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Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Standard:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Cluster:
Use the four operations with whole numbers to solve problems.

Standard:
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Cluster:
Use the four operations with whole numbers to solve problems.

Standard:
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Footnote:
See Glossary, Table 2.

Cluster:
Use the four operations with whole numbers to solve problems.

Standard:
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Overarching Standard Description:
The student will organize, synthesize, create, and communicate information.

Standard:
Use information and technology creatively to answer a question, solve a problem, or enrich understanding: a. Understand and use a variety of organizational structures, as appropriate, to convey information (e.g., chronological order, cause and effect, similarity and difference, posing and answering a question). b. Select a focus, an organizational structure, and a point of view for a report or presentation based upon purpose, audience, length, and format requirements.

Title: 3–5-ETS1 Engineering, Technology, and Applications of Science

Performance Expectation: Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.

Disciplinary Core Idea(s):
ETS1.A: Defining and Delimiting Engineering Problems Possible solutions to a problem are limited by available materials and resources (constraints). The success of a designed solution is determined by considering the desired features of a solution (criteria). Different proposals for solutions can be compared on the basis of how well each one meets the specified criteria for success or how well each takes the constraints into account.

Science & Engineering Practices: Asking Questions and Defining Problems Define a simple design problem that can be solved through the development of an object, tool, process, or system and includes several criteria for success and constraints on materials, time, or cost.

Crosscutting Concepts: Influence of Engineering, Technology, and Science on Society and the Natural World People’s needs and wants change over time, as do their demands for new and improved technologies.

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:
ELA/Literacy W.5.7: Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. W.5.8: Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources. W.5.9.a-b: Draw evidence from literary or informational texts to support analysis, reflection, and research. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. MP.5: Use appropriate tools strategically. 3.OA.1-4: Represent and solve problems involving multiplication and division. 3.OA.5-6: Understand properties of multiplication and the relationship between multiplication and division. 3.OA.7: Multiply and divide within 100. 3.OA.8-9: Solve problems involving the four operations, and identify and explain patterns in arithmetic. 4.OA.1-3: Use the four operations with whole numbers to solve problems. 4.OA.4: Gain familiarity with factors and multiples. 4.OA.5: Generate and analyze patterns. 5.OA.1-2.1: Write and interpret numerical expressions. 5.OA.3: Analyze patterns and relationships.

DCI Connections:
Connections to 3-5-ETS1.A: Defining and Delimiting Engineering Problems include: Fourth Grade: 4-PS3-4 Articulation across grade-bands: K-2.ETS1.A; MS.ETS1.A; MS.ETS1.B

Title: 3–5-ETS1 Engineering, Technology, and Applications of Science

Performance Expectation: Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.

Disciplinary Core Idea(s):
ETS1.B: Developing Possible Solutions Research on a problem should be carried out before beginning to design a solution. Testing a solution involves investigating how well it performs under a range of likely conditions. At whatever stage, communicating with peers about proposed solutions is an important part of the design process, and shared ideas can lead to improved designs.

Science & Engineering Practices: Constructing Explanations and Designing Solutions Generate and compare multiple solutions to a problem based on how well they meet the criteria and constraints of the design problem.

Crosscutting Concepts: Influence of Engineering, Technology, and Science on Society and the Natural World Engineers improve existing technologies or develop new ones to increase their benefits, decrease known risks, and meet societal demands.

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:
ELA/Literacy RI.5.1: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. RI.5.7: Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. RI.5.9: Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. MP.5: Use appropriate tools strategically. 3.OA.1-4: Represent and solve problems involving multiplication and division. 3.OA.5-6: Understand properties of multiplication and the relationship between multiplication and division. 3.OA.7: Multiply and divide within 100. 3.OA.8-9: Solve problems involving the four operations, and identify and explain patterns in arithmetic. 4.OA.1-3: Use the four operations with whole numbers to solve problems. 4.OA.4: Gain familiarity with factors and multiples. 4.OA.5: Generate and analyze patterns. 5.OA.1-2.1: Write and interpret numerical expressions. 5.OA.3: Analyze patterns and relationships.

DCI Connections:
Connections to 3-5-ETS1.B: Developing Possible Solutions Problems include: Fourth Grade: 4-ESS3-2 Articulation across grade-bands: K-2.ETS1.A; K-2.ETS1.B; K-2.ETS1.C; MS.ETS1.B; MS.ETS1.C

Title: 3–5-ETS1 Engineering, Technology, and Applications of Science

Performance Expectation: Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved.

Disciplinary Core Idea(s):
ETS1.B: Developing Possible Solutions Tests are often designed to identify failure points or difficulties, which suggest the elements of the design that need to be improved. ETS1.C: Optimizing the Design Solution Different solutions need to be tested in order to determine which of them best solves the problem, given the criteria and the constraints.

Science & Engineering Practices: Planning and Carrying Out Investigations Plan and conduct an investigation collaboratively to produce data to serve as the basis for evidence, using fair tests in which variables are controlled and the number of trials considered.

Crosscutting Concepts: N/A

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:
ELA/Literacy W.5.7: Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. W.5.8: Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources. W.5.9.a-b: Draw evidence from literary or informational texts to support analysis, reflection, and research. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. MP.5: Use appropriate tools strategically.

DCI Connections:
Connections to 3-5-ETS1.B: Developing Possible Solutions Problems include: Fourth Grade: 4-ESS3-2 Connections to K-2-ETS1.C: Optimizing the Design Solution include: Fourth Grade: 4-PS4-3 Articulation across grade-bands: K-2.ETS1.A; K-2.ETS1.C; MS.ETS1.B; MS.ETS1.C

Title: 5-ESS1 Earth’s Place in the Universe

Performance Expectation: Support an argument that differences in the apparent brightness of the sun compared to other stars is due to their relative distances from Earth. [Clarification Statement: Absolute brightness of stars is the result of a variety factors. Relative distance from Earth is one factor that affects apparent brightness and is the one selected to be addressed by the performance expectation.] [Assessment Boundary: Assessment is limited to relative distances, not sizes, of stars. Assessment does not include other factors that affect apparent brightness (such as stellar masses, age, stage).]

Disciplinary Core Idea(s):
ESS1.A: The Universe and its Stars The sun is a star that appears larger and brighter than other stars because it is closer. Stars range greatly in their distance from Earth.

Science & Engineering Practices: Engaging in Argument from Evidence Support an argument with evidence, data, or a model.

Crosscutting Concepts: Scale, Proportion, and Quantity Natural objects exist from the very small to the immensely large.

California Environmental Principles and Concepts:
N/A

California Common Core State Standards Connections:
ELA/Literacy RI.5.1.a-d: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. RI.5.7: Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. RI.5.8: Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s). RI.5.9: Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. W.5.1.a–d: Write opinion pieces on topics or texts, supporting a point of view with reasons and information. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

DCI Connections:
Connections to other DCIs in fifth grade: N/A Articulation across grade-levels: MS.ESS1.A; MS.ESS1.B

Title: 5-ESS2 Earth’s Systems

Performance Expectation: Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact. [Clarification Statement: The geosphere, hydrosphere (including ice), atmosphere, and biosphere are each system is a part of the whole Earth System. Examples could include the influence of the ocean on ecosystems, landform shape, and climate; the influence of the atmosphere on landforms and ecosystems through weather and climate; and the influence of mountain ranges on winds and clouds in the atmosphere. The geosphere, hydrosphere, atmosphere, and biosphere are each a system.] [Assessment Boundary: Assessment is limited to the interactions of two systems at a time.]

Disciplinary Core Idea(s):
ESS2.A: Earth Materials and Systems Earth’s major systems are the geosphere (solid and molten rock, soil, and sediments), the hydrosphere (water and ice), the atmosphere (air), and the biosphere (living things, including humans). These systems interact in multiple ways to affect Earth’s surface materials and processes. The ocean supports a variety of ecosystems and organisms, shapes landforms, and influences climate. Winds and clouds in the atmosphere interact with the landforms to determine patterns of weather.

Science & Engineering Practices: Developing and Using Models Develop a model using an example to describe a scientific principle.

Crosscutting Concepts: Systems and System Models A system can be described in terms of its components and their interactions.

California Environmental Principles and Concepts:
Principle III Natural systems proceed through cycles that humans depend upon, benefit from, and can alter.

California Common Core State Standards Connections:
ELA/Literacy RI.5.7: Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. SL.5.5: Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes. Mathematics MP.2: Reason abstractly and quantitatively. MP.4: Model with mathematics. 5.G.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

DCI Connections:
Connections to other DCIs in fifth grade: N/A Articulation across grade-levels: 2.ESS2.A; 3.ESS2.D; 4.ESS2.A; MS.ESS2.A; MS.ESS2.C; MS.ESS2.D