Search the California Content Standards

Title: MS-PS4 Waves and Their Applications in Technologies for Information Transfer

Performance Expectation: Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. [Clarification Statement: Emphasis is on describing waves with both qualitative and quantitative thinking.] [Assessment Boundary: Assessment does not include electromagnetic waves and is limited to standard repeating waves.]

Disciplinary Core Idea(s):
PS4.A: Wave Properties A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical representations to describe and/or support scientific conclusions and design solutions. Connections to Nature of Science: Scientific Knowledge is Based on Empirical Evidence Science knowledge is based upon logical and conceptual connections between evidence and explanations.

Crosscutting Concepts: Patterns Graphs and charts can be used to identify patterns in data.

California Environmental Principles and Concepts:
N/A

California Common Core State Standards Connections:
ELA/Literacy SL.8.5: Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.3.a-d: Use ratio and rate reasoning to solve real-world and mathematical problems. 7.RP.2.a-d: Recognize and represent proportional relationships between quantities. 8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

DCI Connections:
Connections to other DCIs in this grade-band: N/A Articulation across grade-bands: 4.PS3.A; 4.PS3.B; 4.PS4.A; HS.PS4.A; HS.PS4.B

Title: HS-ESS1 Earth’s Place in the Universe

Performance Expectation: Use mathematical or computational representations to predict the motion of orbiting objects in the solar system. [Clarification Statement: Emphasis is on Newtonian gravitational laws governing orbital motions, which apply to human-made satellites as well as planets and moons.] [Assessment Boundary: Mathematical representations for the gravitational attraction of bodies and Kepler’s Laws of orbital motions should not deal with more than two bodies, nor involve calculus.]

Disciplinary Core Idea(s):
ESS1.B: Earth and the Solar System Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun. Orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system.

Science & Engineering Practices: Using Mathematical and Computational Thinking Use mathematical or computational representations of phenomena to describe explanations.

Crosscutting Concepts: Scale, Proportion, and Quantity Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth). Connections to Engineering, Technology, and Applications of Science: Interdependence of Science, Engineering, and Technology Science and engineering complement each other in the cycle known as research and development (R&D). Many R&D projects may involve scientists, engineers, and others with wide ranges of expertise.

California Environmental Principles and Concepts:
N/A

California Common Core State Standards Connections:
Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. N-Q.1-3: Reason quantitatively and use units to solve problems. A-SSE.1.a-b: Interpret expressions that represent a quantity in terms of its context. A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

DCI Connections:
Connections to other DCIs in this grade-band: HS.PS2.B Articulation across grade-bands: MS.PS2.A; MS.PS2.B; MS.ESS1.A; MS.ESS1.B

Title: HS-ESS1 Earth’s Place in the Universe

Performance Expectation: Evaluate evidence of the past and current movements of continental and oceanic crust and the theory of plate tectonics to explain the ages of crustal rocks. [Clarification Statement: Emphasis is on the ability of plate tectonics to explain the ages of crustal rocks. Examples include evidence of the ages oceanic crust increasing with distance from mid-ocean ridges (a result of plate spreading) and the ages of North American continental crust decreasing with distance away from a central ancient core of the continental plate (a result of past plate interactions).]

Disciplinary Core Idea(s):
ESS1.C: The History of Planet Earth Continental rocks, which can be older than 4 billion years, are generally much older than the rocks of the ocean floor, which are less than 200 million years old. ESS2.B: Plate Tectonics and Large-Scale System Interactions Plate tectonics is the unifying theory that explains the past and current movements of the rocks at Earth’s surface and provides a framework for understanding its geologic history. (ESS2.B Grade 8 GBE) (secondary to HS-ESS1-5) PS1.C: Nuclear Processes Spontaneous radioactive decays follow a characteristic exponential decay law. Nuclear lifetimes allow radiometric dating to be used to determine the ages of rocks and other materials. (secondary to HS-ESS1-5)

Science & Engineering Practices: Engaging in Argument from Evidence Evaluate evidence behind currently accepted explanations or solutions to determine the merits of arguments.

Crosscutting Concepts: Patterns Empirical evidence is needed to identify patterns.

California Environmental Principles and Concepts:
N/A

California Common Core State Standards Connections:
ELA/Literacy RST.11-12.1: Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. RST.11-12.8: Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. WHST.9-10.2: Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes. WHST.11-12.2: Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes. Mathematics MP.2: Reason abstractly and quantitatively. N-Q.1-3: Reason quantitatively and use units to solve problems.

DCI Connections:
Connections to other DCIs in this grade-band: HS.PS3.B; HS.ESS2.A Articulation across grade-bands: MS.ESS1.C; MS.ESS2.A; MS.ESS2.B

Title: HS-ESS3 Earth and Human Activity

Performance Expectation: Use a computational representation to illustrate the relationships among Earth systems and how those relationships are being modified due to human activity. [Clarification Statement: Examples of Earth systems to be considered are the hydrosphere, atmosphere, cryosphere, geosphere, and/or biosphere. An example of the far-reaching impacts from a human activity is how an increase in atmospheric carbon dioxide results in an increase in photosynthetic biomass on land and an increase in ocean acidification, with resulting impacts on sea organism health and marine populations.] [Assessment Boundary: Assessment does not include running computational representations but is limited to using the published results of scientific computational models.]

Disciplinary Core Idea(s):
ESS2.D: Weather and Climate Current models predict that, although future regional climate changes will be complex and varied, average global temperatures will continue to rise. The outcomes predicted by global climate models strongly depend on the amounts of human-generated greenhouse gases added to the atmosphere each year and by the ways in which these gases are absorbed by the ocean and biosphere. (secondary to HS-ESS3-6) ESS3.D: Global Climate Change Through computer simulations and other studies, important discoveries are still being made about how the ocean, the atmosphere, and the biosphere interact and are modified in response to human activities.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use a computational representation of phenomena or design solutions to describe and/or support claims and/or explanations.

Crosscutting Concepts: Systems and System Models When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models.

California Environmental Principles and Concepts:
Principle I The continuation and health of individual human lives and of human communities and societies depend on the health of the natural systems that provide essential goods and ecosystem services. Principle II The long-term functioning and health of terrestrial, freshwater, coastal, and marine ecosystems are influenced by their relationships with human societies. Principle III Natural systems proceed through cycles that humans depend upon, benefit from, and can alter. Principle IV The exchange of matter between natural systems and human societies affects the long-term functioning of both. Principle V Decisions affecting resources and natural systems are based on a wide range of considerations and decision-making processes.

California Common Core State Standards Connections:
Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. N-Q.1-3: Reason quantitatively and use units to solve problems.

DCI Connections:
Connections to other DCIs in this grade-band: HS.LS2.B; HS.LS2.C; HS.LS4.D; HS.ESS2.A Articulation across grade-bands: MS.LS2.C; MS.ESS2.A; MS.ESS2.C; MS.ESS3.C; MS.ESS3.D

Title: HS-ETS1 Engineering, Technology, and Applications of Science

Performance Expectation: Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints on interactions within and between systems relevant to the problem.

Disciplinary Core Idea(s):
ETS1.B: Developing Possible Solutions Both physical models and computers can be used in various ways to aid in the Engineering, Technology, and Applications of Science process. Computers are useful for a variety of purposes, such as running simulations to test different ways of solving a problem or to see which one is most efficient or economical; and in making a persuasive presentation to a client about how a given design will meet his or her needs.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical models and/or computer simulations to predict the effects of a design solution on systems and/or the interactions between systems.

Crosscutting Concepts: Systems and System Models Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales.

California Environmental Principles and Concepts:
Principle V Decisions affecting resources and natural systems are based on a wide range of considerations and decision-making processes.

California Common Core State Standards Connections:
Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics.

DCI Connections:
Connections to HS-ETS1.B: Designing Solutions to Engineering Problems include: Earth and Space Science: HS-ESS3-2; HS-ESS3-4 Life Science: HS-LS2-7; HS-LS4-6 Articulation across grade-bands: MS.ETS1.A ; MS.ETS1.B ; MS.ETS1.C

Title: HS-LS2 Ecosystems: Interactions, Energy, and Dynamics

Performance Expectation: Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales. [Clarification Statement: Emphasis is on quantitative analysis and comparison of the relationships among interdependent factors including boundaries, resources, climate, and competition. Examples of mathematical comparisons could include graphs, charts, histograms, and population changes gathered from simulations or historical data sets.] [Assessment Boundary: Assessment does not include deriving mathematical equations to make comparisons.]

Disciplinary Core Idea(s):
LS2.A: Interdependent Relationships in Ecosystems Ecosystems have carrying capacities, which are limits to the numbers of organisms and populations they can support. These limits result from such factors as the availability of living and nonliving resources and from such challenges such as predation, competition, and disease. Organisms would have the capacity to produce populations of great size were it not for the fact that environments and resources are finite. This fundamental tension affects the abundance (number of individuals) of species in any given ecosystem.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical and/or computational representations of phenomena or design solutions to support explanations.

Crosscutting Concepts: Scale, Proportion, and Quantity The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs.

California Environmental Principles and Concepts:
Principle II The long-term functioning and health of terrestrial, freshwater, coastal, and marine ecosystems are influenced by their relationships with human societies. Principle IV The exchange of matter between natural systems and human societies affects the long-term functioning of both.

California Common Core State Standards Connections:
ELA/Literacy RST.11-12.1: Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. WHST.9–12.2.a–e: Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. N-Q.1-3: Reason quantitatively and use units to solve problems.

DCI Connections:
Connections to other DCIs in this grade-band: N/A Articulation across grade-bands: MS.LS2.A; MS.LS2.C; MS.ESS3.A; MS.ESS3.C

Title: HS-LS2 Ecosystems: Interactions, Energy, and Dynamics

Performance Expectation: Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales. [Clarification Statement: Examples of mathematical representations include finding the average, determining trends, and using graphical comparisons of multiple sets of data.] [Assessment Boundary: Assessment is limited to provided data.]

Disciplinary Core Idea(s):
LS2.A: Interdependent Relationships in Ecosystems Ecosystems have carrying capacities, which are limits to the numbers of organisms and populations they can support. These limits result from such factors as the availability of living and nonliving resources and from such challenges such as predation, competition, and disease. Organisms would have the capacity to produce populations of great size were it not for the fact that environments and resources are finite. This fundamental tension affects the abundance (number of individuals) of species in any given ecosystem. LS2.C: Ecosystem Dynamics, Functioning, and Resilience A complex set of interactions within an ecosystem can keep its numbers and types of organisms relatively constant over long periods of time under stable conditions. If a modest biological or physical disturbance to an ecosystem occurs, it may return to its more or less original status (i.e., the ecosystem is resilient), as opposed to becoming a very different ecosystem. Extreme fluctuations in conditions or the size of any population, however, can challenge the functioning of ecosystems in terms of resources and habitat availability.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical representations of phenomena or design solutions to support and revise explanations. Connections to Nature of Science: Scientific Knowledge is Open to Revision in Light of New Evidence Most scientific knowledge is quite durable, but is, in principle, subject to change based on new evidence and/or reinterpretation of existing evidence.

Crosscutting Concepts: Scale, Proportion, and Quantity Using the concept of orders of magnitude allows one to understand how a model at one scale relates to a model at another scale.

California Environmental Principles and Concepts:
Principle II The long-term functioning and health of terrestrial, freshwater, coastal, and marine ecosystems are influenced by their relationships with human societies. Principle IV The exchange of matter between natural systems and human societies affects the long-term functioning of both.

California Common Core State Standards Connections:
ELA/Literacy RST.11-12.1: Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. WHST.9–12.2.a–e: Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. N-Q.1-3: Reason quantitatively and use units to solve problems.

DCI Connections:
Connections to other DCIs in this grade-band: HS.ESS2.E; HS.ESS3.A; HS.ESS3.C; HS.ESS3.D Articulation across grade-bands: MS.LS2.A; MS.LS2.C; MS.ESS3.C

Title: HS-LS2 Ecosystems: Interactions, Energy, and Dynamics

Performance Expectation: Use mathematical representations to support claims for the cycling of matter and flow of energy among organisms in an ecosystem. [Clarification Statement: Emphasis is on using a mathematical model of stored energy in biomass to describe the transfer of energy from one trophic level to another and that matter and energy are conserved as matter cycles and energy flows through ecosystems. Emphasis is on atoms and molecules such as carbon, oxygen, hydrogen and nitrogen being conserved as they move through an ecosystem.] [Assessment Boundary: Assessment is limited to proportional reasoning to describe the cycling of matter and flow of energy.]

Disciplinary Core Idea(s):
LS2.B: Cycles of Matter and Energy Transfer in Ecosystems Plants or algae form the lowest level of the food web. At each link upward in a food web, only a small fraction of the matter consumed at the lower level is transferred upward, to produce growth and release energy in cellular respiration at the higher level. Given this inefficiency, there are generally fewer organisms at higher levels of a food web. Some matter reacts to release energy for life functions, some matter is stored in newly made structures, and much is discarded. The chemical elements that make up the molecules of organisms pass through food webs and into and out of the atmosphere and soil, and they are combined and recombined in different ways. At each link in an ecosystem, matter and energy are conserved.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical representations of phenomena or design solutions to support claims.

Crosscutting Concepts: Energy and Matter Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems.

California Environmental Principles and Concepts:
Principle II The long-term functioning and health of terrestrial, freshwater, coastal, and marine ecosystems are influenced by their relationships with human societies. Principle IV The exchange of matter between natural systems and human societies affects the long-term functioning of both.

California Common Core State Standards Connections:
Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. N-Q.1-3: Reason quantitatively and use units to solve problems.

DCI Connections:
Connections to other DCIs in this grade-band: HS.PS3.B; HS.PS3.D Articulation across grade-bands: MS.PS3.D; MS.LS1.C; MS.LS2.B

Title: HS-PS1 Matter and Its Interactions

Performance Expectation: Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. [Clarification Statement: Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students’ use of mathematical thinking and not on memorization and rote application of problem-solving techniques.] [Assessment Boundary: Assessment does not include complex chemical reactions.]

Disciplinary Core Idea(s):
PS1.B: Chemical Reactions The fact that atoms are conserved, together with knowledge of the chemical properties of the elements involved, can be used to describe and predict chemical reactions.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical representations of phenomena to support claims.

Crosscutting Concepts: Energy and Matter The total amount of energy and matter in closed systems is conserved. Connections to Nature of Science: Scientific Knowledge Assumes an Order and Consistency in Natural Systems Science assumes the universe is a vast single system in which basic laws are consistent.

California Environmental Principles and Concepts:
N/A

California Common Core State Standards Connections:
Mathematics MP.2: Reason abstractly and quantitatively. N-Q.1-3: Reason quantitatively and use units to solve problems.

DCI Connections:
Connections to other DCIs in this grade-band: HS.PS3.B; HS.LS1.C Articulation across grade-bands: MS.PS1.A; MS.PS1.B; MS.LS1.C; MS.LS2.B; MS.ESS2.A

Title: HS-PS2 Motion and Stability: Forces and Interactions

Performance Expectation: Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system. [Clarification Statement: Emphasis is on the quantitative conservation of momentum in interactions and the qualitative meaning of this principle.] [Assessment Boundary: Assessment is limited to systems of two macroscopic bodies moving in one dimension.]

Disciplinary Core Idea(s):
PS2.A: Forces and Motion Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object. If a system interacts with objects outside itself, the total momentum of the system can change; however, any such change is balanced by changes in the momentum of objects outside the system.

Science & Engineering Practices: Using Mathematics and Computational Thinking Use mathematical representations of phenomena to describe explanations.

Crosscutting Concepts: Systems and System Models When investigating or describing a system, the boundaries and initial conditions of the system need to be defined.

California Environmental Principles and Concepts:
N/A

California Common Core State Standards Connections:
Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. N-Q.1-3: Reason quantitatively and use units to solve problems. A-CED.1: Create equations and inequalities in one variable and use them to solve problems. A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

DCI Connections:
Connections to other DCIs in this grade-band: HS.ESS1.A; HS.ESS1.C Articulation across grade-bands: MS.PS2.A; MS.PS3.C