Long Range Plans: 6th grade

• Mathematical Process Standards MPS 
• 1
• Problem Solving MPS.PS 
• 1a
• Make sense of problems and persevere in solving them strategically. MPS.PS.1 
• 2
• Representation & Communication MPS.RC 
• 2a
• Explain ideas using precise and contextually appropriate mathematical language, tools, and models. MPS.RC.1 
• 3
• Connections MPS.C 
• 3a
• Demonstrate a deep and flexible conceptual understanding of mathematical ideas, operations, and relationships while making real-world connections. MPS.C.1 
• 4
• Analyze & Justify MPS.AJ 
• 4a
•  Use critical thinking skills to reason both abstractly and quantitatively. MPS.AJ.1 
• 5
• Structure & Patterns MPS.SP 
• 5a
• Identify and apply regularity in repeated reasoning to make generalizations. MPS.SP.1 
• II
• Data, Probability, and Statistical Reasoning 6.DPSR 
• 1
• Analyze data sets to identify their statistical elements. 6.DPSR.1 
• 1a
• Identify the sample size for a numerical set of data in mathematical and real-world situations. 6.DPSR.1.1 
• 1b
• Create box plots to represent numerical data sets in mathematical and real-world situations. 6.DPSR.1.2 
• 1c
• Use the shape of the graph to determine whether median or mode best describes the data set. 6.DPSR.1.3 
• 1d
• Calculate and interpret the median, mode, range, interquartile range in mathematical and real-world situations. 6.DPSR.1.4 
• 2
• Calculate and interpret probability. 6.DPSR.2 
• 2a
• Given the probability of a random event, expressed as a number from 0 to 1, state the likelihood of the event occurring. 6.DPSR.2.1 
• 2b
• Find the probability of simple events in mathematical and real-world situations. Limit denominators to 2, 4, 5, 8, 10, 25, 50, and 100. 6.DPSR.2.2 
• 2c
• Given the probability of an event, identify and calculate the complement of that event. 6.DPSR.2.3 
• III
• Measurement, Geometry, and Spatial Reasoning 6.MGSR 
• 1
• Determine the measurements of geometric figures. 6.MGSR.1 
• 1a
• Find the area of a triangle, square, rectangle, parallelogram, and trapezoid. 6.MGSR.1.1 
• 1b
• Create nets to represent three-dimensional shapes. 6.MGSR.1.2 
• 1c
• Calculate the surface area of rectangular prisms, right triangular prisms, rectangular pyramids, and right triangular pyramids using two-dimensional nets. 6.MGSR.1.3 
• 1d
• Find the area of composite figures by decomposing them into triangles and rectangles to solve mathematical and real-world situations. 6.MGSR.1.4 
• 1e
• Calculate the volume of a right rectangular prism using the formula (V = Bh) in mathematical and real-world situations. 6.MGSR.1.5 
• 2
• Determine angle and/or side relationships. 6.MGSR.2 
• 2a
• Determine if two angles are complementary or supplementary. 6.MGSR.2.1 
• 2b
• Determine the measure of angles using a protractor. 6.MGSR.2.2 
• 3
• Graph on the coordinate plane. 6.MGSR.3 
• 3a
• Plot ordered pairs in all four quadrants and identify points on a graph by writing ordered pairs. 6.MGSR.3.1 
• 3b
• Graph a polygon on a coordinate plane given the coordinates of the vertices. 6.MGSR.3.2 
• IV
• Numerical Reasoning 6.NR 
• 1
• Translate among multiple representations of rational numbers. 6.NR.1 
• 1a
• Convert positive rational numbers into equivalent forms among terminating decimals, fractions (including mixed numbers), and percentages. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200. 6.NR.1.1 
• 2
• Utilize rational numbers in mathematical and real-world situations. 6.NR.2 
• 2a
• Compare two positive rational numbers and write statements using the symbols for is equal to (=), is not equal to (≠), is less than (<), and/or is greater than (>) in mathematical and real-world situations. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200. 6.NR.2.1 
• 2b
• Sort a set of positive rational numbers in ascending and/or descending order in mathematical and real-world situations. Limit sets to no more than 5 numbers. Limit fractions to denominators of 2, 4, 5, 8, 10, 20, 25, 50, 100, and 200. 6.NR.2.2 
• 2c
• Represent quantities with integers in realworld situations and explain the meaning of zero. 6.NR.2.3 
• 2d
• Identify and compare the opposite value and absolute value of positive and negative rational numbers. 6.NR.2.4 
• V
• Patterns, Algebra, and Functional Reasoning 6.PAFR 
• 1
• Use tables, graphs, verbal descriptions, or equations to represent a function. 6.PAFR.1 
• 1a
• Use tables, graphs, verbal descriptions, and equations to represent the relationship between independent and dependent variables of functions. 6.PAFR.1.1 
• 1b
• Identify the independent and dependent variable of a function in mathematical and real-world situations. 6.PAFR.1.2 
• 2
• . Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities. 6.PAFR.2 
• 2a
• Identify parts of an algebraic expression using the mathematical terms sum, difference, term, variable, product, factor, quotient, coefficient, and constant. 6.PAFR.2.1 
• 2b
• Write and evaluate numerical expressions containing powers. Limit to positive whole number bases and positive whole number exponents. 6.PAFR.2.2 
• 2c
• Evaluate numerical expressions with positive whole number bases and positive whole number exponents using the Order of Operations. 6.PAFR.2.3 
• 2d
• Write and evaluate expressions using variables to represent quantities in mathematical and real-world situations. 6.PAFR.2.4 
• 2e
• Write and solve one-step equations and inequalities with one variable involving positive rational numbers in mathematical and real-world situations. 6.PAFR.2.5 
• 2f
• Interpret the concept of a ratio as the relationship between two quantities, including part-to-part and part-to-whole. 6.PAFR.2.6 
• 2g
• Explain the relationship between ratios and rates, including unit rates. 6.PAFR.2.7 
• 2h
• Solve ratio and rate problems in real-world situations. 6.PAFR.2.8 
• 2i
• Use one-step dimensional analysis to convert units within the metric or customary systems. 6.PAFR.2.9 
• 3
• Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions. 6.PAFR.3 
• 3a
• Represent the solutions of inequalities on a number line and explain that the solution set may contain an infinite number of solutions. Limited to the symbols for is less than (<) and is greater than (>). 6.PAFR.3.1 
• 3b
• Identify the multiplicative inverse of a number and multiply multiplicative inverses to find their product is equal to 1. 6.PAFR.3.2 
• 3c
• Identify the additive inverse of a number and add additive inverses to find their sum is equal to zero. 6.PAFR.3.3 
• 3d
• Apply the properties of operations to create equivalent algebraic expressions and justify the properties used. Limit properties to the Identity, Inverse, Commutative, Associative, and Distributive Properties.  6.PAFR.3.4 
• 3e
• Add, subtract, multiply, and divide integers in mathematical and real-world situations.  6.PAFR.3.5 
• 3f
• Add, subtract, multiply, and divide positive fractions, including mixed numbers in mathematical and real-world situations.  6.PAFR.3.6 
• 3g
• Add, subtract, multiply, and divide multidigit positive decimals, up to the thousandths place, to solve problems in mathematical and real-world situations.  6.PAFR.3.7 

7th Grade:

• Analyze data sets to identify their statistical elements.       7.DPSR.1 
• Create stem-and-leaf plots to represent numerical data sets in mathematical and real-world situations.  7.DPSR.1.1 
• Use the shape of the graph to select the measure of center (mean, median, or mode) that best describes the data set.  7.DPSR.1.2 
• Calculate and interpret the measures of center (mean, median, mode) and spread (mean absolute deviation, interquartile range, range) in mathematical and real world situations.  7.DPSR.1.3 
• Create histograms to represent data sets and interpret histograms to answer questions or draw conclusions about data sets.  7.DPSR.1.4  
• Calculate and interpret probability.       7.DPSR.2 
• Identify the sample space for a simple event.  7.DPSR.2.1  
• Calculate and interpret the theoretical probability of a simple random event.  7.DPSR.2.2 
• Calculate and interpret the experimental probability of a random event related to a simple experiment. 7.DPSR.2.3  
• Compare and contrast the experimental and theoretical probabilities for a simple experiment.  7.DPSR.2.4  
• Determine the measurements of geometric figures.       7.MGSR.1 
• Identify the parts of a circle. Limit the parts to center, radius, diameter, and chord.  7.MGSR.1.1 
• Describe the relationship between the radius, diameter, and circumference of a circle.  7.MGSR.1.2 
• Solve mathematical and real-world situations involving circumference or area of circles. 7.MGSR.1.3 
• Determine if three given side lengths can form a triangle using the Triangle Inequality Theorem.  7.MGSR.1.4 
• In mathematical and real-world situations, find the volume of right prisms and right pyramids having triangular or quadrilateral bases.  7.MGSR.1.5 
• In mathematical and real-world situations, find the surface area of right prisms and right pyramids having triangular or quadrilateral bases. 7.MGSR.1.6 
• Determine angle relationships.       7.MGSR.2 
• Determine the measure of the third angle given the measure of the other two angles of a triangle using the Triangle Sum Theorem.  7.MGSR.2.1 
• Solve mathematical and real-world situations involving dimensions and areas of geometric figures including scale drawings and scale factors.  7.MGSR.2.2 
• Identify the relationships and measures among angles formed by two intersecting lines, given the measure of one angle. Limit to supplementary, complementary, vertical, and adjacent relationships.  7.MGSR.2.3 
• Write and solve equations to solve mathematical and real-world situations involving the relationships among angles formed by two intersecting lines. Limit to supplementary, complementary, vertical, and adjacent relationships.  7.MGSR.2.4 
• Graph on the coordinate plane.       7.MGSR.3 
• Find distances between ordered pairs on the coordinate plane, limited to the same x-coordinate or the same y-coordinate. 7.MGSR.3.1 
• Translate among multiple representations of rational numbers.       7.NR.1 
• Convert rational numbers into equivalent forms among fractions (including mixed numbers), decimals, and percentages. Exclude the conversion of repeating decimals to fractions.  7.NR.1.1 
• Utilize rational numbers in mathematical and real-world situations.       7.NR.2 
• Compare two rational numbers and write statements using is equal to (=), is not equal to (≠), is less than (<), is greater than (>), is greater than or equal to (≥), and/or is less than or equal to (≤) in mathematical and real-world situations.  7.NR.2.1 
• Use tables, graphs, verbal descriptions, or equations to represent a function.       7.PAFR.1 
• Apply proportional reasoning to solve problems in mathematical and real-world situations involving ratios and percentages.  7.PAFR.1.1 
• Create a model with functions that address a proportional relationship in real world situations.  7.PAFR.1.2 
• Identify the constant of proportionality within proportional relationships.  7.PAFR.1.3 
• Write, simplify, and solve algebraic expressions, equations, and inequalities.        7.PAFR.2 
• Write and solve multi-step equations and inequalities in one variable involving rational numbers in mathematical and real-world situations.  7.PAFR.2.1 
• Write and evaluate expressions in one variable that model mathematical and real world situations.  7.PAFR.2.2 
• Compute unit rates, including those involving complex fractions with like or different units.  7.PAFR.2.3 
• Use dimensional analysis to convert units between metric and customary systems.  7.PAFR.2.4 
• Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions.        7.PAFR.3 
• Simplify numerical expressions that include integer exponents using the laws of exponents: the Product of Powers, Quotient of Powers, Power of a Power, Power of a Product, Power of a Quotient, Zero Power, and Negative Exponent. 7.PAFR.3.1 
• Identify linear expressions that are equivalent.  7.PAFR.3.2 
• Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.  7.PAFR.3.3 
• Factor linear expressions with integer coefficients using the greatest common factor (GCF).  7.PAFR.3.4 
• Apply all operations with rational numbers to solve problems in mathematical and real-world situations. 7.PAFR.3.5 

8th Grade:

• Mathematical Process Standards MPS 
• 1
• Problem Solving MPS.PS 
• 1a
•  Make sense of problems and persevere in solving them strategically. MPS.PS.1 
• 2
• Representation & Communication MPS.RC 
• 2a
• Explain ideas using precise and contextually appropriate mathematical language, tools, and models. MPS.RC.1 
• 3
• Connections MPS.C 
• 3a
• Demonstrate a deep and flexible conceptual understanding of mathematical ideas, operations, and relationships while making real-world connections. MPS.C.1 
• 4
• Analyze & Justify MPS.AJ 
• 4a
•  Use critical thinking skills to reason both abstractly and quantitatively. MPS.AJ.1 
• 5
• Structure & Patterns MPS.SP  
• 5a
•  Identify and apply regularity in repeated reasoning to make generalizations. MPS.SP.1  
• II
• Data, Probability, and Statistical Reasoning 8.DPSR 
• 1
• Analyze data sets to identify their statistical elements. 8.DPSR.1 
• 1a
• Create and analyze scatter plots to represent numerical data sets in mathematical and real-world situations. 8.DPSR.1.1 
• 1b
• Draw inferences about data sets from two populations using the shape of the distribution, measures of center, and measures of variability. Limit measures to mean, median, mode, range, mean absolute deviation, and interquartile range. 8.DPSR.1.2 
• 1c
• Describe how adding and deleting data throughout the data set can affect the mean, median, mode, and distribution of the data set. 8.DPSR.1.3 
• 1d
• For two data sets (numerical or graphical), compare and interpret the centers, spreads, and overlap of data to draw inferences about data in mathematical and real-world situations. Limit displays to double line graphs, back-to-back stem-and-leaf plots, and double box plots. 8.DPSR.1.4 
• 2
• Calculate and interpret probability. 8.DPSR.2 
• 2a
• Determine the sample space for a compound event. 8.DPSR.2.1 
• 2b
• Calculate and interpret the probability of compound independent and dependent events. 8.DPSR.2.3 
• III
• Measurement, Geometry, and Spatial Reasoning 8.MGSR 
• 1
• Determine the measurements of geometric figures. 8.MGSR.1 
• 1a
• Given the geometric formulas, find the volume of cones, cylinders, and spheres in mathematical and real-world situations. 8.MGSR.1.1 
• 1b
• Find the distance between any two points in the coordinate plane using the Pythagorean Theorem. 8.MGSR.1.2 
• 1c
• Given the Pythagorean Theorem, determine unknown side lengths in right triangles in mathematical and real-world situations. 8.MGSR.1.3 
• 1d
• Determine if a given set of sides forms a right triangle. 8.MGSR.1.4 
• 2
• Determine angle and/or side relationships. 8.MGSR.2 
• 2a
• Determine missing angle measurements created when parallel lines are cut by a transversal. 8.MGSR.2.1 
• 2b
• Determine if two-dimensional figures are congruent or similar. 8.MGSR.2.2 
• 2c
• Identify the congruent corresponding angles of similar polygons. 8.MGSR.2.3 
• 2d
• Discover and apply the Exterior Angle Theorem of triangles to find a missing angle. 8.MGSR.2.4 
• 2e
• Apply proportional reasoning to find the missing side lengths of two similar figures. 8.MGSR.2.5 
• 3
• Graph on a coordinate plane. 8.MGSR.3 
• 1a
• Identify the transformation as a rotation, reflection, and/or translation. Limit rotations to multiples of 90 degrees centered on the origin. 8.MGSR.3.1 
• 1b
• Identify congruent angles and congruent line segments of a pre-image and its image. 8.MGSR.3.2 
• 1c
• Translate geometric figures vertically and/or horizontally. 8.MGSR.3.3 
• 1d
• Reflect geometric figures with respect to the x-axis and/or y-axis. 8.MGSR.3.4 
• 1e
• Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin in a coordinate plane.Create a dilation using a given scale factor and describe the effect of a dilation. 8.MGSR.3.5 
• 1f
• Create a dilation using a given scale factor and describe the effect of a dilation. 8.MGSR.3.6 
• 1g
• Describe the effect of a series of transformations, including dilations, translations, rotations, and reflections, on two-dimensional figures using coordinates on the coordinate plane. 8.MGSR.3.7 
• IV
• Numerical Reasoning 8.NR 
• 1
• Translate among multiple representations of rational numbers. 8.NR.1 
• 1a
• Convert any form of a rational number to any other form including fractions (mixed numbers), decimals, and percentages. 8.NR.1.1 
• 2
• Utilize real numbers in mathematical and real-world situations. 8.NR.2 
• 2a
• Compare real numbers and write statements using is equal to (=), is not equal to (≠), is less than (<), is greater than (>), is greater than or equal to (≥), or is less than or equal to (≤). 8.NR.2.1 
• 2b
• Classify and order the subsets of real numbers in the number system including natural, whole, integer, rational, and irrational numbers. 8.NR.2.2 
• V
• Patterns, Algebra, and Functional Reasoning 8.PAFR 
• 1
• Determine if a table, graph, verbal description, or equation represents a function and describe its characteristics. 8.PAFR.1 
• 1a
• Determine if a table, graph, verbal description, or equation represents a function and describe its characteristics. 8.PAFR.1.1 
• 1b
• Identify and describe the constant rate of change and the y-intercept of a linear function. 8.PAFR.1.2 
• 1c
• Determine if a graph, table, mapping, or verbal description is a function (linear or nonlinear) or not a function. 8.PAFR.1.3 
• 1d
• Describe the key features of given functions, including domain, range, intervals of increasing or decreasing, constant, discrete, continuous, and intercepts. 8.PAFR.1.4 
• 1e
• Use multiple representations including mappings, tables, graphs, verbal description, and equations (only when linear) of two functions to compare the functions and draw conclusions. 8.PAFR.1.5 
• 1f
• Translate among the multiple representations, including mappings, tables, graphs, verbal description, and equations (only when linear) of a function. 8.PAFR.1.6 
• 2
• Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities. 8.PAFR.2 
• 2a
• Solve multi-step one-variable equations and inequalities with variables on both sides with rational coefficients. 8.PAFR.2.1 
• 2b
• Describe single-variable equations as having one solution, no solution, or an infinite number of solutions. 8.PAFR.2.2 
• 2c
• Identify the rate of change for a linear function as the slope of the line. 8.PAFR.2.3 
• 2d
• Explain why the slope, m, is the same between any two distinct points on a linear graph. 8.PAFR.2.4 
• 2e
• Given a table or a graph, identify the slope and the y-intercept of a line and write a linear equation to express that line. 8.PAFR.2.5 
• 3
• Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equivalent expressions. 8.PAFR.3 
• 3a
• Analyze patterns of perfect squares and perfect cubes to evaluate square roots and cube roots. Limit to square roots less than or equal to 400 and cube roots less than or equal to 1,000. 8.PAFR.3.1 
• 3b
• Approximate non-perfect square roots and cube roots to nearest tenth. Limit to square roots less than or equal to 400 and cube roots less than or equal to 1,000. 8.PAFR.3.2 
• 3c
• Apply laws of exponents to simplify algebraic expressions involving no more than three variables and integer exponents. 8.PAFR.3.3