Pennsylvania State Standards for Mathematics: Grade 5

PA.2.1.5. Numbers, Number Systems and Number Relationships: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.1.5.A. Apply number patterns to count and compare values of whole numbers, fractions, and decimals.

2.1.5.B. Use number theory concepts and models to represent or rename whole numbers, fractions, and decimals.

2.1.5.C. Use models to represent the concept of an integer, fraction, decimal, or percent.

2.1.5.D. Apply place value concepts to order and compare decimals and to express whole numbers and decimals in expanded notation.

2.1.5.E. Develop and apply number theory concepts (e.g., primes, factors, multiples, composites) to represent numbers in various ways.

2.1.5.F. Understand the concepts of multiplication and division and use the inverse relationships between multiplication and division, to determine unknown quantities in equations.

2.1.5.G. Develop and apply number theory concepts (e.g., primes, factors, multiples, composites) to represent numbers in various ways.

PA.2.2.5. Computation and Estimation: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.2.5.A. Intentionally Blank

2.2.5.B. Multiply and divide single- and double-digit numbers; add and subtract fractions and mixed numbers; add, subtract, multiply and divide decimals.

2.2.5.C. Intentionally Blank

2.2.5.D. Estimate results from calculations with basic operations of whole numbers and decimals and check the reasonableness of those estimates.

2.2.5.E. Determine through estimations the reasonableness of answers to problems involving addition, subtraction, multiplication and division of whole numbers.

2.2.5.F. Demonstrate skills for using fraction calculators to verify conjectures, confirm computations and explore complex problem-solving situations.

2.2.5.G. Apply estimation strategies to a variety of problems including time and money.

2.2.5.H. Explain multiplication and division algorithms.

2.2.5.I. Select a method for computation and explain why it is appropriate.

PA.2.3.5. Measurement and Estimation: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.3.5.A. Use concrete objects to demonstrate the meaning of measurement quantities (e.g., perimeter, area, weight, capacity).

2.3.5.B. Select and use appropriate instruments and units for measuring quantities to a specified level of accuracy.

2.3.5.C. Calculate perimeter and area, and sums and differences of measurements.

2.3.5.D. Perform basic conversions within a system.

2.3.5.E. Intentionally Blank

PA.2.4.5. Mathematical Reasoning and Connections: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.4.5.A. Use models, number facts, properties and relationships to draw conclusions and explain reasons for conclusions.

2.4.5.B. Use if...then statements to express conditional relationships.

2.4.5.C. Draw inductive and deductive conclusions within mathematical contexts.

2.4.5.D. Distinguish between relevant and irrelevant information in a mathematical problem.

2.4.5.E. Interpret statements made with precise language of logic (e.g., all, or, every, none, some, or, many).

2.4.5.F. Use statistics to quantify issues (e.g., in social studies, in science).

PA.2.5.5. Mathematical Problem Solving and Communication: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.5.5.A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.

2.5.5.B. Use appropriate mathematical terms, vocabulary, language, symbols, and graphs to explain clearly and logically solutions to problems.

2.5.5.C. Show ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams and models.

2.5.5.D. Connect, extend and generalize problem solutions to other concepts, problems and circumstances in mathematics.

2.5.5.E. Select, use and justify the methods, materials and strategies used to solve problems.

2.5.5.F. Use appropriate problem-solving strategies (e.g., solving a simpler problem, drawing a picture or diagram).

PA.2.6.5. Statistics and Data Analysis: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.6.5.A. Gather data from surveys and observations from sources outside the classroom or home.

2.6.5.B. Use pictures, tallies, tables, charts, bar graphs, line graphs, diagrams, and graphs to organize, display, and analyze data.

2.6.5.C. Calculate mean and range, identify the median and the mode of a set of data, and use these quantities to describe the data.

2.6.5.D. Compare data using multiple categories displayed in a graph.

2.6.5.E. Determine the reasonableness of a statement based on a comparison to data displayed in a graph and summarized by numerical measures.

PA.2.7.5. Probability and Predictions: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.7.5.A. Predict and calculate the likelihood of simple events.

2.7.5.B. Predict and determine why some outcomes of a particular event are certain, more likely, less likely, equally likely, or impossible.

2.7.5.C. Express probabilities as fractions and/or decimals.

2.7.5.D. List all possible combinations and arrangements of outcomes of an experiment (e.g., tree diagrams, matrices)

2.7.5.E. Compare predictions based on theoretical probability and experimental results.

2.7.5.F. Determine patterns generated as a result of an experiment.

2.7.5.G. Determine the probability of an event involving ''and'', ''or'' or ''not''.

2.7.5.H. Predict and determine why some outcomes are certain, more likely, less likely, equally likely or impossible.

2.7.5.I. Find all possible combinations and arrangements involving a limited number of variables.

2.7.5.J. Develop a tree diagram and list the elements.

PA.2.8.5. Algebra and Functions: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.8.5.A. Use the concept of equality to demonstrate understanding of the distributive property

2.8.5.B. Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) and explain the method of solution.

2.8.5.C. Recognize, describe, extend, create, replicate, and form a rule for a variety of patterns, sequences, and relationships verbally, numerically, symbolically, and graphically.

2.8.5.D. Determine a functional rule from a table or graph.

2.8.5.E. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.

2.8.5.F. Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

2.8.5.G. Select and use appropriate strategies, including concrete materials, to solve number sentences and explain the method of solution.

2.8.5.H. Locate and identify points on a coordinate system.

2.8.5.I. Generate functions from tables of data and relate data to corresponding graphs and functions.

PA.2.9.5. Geometry: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.9.5.A. Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts, and classify and compare 2- and 3- dimensional shapes on the basis of their properties.

2.9.5.B. Predict and describe the result of a translation (slide), rotation (turn), or reflection (flip) of a 2- dimensional shape.

2.9.5.C. Identify location of points with fractional or decimal coordinates on a number line or on a 2- dimensional coordinate system.

2.9.5.D. Describe in words how geometric shapes are constructed.

2.9.5.E. Construct two- and three-dimensional shapes and figures using manipulatives, geoboards and computer software.

2.9.5.F. Find familiar solids in the environment and describe them.

2.9.5.G. Create an original tessellation.

2.9.5.H. Describe the relationship between the perimeter and area of triangles, quadrilaterals and circles.

2.9.5.I. Represent and use the concepts of line, point and plane.

2.9.5.J. Define the basic properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres and cylinders.

2.9.5.K. Analyze simple transformations of geometric figures and rotations of line segments.

2.9.5.L. Identify properties of geometric figures (e.g., parallel, perpendicular, similar, congruent, symmetrical).

PA.2.10.5. Trigonometry: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.10.5.A. Identify and compare parts of right triangles, including right angles, acute angles, hypotenuses, and legs.

PA.2.11.5. Concepts of Calculus: Pennsylvania's public schools shall teach, challenge and support every student to realize his or her maximum potential and to acquire the knowledge and skills needed to:

2.11.5.A. Make comparisons of numbers (e.g., more, less, same, least, most, greater than, less than).

2.11.5.B. Describe the relationship between rates of change and another variable (e.g., time, temperature).

2.11.5.C. Estimate areas and volumes of shapes and solids as the sums of areas of tiles and volumes of cubes.

2.11.5.D. Describe the relationship between rates of change and time.

2.11.5.E. Estimate areas and volumes as the sums of areas of tiles and volumes of cubes.

2.11.5.F. Describe the relationship between the size of the unit of measurement and the estimate of the areas and volumes.