- Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
- Solve two-step word problems using the four operations. 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.
- 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.
- 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.
- Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
- Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
- Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
- Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
- Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
- Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
- 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.
- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
- Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
- Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
- Use proportional relationships to solve multistep ratio and percent problems.
- Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
- Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
- Solve real-world and mathematical problems involving the four operations with rational numbers.
- Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
- 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.
- Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.
- Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.
- 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.
- Analyze data from tests of an object or tool to determine if it works as intended.
- Use observations (firsthand or from media) to describe patterns in the natural world in order to answer scientific questions.
- Analyze and interpret data to make sense of phenomena using logical reasoning.
- Represent data in tables and various graphical displays (bar graphs and pictographs) to reveal patterns that indicate relationships.
- Analyze and interpret data to determine similarities and differences in findings.
- Analyze and interpret data to provide evidence for phenomena.
- Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution.
- Analyze data using computational models in order to make valid and reliable scientific claims.
- Ask questions based on observations to find more information about the designed world.
- Ask questions that can be investigated based on patterns such as cause and effect relationships.
- Ask questions to identify and clarify evidence of an argument.
- Ask questions that arise from examining models or a theory to clarify relationships.
- Compare multiple solutions to a problem.
- Use evidence (e.g., observations, patterns) to support an explanation.
- Use evidence (e.g., observations, patterns) to construct an explanation.
- Identify the evidence that supports particular points in an explanation.
- Construct an explanation that includes qualitative or quantitative relationships between variables that describe phenomena.
- Construct and revise an explanation based on valid and reliable evidence obtained from a variety of sources (including students' own investigations, models, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future.
- Use a model to represent relationships in the natural world.
- Develop a simple model based on evidence to represent a proposed object or tool.
- Develop a model to represent patterns in the natural world.
- Develop a model using an analogy, example, or abstract representation to describe a scientific principle.
- Use a model to test interactions concerning the functioning of a natural system.
- Develop a model to describe phenomena.
- Develop a model using an example to describe a scientific principle.
- Develop a model to predict and/or describe phenomena.
- Develop and use a model to describe phenomena.
- Develop a model to generate data to test ideas about designed systems, including those representing inputs and outputs.
- Develop a model based on evidence to illustrate the relationships between systems or between components of a system.
- Use a model to predict the relationships between systems or between components of a system.
- Construct an argument with evidence to support a claim.
- Construct an argument with evidence, data, and/or a model.
- Construct an argument with evidence.
- Make a claim about the merit of a solution to a problem by citing relevant evidence about how it meets the criteria and constraints of the problem.
- Support an argument with evidence, data, or a model.
- Evaluate competing design solutions based on jointly developed and agreed-upon design criteria.
- Evaluate the evidence behind currently accepted explanations or solutions to determine the merits of arguments.
- Evaluate competing design solutions to a real-world problem based on scientific ideas and principles, empirical evidence, and logical arguments regarding relevant factors (e.g. economic, societal, environmental, ethical considerations).
- With guidance, plan and conduct an investigation in collaboration with peers.
- Plan and conduct investigations collaboratively to produce data to serve as the basis for evidence to answer a question.
- 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.
- Make observations and/or measurements to produce data to serve as the basis for evidence for an explanation of a phenomenon or test a design solution.
- Conduct an investigation to produce data to serve as the basis for evidence that meet the goals of an investigation.
- Scientific inquiry is characterized by a common set of values that include: logical thinking, precision, open-mindedness, objectivity, skepticism, replicability of results, and honest and ethical reporting of findings.
- Science investigations use diverse methods and do not always use the same set of procedures to obtain data.
- New technologies advance scientific knowledge.
- Scientists look for patterns and order when making observations about the world.
- Science findings are based on recognizing patterns.
- Science knowledge is based upon logical and conceptual connections between evidence and explanations.
- Use mathematical representations to describe and/or support scientific conclusions and design solutions.
- Use mathematical representations to support scientific conclusions and design solutions.
- Use mathematical representations of phenomena to support claims.
- Use mathematical representations of phenomena to describe explanations.
- Create a computational model or simulation of a phenomenon, designed device, process, or system.
- Create or revise a simulation of a phenomenon, designed device, process, or system.
- Use mathematical models and/or computer simulations to predict the effects of a design solution on systems and/or the interactions between systems.
- Patterns in the natural and human designed world can be observed and used as evidence.
- Patterns in the natural world can be observed.
- Patterns of change can be used to make predictions.
- Similarities and differences in patterns can be used to sort and classify natural phenomena.
- Patterns can be used as evidence to support an explanation.
- Similarities and differences in patterns can be used to sort, classify, communicate and analyze simple rates of change for natural phenomena.
- Graphs and charts can be used to identify patterns in data.
- Patterns can be used to identify cause and effect relationships.
- Events have causes that generate observable patterns.
- Cause and effect relationships are routinely identified.
- A system can be described in terms of its components and their interactions.
- Systems may interact with other systems; they may have sub-systems and be a part of larger complex systems.
- Models can be used to represent systems and their interactions.
- People depend on various technologies in their lives; human life would be very different without technology.
- Every human-made product is designed by applying some knowledge of the natural world and is built using materials derived from the natural world.
- Engineers improve existing technologies or develop new ones to increase their benefits (e.g., better artificial limbs), decrease known risks (e.g., seatbelts in cars), and meet societal demands (e.g., cell phones).
- Engineers improve existing technologies or develop new ones.
- Technologies extend the measurement, exploration, modeling, and computational capacity of scientific investigations.
- Modern civilization depends on major technological systems.
- Scientific discoveries about the natural world can often lead to new and improved technologies, which are developed through the engineering design process.
- Advances in technology influence the progress of science and science has influenced advances in technology.

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