisms, andTheories Explain Natural PhenomenaLaws are regularities or mathematical descriptions of naturalphenomena. (MSPS15)

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. Thus technology usevaries from region to region and over time. (MSPS13)


Interdependence of Science, Engineering, andTechnologyEngineering advances have led to important discoveries in virtuallyevery field of science and scientific discoveries have led to thedevelopment of entire industries and engineered systems. (MSPS13)


Science Knowledge Is Based on EmpiricalEvidenceScience knowledge is based upon logical connections betweenevidence and explanations. (MSLS16)


Science Addresses Questions About the Naturaland Material WorldScientific knowledge can describe the consequences of actions butdoes not necessarily prescribe the decisions that society takes. (MSESS34)


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. Thus technology usevaries from region to region and over time. (MSESS33)


Influence of Science, Engineering, andTechnology on Society and the Natural WorldAll human activity draws on natural resources and has both shortand longterm consequences, positive as well as negative, for thehealth of people and the natural environment. (MSESS34)

Common Core State Standards for ELA/Literacy

Reading in ScienceRST.68.1 Key Ideas and DetailsCite specific textual evidence to support analysis of science andtechnical texts. (MSPS12), (MSPS13)


Reading in ScienceRST.68.3 Key Ideas and DetailsFollow precisely a multistep procedure when carrying outexperiments, taking measurements, or performing technical tasks.(MSPS16)


Reading in ScienceRST.68.7 Integration of Knowledge and IdeasIntegrate quantitative or technical information expressed in words ina text with a version of that information expressed visually (e.g., in aflowchart, diagram, model, graph, or table). (MSPS11), (MSPS12), (MSPS14), (MSPS15)


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. (MSPS16)


Writing in Science

WHST.68.8 Research to Build and Present

Knowledge

Gather relevant information from multiple print and digital sources,using search terms effectively; assess the credibility and accuracy ofeach source; and quote or paraphrase the data and conclusions ofothers while avoiding plagiarism and following a standard format forcitation. (MSPS13)

Common Core State Standards for Mathematics

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. (MSPS14)


Ratios & Proportional Relationships6.RP.A.3 Understand ratio concepts and use ratioreasoning to solve problems.Use ratio and rate reasoning to solve realworld and mathematicalproblems, e.g., by reasoning about tables of equivalent ratios, tapediagrams, double number line diagrams, or equations. (MSPS11), (MSPS12),(MSPS15)


Statistics & Probability6.SP.B.4 Summarize and describe distributions.Display numerical data in plots on a number line, including dot plots,histograms, and box plots. (MSPS12)


Statistics & Probability6.SP.B.5 Summarize and describe distributions.Summarize numerical data sets in relation to their context. (MSPS12)


Expressions & Equations8.EE.A.3 Expressions and Equations Work with radicalsand integer exponents.Use numbers expressed in the form of a single digit times an integer powerof 10 to estimate very large or very small quantities, and to express howmany times as much one is than the other. (MSPS11)


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. (MSPS11), (MSPS12), (MSPS15)


Mathematical PracticesMP.4 Model with mathematicsMathematically proficient students can apply the mathematics they know tosolve problems arising in everyday life, society, and the workplace. Astudent might apply proportional reasoning to plan a school event oranalyze a problem in the community. Mathematically proficient studentswho can apply what they know are comfortable making assumptions andapproximations to simplify a complicated situation, realizing that these mayneed revision later. They are able to identify important quantities in apractical situation and map their relationships using such tools asdiagrams, twoway tables, graphs, flowcharts and formulas. They cananalyze those relationships mathematically to draw conclusions. Theyroutinely interpret their mathematical results in the context of the situationand reflect on whether the results make sense, possibly improving themodel if it has not served its purpose. (MSPS11), (MSPS15)

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