8TH GRADE MATH TOOL

EIGHTH GRADE MATH TOOL

8TH GRADE INTRODUCTION

In Grade 8, instructional time should focus on three critical areas:

(1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations

(2) grasping the concept of a function and using functions to describe quantitative relationships(3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the

Pythagorean Theorem.

1. Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m·A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.

Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

2. Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.

3. Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.

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EIGHTH GRADE MATH TOOL

The Number System 8.NS.1 Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Weak match to: SD.9-12.N.1.1 (Comprehension) Students are able to identify multiple representations of a real number. -1 to -4

I can classify a number as rational or irrational based on its decimal expansion.

I can convert a repeating decimal into a rational number.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

In what ways can rational numbers be useful?Rational numbers can be represented in multiple ways and are useful when examining situations involving numbers that are not whole.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyRational number, irrational number

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EIGHTH GRADE MATH TOOL

The Number System 8.NS.2 Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^2). For example, by truncating the decimal expansion of √2 (square root of 2), show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Weak match to:SD.9-12.N.1.2A (Application) Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure. -1 to -4

I can use reasoning to determine between which two consecutive whole numbers a square root will fall (e.g., I can reason that √39 is 6 and 7, because it is between √36 and √49).

I can plot the estimated value of an irrational number on a number line.

I can estimate the value of an irrational number by rounding to a specific place value.

I can use estimated values to compare two or more irrational numbers.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

In what ways can rational numbers be useful?Rational numbers can be represented in multiple ways and are useful when examining situations involving numbers that are not whole.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyRational number, irrational number

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.1 Cluster: Work with radicals and integer exponents.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

For example, 3^2 × 3^(–5) = 3^(–3) = 1/(3^3) = 1/27.

Weak match to:SD.9-12.N.2.1 (Comprehension) Students are able to add, subtract, multiply, and divide real numbers including integral exponents. -1 to -4

I can determine the properties of integer exponents by exploring patterns and applying my understanding of properties of whole number exponents.

I can use the properties of integer exponents to simplify expressions.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyInteger, exponent

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.2 Cluster: Work with radicals and integer exponents

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.2. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can recognize taking a square root as the inverse of squaring a number.

I can recognize taking a cube root as the inverse of cubing a number.

I can evaluate the square root of a perfect square.

I can evaluate the cube root of a perfect cube.

I can justify that the square root of a non-perfect square will be irrational.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyCube, square, cube root, square root, radical, perfect square, perfect cube, irrational

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.3 Cluster: Work with radicals and integer exponents.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

For example, estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and determine that the world population is more than 20 times larger.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can write an estimation of a large quantity by expressing it as the product of a single-digit number and a positive power of ten.

I can write an estimation of a very small quantity by expressing it as the product of a single-digit number and a negative power of ten.

I can compare quantities written as the product of a single-digit number and a power of ten by stating their multiplicative relationships.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyPower of ten, multiplicative relationships

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.4 Cluster: Work with radicals and integer exponents.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Weak match to:SD.9-12.N.1.2 (Comprehension) Students are able to apply the concept of place value, magnitude, and relative magnitude of real numbers. -1 to -4

I can add and subtract two numbers written in scientific notation.

I can multiply and divide two numbers written in scientific notation.

I can select the appropriate units for measuring derived measurements when comparing quantities written in scientific notation.

I can identify and interpret the various ways scientific notation is displayed on calculators and through computer software.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyScientific notation, power of ten, derived measurements

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.5 Cluster: Understand the connections between proportional relationships, lines, and linear equations.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Weak match to:SD.8.A.3.1 (Comprehension) Students are able to describe and determine linear relationships.

SD.9-12.A.3.1 (Application) Students are able to create linear models to represent problem situations. -1 to -4

I can graph a proportional relationship in the coordinate plane.

I can interpret the unit rate of a proportional relationship as the slope of the graph.

I can justify that the graph of a proportional relationship will always intersect the origin (0,0) of the graph.

I can use a graph, a table, or an equation to determine the unit rate of a proportional relationship and use the unit rate to make comparisons between various proportional relationships.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyProportional relationships, coordinate plane, unit rate, slope

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.6 Cluster: Understand the connections between proportional relationships, lines, and linear equations.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can create right triangles by drawing a horizontal line segment and a vertical line segment from any two points on a non-vertical line in the coordinate plane.

I can justify that these right triangles are similar by comparing the ratios of lengths of the corresponding legs.

I can justify that since the triangles are similar, the ratios of all corresponding hypotenuses, representing the slope of the line, will be equivalent.

I can justify that an equation in the form y=mx will represent the graph of a proportional relationship with a slope of m and a y-intercept of 0.

I can justify that an equation in the form y=mx + b represents the graph of a linear relationship with a slope of m and a y-intercept of b.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving

them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyRight triangle, leg, hypotenuse, similar triangles, ratio, slope, proportional relationship, y-intercept

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.7 Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.7 Solve linear equations in one variable.

Excellent match to:SD.6.A.2.1 (Application) Students are able to write and solve one-step 1st degree equations, with one variable, involving inverse operations using the set of whole numbers. +2

SD.7.A.2.1 (Application) Students are able to write and solve one-step 1st degree equations, with one variable, using the set of integers and inequalities, with one variable, using the set of whole numbers. +1

SD.8.A.2.1 (Application) Students are able to write and solve two-step 1st degree equations, with one variable, and one-step inequalities, with one variable, using the set of integers.

I can use the properties of real numbers to determine the solution of a linear equation.

I can simplify a linear equation by using the distributive property and/or combining like terms.

I can give examples of linear equations with one solution, infinitely many solutions, or no solution.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear equation, equivalent equations, ratio, like terms, rational number, coefficient, solution

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.7a-8.EE.7b Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Weak match to: SD.8.A.4.2 (Analysis) Students are able to describe and represent relations using tables, graphs, and rules.

8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Weak match to:SD.8.A.1.1 (Application) Students are able to use properties to expand, combine, and simplify 1st degree algebraic expressions with the set of integers.SD.9-12.A.1.1A (Application) Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers. -1 to -4

I can use the properties of real numbers to determine the solution of a linear equation.

I can simplify a linear equation by using the distributive property and/or combining like terms.

I can give examples of linear equations with one solution, infinitely many solutions, or no solution.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Quest/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning of

others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear equation, equivalent equations, ratio, like terms, rational number, coefficient, solution

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.8 - 8.EE.8 a Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.8 Analyze and solve pairs of simultaneous linear equations.

Weak match to: SD.9-12.A.2.1A (Analysis) Students are able to determine solutions of quadratic equations. -1 to -4

8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can explain how a line represents the infinite numbers of solutions to a linear equation with two variables.

I can explain how the point(s) of intersection of two graphs will represent the solution to the system of two linear equations because that/those point(s) are solutions to both equations.

I can use mathematical reasoning to solve simple systems of linear equations.

I can solve real-world problems and mathematical problems dealing with systems of linear equations and interpret the solution in the context of the problem.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear equation, system of linear equations (also simultaneous linear equations), intersection

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EIGHTH GRADE MATH TOOL

Expressions and Equations 8.EE.8b - 8.EE.8c Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Weak match to: SD.9-12.A.2.2A (Application) Students are able to determine the solution of systems of equations and systems of inequalities. -1 to -4

8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can use algebraic reasoning (simple substitution) and the properties of real numbers to solve a system of linear equations.

I can use the graphs of two linear equations to estimate the solution of the system.

I can use mathematical reasoning to solve simple systems of linear equations.

I can solve real-world problems and mathematical problems dealing with systems of linear equations and interpret the solution in the context of the problem.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?Algebraic expressions and equations are used to model real-life problems and represent quantitative relationships, so that the numbers and symbols can be mindfully manipulated to reach a solution or make sense of the quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear equation, system of linear equations (also simultaneous linear equations), intersection

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EIGHTH GRADE MATH TOOL

Functions 8.F.1 Cluster: Define, evaluate, and compare functions.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

*Function notation is not required in Grade 8.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can explain that a function represents the relationship between an input and an output where the output depends on the input; therefore, there can be only one output for each input.

I can show the relationship between the inputs and outputs of a function by graphing them as ordered pairs on a coordinate grid.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How are functions useful?The characteristics of functions and their representations are useful in making sense of patterns and solving problems involving quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyFunction, input, output, coordinate grid

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EIGHTH GRADE MATH TOOL

Functions 8.F.2 Cluster: Define, evaluate, and compare functions.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can determine the properties of a function written in algebraic form (e.g., rate of change, meaning of y-intercept, linear, non-linear).

I can determine the properties of a function when given inputs and outputs in a table.

I can determine the properties of a function represented as a graph.

I can determine the properties of a function when given the situation verbally.

I can compare the properties of two functions that are represented differently (e.g., as an equation, in a table, graphically, or a verbal representation).

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How are functions useful?The characteristics of functions and their representations are useful in making sense of patterns and solving problems involving quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyFunction, linear function, rate of change

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EIGHTH GRADE MATH TOOL

Functions 8.F.3 Cluster: Define, evaluate, and compare functions.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can explain why the equation y=mx + b represents a linear function and interpret the slope and y-intercept in relation to the function.

I can give examples of relationships that are non-linear functions.

I can analyze the rate of change between input and output values to determine if function is linear or non-linear.

I can create a table of values that can be defined as a non-linear function.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How are functions useful?The characteristics of functions and their representations are useful in making sense of patterns and solving problems involving quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear function

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EIGHTH GRADE MATH TOOL

Functions 8.F.4 Cluster: Use functions to model relationships between quantities.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can write a linear function that models a given situation given verbally as a table of x- and y- values or as a graph.

I can define the initial value of the function in relation to the situation.

I can define the rate of change in relation to the situation.

I can define the y- intercept in relation to the situation.

I can explain any constraints on the domain in relation to the situation.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving

them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How are functions useful?The characteristics of functions and their representations are useful in making sense of patterns and solving problems involving quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear function, rate of change, domain

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EIGHTH GRADE MATH TOOL

Functions 8.F.5 Cluster: Use functions to model relationships between quantities.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can match the graph of function to a given situation.

I can write a story that describes the functional relationship between two variables depicted in the graph.

I can create a graph of function that describes the relationship between two variables.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How are functions useful?The characteristics of functions and their representations are useful in making sense of patterns and solving problems involving quantitative relationships.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyIncreasing, decreasing, linear, nonlinear

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EIGHTH GRADE MATH TOOL

Geometry 8.G.1 - 8.G.1 a- 8.G.1 b- 8.G.1 c Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.1 Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can verify-by measuring and comparing lengths, angle measures, and parallelism of a figure and its image-that after a figure has been translated, corresponding lines and line segments remain the same length, corresponding angles have the same measure, and corresponding parallel lines remain parallel.

I can verify-by measuring and comparing lengths, angle measures, and parallelism of a figure and its image-that after a figure has been reflected, corresponding lines and line segments remain the same length, corresponding angles have the same measure, and corresponding parallel lines remain parallel.

I can verify-by measuring and comparing lengths, angle measures, and parallelism of a figure and its image-that after a figure has been rotated, corresponding lines and line segments remain the same length, corresponding angles have the same measure, and corresponding parallel lines remain parallel.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving

them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the

reasoning of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated

reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyTransformation, translation, reflection, rotation, parallel line

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EIGHTH GRADE MATH TOOL

Geometry 8.G.2 Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can explain how transformations can be used to prove that two figures are congruent.

I can perform a series of transformations (reflections, rotations, and/or translations) to prove or disprove that two given figures are congruent.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyCongruent, transformation, reflection, rotation, translation

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EIGHTH GRADE MATH TOOL

Geometry 8.G.3 Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can describe the changes occurring to the x- and y- coordinates of a figure after a translation.

I can describe the changes occurring to the x- and y- coordinates of a figure after a reflection.

I can describe the changes occurring to the x- and y- coordinates of a figure after a rotation.

I can describe the changes occurring to the x- and y- coordinates of a figure after dilation.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyTransformation, translation, reflection, rotation, dilation

Template created by Region 1 ESA Page 22 of 32

EIGHTH GRADE MATH TOOL

Geometry 8.G.4 Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can explain how transformations can be used to prove that two figures are similar.

I can describe a sequence of transformations to prove or disprove that two given figures are similar.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularySimilar, transformation, reflection, rotation, translation, dilation

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EIGHTH GRADE MATH TOOL

Geometry 8.G.5 Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.

Weak match to:SD.9-12.G.1.2 (Application) Students are able to identify and apply relationships among triangles. -1 to -4

SD.9-12.G.1.1A (Evaluation) Students are able to justify properties of geometric figures. -1 to -4

I can informally prove that the sum of any triangle’s interior angles will have the same measure as a straight angle (i.e., by tearing off the three corners of a triangle and arranging them to form a 180⁰ straight angle).

I can informally prove that the sum of any polygon’s exterior angles will be 360-degrees.

I can make conjectures regarding the relationships and measurements of angles created when two parallel lines are cut by a transversal.

I can apply proven relationships to establish minimal properties to justify similarity.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyInterior angle, exterior angle, parallel lines, transversal, similar

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EIGHTH GRADE MATH TOOL

Geometry 8.G.6 Cluster: Understand and apply the Pythagorean Theorem.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can use visual models to demonstrate the relationship of the three side lengths of any right triangle.

I can use algebraic reasoning to relate the visual model to the Pythagorean Theorem.

I can use the Pythagorean Theorem to determine if a given triangle is a right triangle.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyPythagorean Theorem, leg, hypotenuse, converse

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EIGHTH GRADE MATH TOOL

Geometry 8.G.7 Cluster: Understand and apply the Pythagorean Theorem.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Weak match to:SD.8.G.1.2 (Application) Students, when given any two sides of an illustrated right triangle, are able to use the Pythagorean Theorem to find the third side.

I can apply the Pythagorean Theorem to find an unknown side length of a right triangle.

I can draw a diagram and use the Pythagorean Theorem to solve real-world problems involving right triangles.

I can draw a diagram to find right triangles in a three- dimensional figure and use the Pythagorean Theorem to calculate various dimensions.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyPythagorean Theorem, leg, hypotenuse

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EIGHTH GRADE MATH TOOL

Geometry 8.G.8 Cluster: Understand and apply the Pythagorean Theorem.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Weak match to:SD.9-12.G.2.1 (Analysis) Students are able to recognize the relationship between a three-dimensional figure and its two-dimensional representation. -1 to -4

I can connect any two points on a coordinate grid to a third point so that the three points form a right triangle.

I can use the right triangle and the Pythagorean Theorem to find the distance between the original two points.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyPythagorean Theorem, leg, hypotenuse

Template created by Region 1 ESA Page 27 of 32

EIGHTH GRADE MATH TOOL

Geometry 8.G.9 Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.G.9 Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Weak match to:SD.9-12.G.1.4A (Analysis) Students are able to use formulas for surface area and volume to solve problems involving three-dimensional figures. -1 to -4

I can describe the similarity between finding volume of a cylinder and the volume of a right prism.

I can recall the formula to find the volume of a cylinder.

I can informally prove the relationship between the volume of a cylinder and the volume of a cone with the same base.

I can recall the formula to find the volume of a cone.

I can informally prove the relationship between the volume of a sphere and the volume of a circumscribed cylinder.

I can recall the formula to find the volume of a sphere.

I can use the formulas to find the volume of cylinders, cones, and spheres.

I can solve real-world problems involving the volume of cylinders, cones, and spheres.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How does geometry better describe objects?Geometric attributes (such as shapes, lines, angles, figures, and planes) provide descriptive information about an object’s properties and position in place and support visualization and problem solving.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyCylinder, cone, sphere, volume, right prism, circumscribed cylinder

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EIGHTH GRADE MATH TOOL

Statistics and Probability 8.SP.1 Cluster: Investigate patterns of association in bivariate data.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Good match to:SD.8.S.1.2 (Application) Students are able to use a variety of visual representations to display data to make comparisons and predictions.

SD.9-12.S.1.2A (Evaluation) Students are able to analyze and evaluate graphical displays of data. -1 to -4

SD.9-12.S.1.5A (Application) Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions. -1 to -4

I can plot ordered pairs on a coordinate grid representing the relationship between two data sets.

I can describe patterns in the plotted points such as clustering, outliers, positive or negative association, and linear or nonlinear association and describe the pattern in the context of the measurement data.

I can interpret the patterns of association in the context of the data sample.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How is probability used to make informed decisions about uncertain events?The rules of probability can lead to more valid and reliable predictions about the likelihood of an event occurring.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyScatter plot, bivariate, clustering, outliers, positive association, negative association, linear association, nonlinear association

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EIGHTH GRADE MATH TOOL

Statistics and Probability 8.SP.2 Cluster: 2 Investigate patterns of association in bivariate data.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.SP. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Good match to:SD.9-12.S.1.3 (Analysis) Represent a set of data in a variety of graphical forms and draw conclusions. -1 to -4

SD.9-12.S.1.5A (Application) Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions. -1 to -4

I can recognize whether or not data plotted on a scatter plot have a linear association.

I can draw a straight trend line to approximate the linear relationship between the plotted points of two data sets.

I can make inferences regarding the reliability of the trend line by noting the closeness of the data points to the line.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How is probability used to make informed decisions about uncertain events?The rules of probability can lead to more valid and reliable predictions about the likelihood of an event occurring.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyScatter plot, linear association, trend line, line of best fit

Template created by Region 1 ESA Page 30 of 32

EIGHTH GRADE MATH TOOL

Statistics and Probability 8.SP.3 Cluster: Investigate patterns of association in bivariate data.

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can determine the equation of the trend line that approximates the linear relationship between the plotted points of two data sets.

I can interpret the y-intercept of the equation in the context of the collected data.

I can interpret the slope of the equation in the context of the collected data.

I can use the equation of the trend line to summarize the given data and make predictions regarding additional data points.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How is probability used to make informed decisions about uncertain events?The rules of probability can lead to more valid and reliable predictions about the likelihood of an event occurring.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyLinear model, bivariate, slope, y-intercept, trend line, line of best fit

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EIGHTH GRADE MATH TOOL

Statistics and Probability 8.SP.4 Cluster: Investigate patterns of association in bivariate data

Standard Suggested Learning Targets Directly Aligned

Somewhat Aligned

NotAligned

8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

CC STANDARD NOT ADDRESSED IN SD CONTENT STANDARDS

I can create a two-way table to record the frequencies of bivariate categorical values.

I can determine the relative frequencies for rows and/or columns of a two-way table.

I can use the relative frequencies and context of the problem to describe possible associations between the two sets of data.

Content/Skills Included in Textbook(Include page numbers and comments)

Standards of Mathematical Practice (SMP’s) Essential Questions/ Enduring Understandings Assessment #1 Make sense of problems and persevere in solving them. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning

of others. #4 Model with mathematics. #5 Use appropriate tools strategically. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning.

How is probability used to make informed decisions about uncertain events?The rules of probability can lead to more valid and reliable predictions about the likelihood of an event occurring.

Assessments align to suggested learning targets.Directly Aligned

Somewhat Aligned

NotAligned

Check all assessment types that address this standard Drill and practice Multiple choice Short answer (written) Performance (verbal explanation) Product / Project

VocabularyBivariate, categorical data, two-way table, frequency, relative frequency

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