Concepts developed in previous Key Concept(s) Concepts that a student will study either mathematics course/units which serve later in Algebra II or in future as a foundation for the development of mathematics courses for which this the Concept” Concept” will be a foundation. “Key “Key Students have been exposed to the Complex Numbers In future courses, students will be expected quadratic formula and solutions that are Knowing that in the set of complex to graph complex numbers on the complex square roots of negative numbers. Up to numbers plane and calculate the distance between this point when this type of situation was Perform arithmetic operations with those numbers. encountered, students would give an complex numbers answer of real solutions”. Mention may “no have been made that a new set of numbers would be introduced in Algebra II to handle such situations. (Algebra 1 Unit 4 and Equations A.REI.4b) Students have graphed and solved Quadratic Expressions and Equations Students will continue to use quadratic quadratic equations with real solutions and Solve Quadratic Equations that have models to solve real world problems. understand the existence of non-real Complex Solutions solutions. (Algebra 1 Unit 2, 4 and 5) Quadratics Functions Students will continue to solve systems of equations that are comprised of quadratic Students derived the equation of a circle equations and various other functions. using Pythagorean theorem, complete the square to find the equation. (Geometry Unit As students solve polynomial equations, 5) they will need to understand the connection between the number of times the graph Students derived the equation of a parabola intersects the x-axis and the number of the focus and directrix. (Geometry Unit complex roots of the polynomial equation. 4) For example if the graph of a third degree polynomial equation intersects the x-axis only one time we know that the polynomial
Concepts developed in previous mathematics course/units which serve as a foundation for the development of the “Key Concept” Key Concept(s) Concepts that a student will study either later in Algebra II or in future mathematics courses for which this “Key Concept” will be a foundation. Students have been exposed to the quadratic formula and solutions that are square roots of negative numbers. Up to this point when this type of situation was encountered, students would give an answer of “no real solutions”. Mention may have been made that a new set of numbers would be introduced in Algebra II to handle such situations. (Algebra 1 Unit 4 and Equations A.REI.4b) Complex Numbers Knowing that in the set of complex numbers Perform arithmetic operations with complex numbers In future courses, students will be expected to graph complex numbers on the complex plane and calculate the distance between those numbers. Students have graphed and solved quadratic equations with real solutions and understand the existence of non-real solutions. (Algebra 1 Unit 2, 4 and 5) Students derived the equation of a circle using Pythagorean theorem, complete the square to find the equation. (Geometry Unit 5) Students derived the equation of a parabola the focus and directrix. (Geometry Unit 4) Quadratic Expressions and Equations Solve Quadratic Equations that have Complex Solutions Quadratics Functions Students will continue to use quadratic models to solve real world problems. Students will continue to solve systems of equations that are comprised of quadratic equations and various other functions. As students solve polynomial equations, they will need to understand the connection between the number of times the graph intersects the x-axis and the number of complex roots of the polynomial equation. For example if the graph of a third degree polynomial equation intersects the x-axis only one time we know that the polynomial