function such as. N.RN.2 Rewrite expressions Knowledge of the Example: Given the expression 52/5, a student should be able to involving radicals and rational connection between radical rewrite the expression in radical form. exponents using the and exponential notation A student should also be able to go from radical to exponential form. properties of exponents. Ability to translate between (major)(cross-cutting MD radical and exponential only) notation N.Q.2 Define appropriate Ability to select and use Example: Students would realize that while they could use miles to quantities for the purpose of . units of measure to measure the length of a desk, it would be inappropriate to do so. ★ accurately model a given (supporting)(cross-cutting) real world scenario N.CN.1 Know there is a Ability to extend experience This is a to the complex number system, student’s first exposure complex number i such that i2 with solving quadratic therefore some discussion of real versus imaginary numbers needs equations with no real = and every complex to be included (refer to −1, solutions from Algebra I to the number has the form a + bi Algebra2.unit1.lessonseed.NumberSystems). existence of complex with a and b real. numbers. (e.g. use solving as (additional) Tie the reason for learning about imaginary numbers at this point in a way to introduce complex their study of mathematics to the need to find all of the solutions of numbers) quadratic equations. N.CN.2 Use the relation Knowledge of conjugate pairs Note that N.CN.2, N.CN.7 and N.CN.8 are inter-related. and the nature of their products i2 = and the commutative, –1 associative, and distributive properties to add, subtract, and multiply complex numbers. (additional) N.CN.7 Solve quadratic Ability to use the quadratic Use the quadratic formula to solve problems that will yield complex formula and/or completing the equations with real solutions such as x2 4x + 13 = 0 – square as a means of solving a coefficients that have complex quadratic equation solutions. Relate conjugate pairs to pairs of radical solutions found when Knowledge that complex (additional) solving quadratics in Algebra 1.
function such as. N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. (major)(cross-cutting MD only) Knowledge of the connection between radical and exponential notation Ability to translate between radical and exponential notation Example: Given the expression 52/5, a student should be able to rewrite the expression in radical form. A student should also be able to go from radical to exponential form. N.Q.2 Define appropriate quantities for the purpose of . ★ (supporting)(cross-cutting) Ability to select and use units of measure to accurately model a given real world scenario Example: Students would realize that while they could use miles to measure the length of a desk, it would be inappropriate to do so. N.CN.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real. (additional) Ability to extend experience with solving quadratic equations with no real solutions from Algebra I to the existence of complex numbers. (e.g. use solving as a way to introduce complex numbers) This is a student’s first exposure to the complex number system, therefore some discussion of real versus imaginary numbers needs to be included (refer to Algebra2.unit1.lessonseed.NumberSystems). Tie the reason for learning about imaginary numbers at this point in their study of mathematics to the need to find all of the solutions of quadratic equations. N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. (additional) Knowledge of conjugate pairs and the nature of their products Note that N.CN.2, N.CN.7 and N.CN.8 are inter-related. N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. (additional) Ability to use the quadratic formula and/or completing the square as a means of solving a quadratic equation Knowledge that complex Use the quadratic formula to solve problems that will yield complex solutions such as x2 – 4x + 13 = 0 Relate conjugate pairs to pairs of radical solutions found when solving quadratics in Algebra 1.