I Systems, Lesson 7, Other Systems (r. 2018) – SYSTEMS Other Systems Common Core Standard Next Generation Standard A-REI.D.11 Explain why the x-coordinates of the AI-A.REI.11 Given the equations and y = f(x) y = g(x): points where the graphs of the equations and i) recognize that each x-coordinate of the intersection(s) y=f(x) intersect are the solutions of the equation is the solution to the equation y=g(x) f(x) = g(x); find the solutions approximately, e.g., ii)find the solutions approximately using technology to f(x)=g(x); technology to graph the functions, make tables graph the functions or make tables of values; and of values, or find successive approximations. iii) interpret the solution in context. cases where and/or are linear, (Shared standard with Algebra II) f(x) g(x) rational, absolute value, exponential, and Notes: Algebra I tasks are limited to cases where f(x) functions. and are linear, polynomial, absolute value, and g(x) exponential functions of the form where > 0 and a b PARCC: Tasks that assess conceptual understanding of > 0 (b the indicated concept may involve any of the function types ≠ 1). mentioned in the standard except exponential and logarithmic Students should be taught to find the solutions functions. Finding the solutions approximately is limited to cases by using technology to graph the where f(x) and g(x) are polynomial functions. by making tables of values. When solving and any problem, students can choose either strategy. LEARNING OBJECTIVES Students will be able to: 1) use technology to create tables and graphs to find solutions of systems of equations involving linear and non-linear functions. Overview of Lesson Teacher Centered Introduction Student Centered Activities Overview of Lesson guided practice anticipates, monitors, selects, sequences, and Teacher: connects student work - activate students’ prior knowledge - developing essential skills - vocabulary - Regents exam questions - learning objective(s) - formative assessment assignment (exit slip, explain the math, or journal - big ideas: direct instruction entry) - modeling VOCABULARY absolute value equation linear equation slope intercept form exponential equation piecewise equation solution of a system families of functions quadratic equations
I – Systems, Lesson 7, Other Systems (r. 2018) SYSTEMS Other Systems Common Core Standard A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., technology to graph the functions, make tables of values, or find successive approximations. cases where f(x) and/or g(x) are linear, rational, absolute value, exponential, and functions. PARCC: Tasks that assess conceptual understanding of the indicated concept may involve any of the function types mentioned in the standard except exponential and logarithmic functions. Finding the solutions approximately is limited to cases where f(x) and g(x) are polynomial functions. Next Generation Standard AI-A.REI.11 Given the equations y = f(x) and y = g(x): i) recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x); ii)find the solutions approximately using technology to graph the functions or make tables of values; and iii) interpret the solution in context. (Shared standard with Algebra II) Notes: Algebra I tasks are limited to cases where f(x) and g(x) are linear, polynomial, absolute value, and exponential functions of the form where a > 0 and b > 0 (b ≠ 1). Students should be taught to find the solutions by using technology to graph the and by making tables of values. When solving any problem, students can choose either strategy. LEARNING OBJECTIVES Students will be able to: 1) use technology to create tables and graphs to find solutions of systems of equations involving linear and non-linear functions. Overview of Lesson Teacher Centered Introduction Overview of Lesson - activate students’ prior knowledge - vocabulary - learning objective(s) - big ideas: direct instruction - modeling Student Centered Activities guided practice Teacher: anticipates, monitors, selects, sequences, and connects student work - developing essential skills - Regents exam questions - formative assessment assignment (exit slip, explain the math, or journal entry) VOCABULARY absolute value equation exponential equation families of functions linear equation piecewise equation quadratic equations slope intercept form solution of a system
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