Grades 9-12: Algebra II – Manipulating Radicals


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Content Standards

CCSS.Math.Content.HSA.SSE.B.3  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

CCSS.Math.Content.HSN.RN.A.2  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

CCSS.Math.Content.HSN.CN.A.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.

CCSS.Math.Content.HSN.CN.C.7  Solve quadratic equations with real coefficients that have complex solutions.

Standards for Mathematical Practice

MP3: Construct viable arguments and critique the reasoning of others.

MP7: Look for and make use of structure.


This unit titled “Manipulating Radicals” is from The goals of this unit are focused on concepts in Algebra II related to manipulating radicals, as well as real and complex numbers. In this unit, students will use the properties of exponents, including rational exponents, and manipulate algebraic statements involving radicals in order to discriminate between equations and identities. This mini unit also allows students the chance to use and consider the role of the imaginary number and its application to radicals.


Connecticut teachers should be cautioned that there is a lack of incorporation of technology into the lesson. There are not explicit accommodations made for struggling learners or advanced learners. There is also a lack of information about accommodating for English language learners or students with disabilities. There is an emphasis on conceptual understanding, having a limited focus on a balanced approach to include procedural fluency and promoting transfer.


The unit is a valuable resource due to its rigor within the Common Core standards and the Mathematical Practices. The unit provides areas for pre-assessment, post-assessment, and formative assessment. The sequencing of tasks and sections is conducive to student learning. The prompting questions help for teachers to provide feedback to students and help all students achieve. Assessment tasks, as well as rubrics, have also been included as resources to support teachers as they implement this unit.