Aquatic Quadratics!

Science and Engineering Practices: 1. Asking Questions and Defining Problems 2. Developing and Using Models 3. Planning and Carrying Out Investigations 4. Analyzing and Interpreting Data 5. Using Mathematics and Computational Thinking 6. Constructing Explanations and Designing Solutions 7. Engaging in Argument from Evidence 8. Obtaining, Evaluating, and Communicating Information ||Next Generation Science Standards||Middle School||Science and Engineering Practices|||Mathematical Practices: 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. ||Common Core Mathematics||Grade 8||Mathematical Practices|||8.EE.7. Solve linear equations in one variable.||Common Core Mathematics||Grade 8||Expressions And Equations||Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations|||8.EE.8. Analyze and solve pairs of simultaneous linear equations.||Common Core Mathematics||Grade 8||Expressions And Equations||Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations|||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.1||Common Core Mathematics||Grade 8||Functions||Define, Evaluate, And Compare Functions|||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.||Common Core Mathematics||Grade 8||Functions||Define, Evaluate, And Compare Functions|||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.||Common Core Mathematics||Grade 8||Functions||Use Functions To Model Relationships Between Quantities|||Mathematical Practices: 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. ||Common Core Mathematics||High School||Mathematical Practices|||Science and Engineering Practices: 1. Asking Questions and Defining Problems 2. Developing and Using Models 3. Planning and Carrying Out Investigations 4. Analyzing and Interpreting Data 5. Using Mathematics and Computational Thinking 6. Constructing Explanations and Designing Solutions 7. Engaging in Argument from Evidence 8. Obtaining, Evaluating, and Communicating Information ||Next Generation Science Standards||High School||Science and Engineering Practices|||HS.A.APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.||Common Core Mathematics||High School||Arithmetic With Polynomials And Rational Expressions||Perform Arithmetic Operations On Polynomials|||HS.A.CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.||Common Core Mathematics||High School||Creating Equations||Create Equations That Describe Numbers Or Relationships|||HS.A.REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).||Common Core Mathematics||High School||Reasoning With Equations And Inequalities||Represent And Solve Equations And Inequalities Graphically|||HS.A.REI.4. Solve quadratic equations in one variable.||Common Core Mathematics||High School||Reasoning With Equations And Inequalities||Solve Equations And Inequalities In One Variable|||HS.A.SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 ? y4 as (x2)2 ? (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 ? y2)(x2 + y2).||Common Core Mathematics||High School||Seeing Structure In Expressions||Interpret The Structure Of Expressions|||HS.A.SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.?||Common Core Mathematics||High School||Seeing Structure In Expressions||Write Expressions In Equivalent Forms To Solve Problems|||HS.F.BF.1. Write a function that describes a relationship between two quantities.||Common Core Mathematics||High School||Building Functions||Build A Function That Models A Relationship Between Two Quantities|||HS.F.IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.?||Common Core Mathematics||High School||Interpreting Functions||Analyze Functions Using Different Representations|||HS.F.IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.||Common Core Mathematics||High School||Interpreting Functions||Analyze Functions Using Different Representations|||HS.F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.||Common Core Mathematics||High School||Linear, Quadratic, And Exponential Models||Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems|||HS.F.LE.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).||Common Core Mathematics||High School||Linear, Quadratic, And Exponential Models||Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems|||HS.F.LE.5. Interpret the parameters in a linear or exponential function in terms of a context.||Common Core Mathematics||High School||Linear, Quadratic, And Exponential Models||Interpret Expressions For Functions In Terms Of The Situation They Model