Overview of Math Standards


 Shon Neal
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1 Grade 8A Welcome to math curriculum design maps for Manhattan Ogden USD 383, striving to produce learners who are: Effective Communicators who clearly express ideas and effectively communicate with diverse audiences, Quality Producers who create intellectual, artistic and practical products which reflect high standards Complex Thinkers who identify, access, integrate, and use available resources Collaborative Workers who use effective leadership and group skills to develop positive relationships within diverse settings. Community Contributors who use time, energies and talents to improve the welfare of others SelfDirected Learners who create a positive vision for their future, set priorities and assume responsibility for their actions. Click here for more. Overview of Math Standards Teams of teachers and administrators comprised the pk12+ Vertical Alignment Team to draft the maps below. The full set of Kansas College and Career Standards (KCCRS) for Math, adopted in 2010, can be found here. To reach these standards, teachers use Math in Focus curriculum, resources, assessments and supplemented instructional interventions from additional websites and app for specific skills. Standards of Mathematical Practice 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. Click here for more. Additionally, educators strive to provide math instruction centered on: 1: Focus  Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards. 2: Coherence  Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations. 3: Fluency  Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions. 4: Deep Understanding  Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math. 5: Application  Students are expected to use math concepts and choose the appropriate strategy for application even when they are not prompted. 6: Dual Intensity  Students are practicing and understanding. There is more than a balance between these two things in the classroom both are occurring with intensity. Click here for more. 1
2 KCCRS Standards Vocabulary Essential Questions Resources I Can Learning Target Samples 1. Exponents Exponential Notation, The Product and the Quotient of Powers, The Power of a Power, The Power of a Product and the Power of a Quotient, Zero and Negative Exponents, Real World Problems: Squares and Cubes This should be a review to start the year. 1 The Number System 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. 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. Expressions and Equations 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.2: Use square root and cube root symbols to represent solutions to equations. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. exponential notation base power terminating decimal repeating decimal irrational number integer exponent square root cube root radical How do radicals and exponents influence one s understanding of other content, such as geometry and science? When are radicals and integer exponents used in expressions and equations to tell a story or represent an authentic situation in life? How can you use exponential notation to represent repeated multiplication of the same factor? 8.NS.1 additional tools/resources listed on page 16. Transition Guide Skill 1 & 2 Purple Textbook A pages 3 & 98 8.NS.2 additional tools/resources listed on page 19. Transition Guide Skill 3 8.EE EE NS.1 I can understand that rational and irrational numbers have decimal expansions. I can convert a repeating decimal into a rational number. 8.NS.2 I can approximate the location of irrational numbers on a number line. 8.EE.1 I can understand and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.2 I can solve problems using square root and cube roots symbols and know that the 2 is irrational.
3 2. Scientific Notation Understanding Scientific Notation, Adding and Subtracting in Scientific Notation, Multiplying and Dividing in Scientific Notation 3. Algebraic Solving Linear Equations with One Variable, Identifying the Number of Solutions to a Linear Equation, Understanding with Two Variables, 2 Expressions and Equations 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. 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. 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. Interpret scientific notation that has been generated by technology. Expressions and Equations 8.EE.7: Solve linear equations in one variable. 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. 8.EE.7b: Solve linear equations with rational number scientific notation coefficient coefficient like terms equations How can we measure, model, and calculate using extremely large and small numbers? Why do we utilize algebraic linear equations to solve realworld math problems? How do we solve the equations and check for reasonableness? Textbook 8A page 3 8.EE EE EE EE Purple Textbook A pages , pages EE.1 I can apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.3 I can use scientific notation to estimate very large or very small quantities. 8.EE.4 I can perform operations with numbers expressed in scientific notation. 8.EE.7 I can give examples of linear equations in one variable with one solution, no solution, and infinite many solutions. I can use properties to transform equations into simpler forms. I can solve linear equations with rational coefficients including expanding expressions. 8.EE.5
4 Solving for a Variable in a Twovariable Linear Equation 4. Lines and Finding and Interpreting Slopes of Lines, Understanding SlopeIntercept Form, Writing, Sketching Graphs of Linear Equations, Real World Problems: coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships. Expressions and Equations 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. 8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y= mx for a line. slope yintercept slopeintercept form xintercept linear equation linear relationship What types of real world information can be modeled by linear relationships? How is the graph of a linear equation in two variables a line? 8.EE Purple Textbook A pages , pages EE EE Purple Textbook A pages I can compare two different proportional relationships in different ways. 8.EE.5 I can graph proportional relationships interpreting the unit rate as the slope of the graph. I can compare two different proportional relationships represented in different ways. 8.EE.6 I can derive the equation y = mx + b from a graph. I can explain the slope and yintercept of the context of realworld problems. 3
5 5. Systems of Introduction to Systems of, Solving Systems of Linear Equations Using Algebraic Methods, Real World Problems: Systems of, Solving Systems of Linear Equations by Graphing, Inconsistent and Dependent Systems of Expressions and Equations 8.EE.8: Analyze and solve pairs of simultaneous linear equations. 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. 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. 8.EE.8c: Solve realworld and mathematical problems leading to two linear equations in two variables. simultaneous linear equations (system of linear equations) elimination method substitution method standard form graphical method How can systems of equations be used to represent authentic scenarios and solve problems in life? What does the number of solutions (none, one, or infinite) of a system of linear equations represent? What methods can be used to solve systems of equations? Why do we have different methods for solving systems of equations? 8.EE EE.8 I can analyze and solve pairs of simultaneous linear equations. I can understand that solutions to a system correspond to points of intersection of their graphs. I can demonstrate that solutions to a system satisfy both equations simultaneously. I can determine if a system of equations has one solution, no solution, or infinitely many solutions. I can solve a system of equations by graphing, elimination and substitution. I can solve realworld problems leading to two linear equations in two variables. 6. Functions Understanding Relations and Functions, Representing Functions, Understanding Linear and Nonlinear Functions, Functions 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. 8.F.2: Compare properties of two functions each represented in a different way. output function input vertical line test linear function rate of change nonlinear function How can functional relationships be used to represent authentic situations in life and solve actual problems? Describe what this would look like. 8.F F F.1 I can understand that a function is a rule that assigns exactly one output to each input. I can see that a graph is made up of a set of ordered pairs. 8.F.2 I can compare properties of two functions represented either 4
6 Comparing Two Functions Algebra I book 7. Polynomial Equations and Factoring F3: 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. 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. 8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Algebra AAPR. A.1: Understand that polynomials form a system similar to integers in being closed. AAPR.B.3: Identify zeros of polynomials in factored form. AREI.B.4b: Solve quadratic equations in one variable by inspectionexample x 2 =49, quadratic formula, factoring. ASSE.A.2: Use the structure of an expression to identify ways to rewrite it. AREI.B.3a: Solve linear equations and inequalities in one variable including Polynomial (also monomial, binomial, trinomial) Degree Factored form Standard form Zeroproduct property Leading coefficient FOIL method (special case of distribution) Root (also repeated root) How are polynomials added, subtracted, multiplied and divided? How is a polynomial equation solved? How is factoring used to break a trinomial into a 8.F F F.5 additional 62 algebraically, graphically, numerically in tables, or by verbal description. 8.F.3 I can recognize a linear function and nonlinear function. 8.F.4 I can construct a function to model a linear relationship between two quantities. I can determine the rate of change and y intercept from two (x,y) values or from a table or graph. I can interpret the rate of change from the situation. 8.F.5 I can describe whether the function is increasing, decreasing, linear or nonlinear. I can sketch a graph that has been described verbally. Perform the four basic operations on polynomial expressions (including long and synthetic division). Solve a polynomial equation through factoring and application of the zeroproduct property and recognize the the solutions are the xintercepts o the polynomial equation. Factor a polynomial expression completely using appropriate strategies.
7 equations with coefficients represented by letters. Closed product of two binomials? Math 8 Book B 8. Geometric Transformations Translations, Reflections, Rotations, Dilations, Comparing Transformations Algebra I Book 8. Graphing Functions 8.1 Graphing Functions (with Vertical Stretch/Compres sion) 8.2 Graphing Functions (with Vertical Translations) 8.3 Graphing in Standard Form Geometry 8.G.1: Verify experimentally the properties of rotations, reflections, and translations: 8.G.1a: Lines are taken to lines, and line segments to line segments of the same length. 8.G.1b: Angles are taken to angles of the same measure. 8.G.1c: Parallel lines are taken to parallel lines. 8.G.3: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. Algebra ACED.A.2: Create equations in two or more variables to represent relationships, graph equations on coordinate axes with labels and scales. FIF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima. FBF.B.3: Identify the effect on the graph by replacing f(x) by f(x) + k. kf(x), f(kx) and f(x+k) for specific values of k, experiment using technology. translation image transformation reflection line of reflection rotation angle of rotation center of rotation dilation scale factor center of dilation function Parabola Vertex Axis of symmetry Vertical stretch, shrink Maximum and minimum value Zero Vertex form Intercept form How does one recognize and apply transformations of shapes to solve problems? What are some characteristics of the graph of a quadratic function? How do transformations affect the graph of f(x) = x 2? How do you graph a quadratic function when given in standard, vertex, or intercept form? How can you compare the 8.G.1 additional G.3 additional 73. Graph a quadratic function and transform the parent function to form many other functions. Graph a quadratic function when presented in different forms. Make connections among the different forms of a quadratic function. 8.G.1 I can verify experimentally the properties of rotations, reflections, and translations. 8.G.3 I can describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. ACED.A.2: I can identify and graph quadratic equations on coordinate axes FIF.C.7a: I can write quadratic functions in the form of y = ax 2 + bx + c and identify a, b, c. I can identify the vertex, the minimum or maximum, the domain, and the range for each function. FBF.B.3: I can explain how the graphs of y = 5x 2 and y = 1 5 x2 compare with the parent graph, y = x 2. FIF.C.9: I can compare properties of two functions represented in a different way (algebraically, 6
8 8.4 Graphing in Vertex Form 8.5 Using Intercept Form 8.6 Comparing Linear, Exponential, and Functions FIF.C.9: Compare properties of two functions represented in a different way (algebraically, graphically, numerically in tables, or by verbal description) FIF.B.4: Interpret and sketch graphs. FBF.A.1: Write a function that describes a relationship between two quantities. ASSE.B.3: Factor a quadratic to find zeros. AAPR.B.3: Identify zeros of polynomials when factored and use zeros to construct a graph. ACED.A.2: Create equations to represent relationships, graph equations on coordinate axes. FIF.C.8: Write a function in equivalent and explain properties of the function. FIF.B.6: Calculate and interpret the average rate of change. FLE.A.3: Observe using graphs and tables increasing functions. growth rates of linear, exponential, and quadratic functions? Compare and contrast features of the linear, exponential, and quadratic functions. graphically, numerically in tables, or by verbal description) FIF.B.4: I can interpret and sketch graphs FBF.A.1: I can write a function that describes a relationship between two quantities. ASSE.B.3: I can factor a quadratic equation to find the roots or the solutions. AAPR.B.3: I can use the factored form of a quadratic equation to find the zeroes and sketch a graph. FIF.C.8: I can write the equation in ax 2 + bx + c form and determine if the graph opens upward or downward. FIF.B.6: I can use my slope formula to check the rate of change at different intervals. FLE.A.3: I can determine an increasing function by looking at a table or graph. Algebra I Book 9. Solving Equations 9.1 Properties of Radicals 9.2 Solving NRN.1: Rewrite expressions involving radicals and rational exponents using the properties of exponents. FIF7A: Graph quadratic functions and show intercepts, maxima, and minima. Radical expression Rationalize equation formula Discriminant How are the four basic operations performed on square and cube roots? How are quadratic equations solved? I can simplify radical expressions. I can solve quadratic equations using the methods of graphing, square roots, and quadratic formula. I can determine the number of real solutions to a quadratic equation 7
9 Equations by Graphing 9.3 Solving Equations by Square Roots 9.5 Solving Equations by the Formula 9.6 Systems on NonLinear Equations Algebra I Book 10. Radical Functions and Equations 10.1 Graphing Square Root Functions 10.3 Solving Square Root Equations Math 8 Book B 10. Statistics Scatter Plots, Modeling Linear Associations, TwoWay Tables, 8 FIF7B: Graph square roots and cube roots. Statistics and Probability 8.SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns. 8.SP.2: Know that straight lines are widely used to model relationships between two quantitative variables. For Square root function scatter plot positive association negative association clustering bivariate measurement data line of best fit outlier How can you determine the number of real solutions to a quadratic equation? How many solutions are possible when you have system on nonlinear equations? What are some characteristics of the graph of a square root function? How can you solve an equation involving square roots? What mathematical processes and skills are used to investigate patterns of association in bivariate data? How can we gather, organize, and display bivariate data to 8.SP.1 additional SP.2 additional 94. through graphing or evaluating the discriminant. I can determine how many solutions exist when given the graph of a nonlinear system. I can graph and describe a square root function, including ones that have been transformed. I can solve an equation containing a square root. 8.SP.1 I can construct and interpret scatter plots. 8.SP.2 I can utilize lines of best fit. 8.SP.3
10 11. Probability Compound Events, Probability of Compound Events, Independent Events, Dependent Events KCCRS Math Standards not emphasized in Math in Focus 8 th Grade MIF: scatter plots that suggest a linear association. 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. 8.SP.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table. Probability is not emphasized in the 8 th grade KCCRS. communicate and justify results in authentic situations? How can we analyze bivariate data to make inferences and/or predictions based on surveys, experiments, probability, and observations? 8.SP.3 additional SP.4 additional 99. I can use the line of best fit to find the slope and y intercept. 8.SP.4 I can construct and interpret a twoway table. 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 angleangle criterion for similarity of triangles. 8.G.5. Has very little emphasis in MIF. Need to add more with supplemental materials. 8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. 8.G.9. Has very little emphasis in MIF. Need to add more with supplemental materials. High School currently using Holt for Alg. I, Geom., Adv. Alg. II Adopting for next year either Glencoe or Big Ideas Math 9
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