Pennsylvania State Standards for Mathematics: Grade 6

PA.2.1.8. 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:

2.1.8.A. Represent and use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, exponents, scientific notation, square roots).

2.1.8.B. Simplify numerical expressions involving exponents, scientific notation and using order of operations.

2.1.8.C. Distinguish between and order rational and irrational numbers.

2.1.8.D. Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles.

2.1.8.E. Simplify and expand algebraic expressions using exponential forms.

2.1.8.F. Use the number line model to demonstrate integers and their applications.

2.1.8.G. Use the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations.

PA.2.2.8. 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:

2.2.8.A. Complete calculations by applying the order of operations.

2.2.8.B. Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.

2.2.8.C. Estimate the value of irrational numbers.

2.2.8.D. Estimate amount of tips and discounts using ratios, proportions and percents.

2.2.8.E. Determine the appropriateness of overestimating or underestimating in computation.

2.2.8.F. Identify the difference between exact value and approximation and determine which is appropriate for a given situation.

PA.2.3.8. 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:

2.3.8.A. Develop formulas and procedures for determining measurements (e.g., area, volume, distance).

2.3.8.B. Solve rate problems (e.g., rate x time = distance, principal x interest rate = interest).

2.3.8.C. Measure angles in degrees and determine relations of angles.

2.3.8.D. Estimate, use and describe measures of distance, rate, perimeter, area, volume, weight, mass and angles.

2.3.8.E. Describe how a change in linear dimension of an object affects its perimeter, area and volume.

2.3.8.F. Use scale measurements to interpret maps or drawings.

2.3.8.G. Create and use scale models.

PA.2.4.8. 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:

2.4.8.A. Make conjectures based on logical reasoning and test conjectures by using counter-examples.

2.4.8.B. Combine numeric relationships to arrive at a conclusion.

2.4.8.C. Use if...then statements to construct simple, valid arguments.

2.4.8.D. Construct, use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers.

2.4.8.E. Distinguish between inductive and deductive reasoning.

2.4.8.F. Use measurements and statistics to quantify issues (e.g., in family, consumer science situations).

PA.2.5.8. 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:

2.5.8.A. Invent, select, use and justify the appropriate methods, materials and strategies to solve problems.

2.5.8.B. Verify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams.

2.5.8.C. Justify strategies and defend approaches used and conclusions reached.

2.5.8.D. Determine pertinent information in problem situations and whether any further information is needed for solution.

PA.2.6.8. 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:

2.6.8.A. Compare and contrast different plots of data using values of mean, median, mode, quartiles and range.

2.6.8.B. Explain effects of sampling procedures and missing or incorrect information on reliability.

2.6.8.C. Fit a line to the scatter plot of two quantities and describe any correlation of the variables.

2.6.8.D. Design and carry out a random sampling procedure.

2.6.8.E. Analyze and display data in stem-and-leaf and box-and-whisker plots.

2.6.8.F. Use scientific and graphing calculators and computer spreadsheets to organize and analyze data.

2.6.8.G. Determine the validity of the sampling method described in studies published in local or national newspapers.

PA.2.7.8. 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:

2.7.8.A. Determine the number of combinations and permutations for an event.

2.7.8.B. Present the results of an experiment using visual representations (e.g., tables, charts, graphs).

2.7.8.C. Analyze predictions (e.g., election polls).

2.7.8.D. Compare and contrast results from observations and mathematical models.

2.7.8.E. Make valid inferences, predictions and arguments based on probability.

PA.2.8.8. 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:

2.8.8.A. Apply simple algebraic patterns to basic number theory and to spatial relations

2.8.8.B. Discover, describe and generalize patterns, including linear, exponential and simple quadratic relationships.

2.8.8.C. Create and interpret expressions, equations or inequalities that model problem situations.

2.8.8.D. Use concrete objects to model algebraic concepts.

2.8.8.E. Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy.

2.8.8.F. Solve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets.

2.8.8.G. Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules.

2.8.8.H. Graph a linear function from a rule or table.

2.8.8.I. Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions.

2.8.8.J. Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; explain how a change in one quantity determines another quantity in a functional relationship.

PA.2.9.8. 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:

2.9.8.A. Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software.

2.9.8.B. Draw, label, measure and list the properties of complementary, supplementary and vertical angles.

2.9.8.C. Classify familiar polygons as regular or irregular up to a decagon.

2.9.8.D. Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders.

2.9.8.E. Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles).

2.9.8.F. Distinguish between similar and congruent polygons.

2.9.8.G. Approximate the value of p (pi) through experimentation.

2.9.8.H. Use simple geometric figures (e.g., triangles, squares) to create, through rotation, transformational figures in three dimensions.

2.9.8.I. Generate transformations using computer software.

2.9.8.J. Analyze geometric patterns (e.g., tessellations, sequences of shapes) and develop descriptions of the patterns.

2.9.8.K. Analyze objects to determine whether they illustrate tessellations, symmetry, congruence, similarity and scale.

PA.2.10.8. 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:

2.10.8.A. Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships.

2.10.8.B. Solve problems requiring indirect measurement for lengths of sides of triangles.

PA.2.11.8. 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:

2.11.8.A. Analyze graphs of related quantities for minimum and maximum values and justify the findings.

2.11.8.B. Describe the concept of unit rate, ratio and slope in the context of rate of change.

2.11.8.C. Continue a pattern of numbers or objects that could be extended infinitely.