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A1-N-1-1

Page history last edited by Tashe Harris 6 years, 3 months ago

A1.N.1 Write square roots and cube roots of monomial algebraic expressions in simplest radical form.


In a Nutshell

Students will recognize square and cube roots that can be simplified and apply their knowledge of roots and factoring of whole numbers to simplify them and provide justification for their processes.

Student Actions

Teacher Actions

  • Student will notice numbers and variables under a radical are not simplified and use their knowledge of factors to develop procedural fluency to simplify square and cube roots.

  • Students work to understand how roots will change an expression by comparing equivalent representations of the same expression, developing mathematical reasoning and justifying the processes they use to simplify radicals .

  • Students will develop the ability to communicate mathematically as they  discuss and justify their processes to both teachers and peers using appropriate mathematical vocabulary and notation.

 

  • Elicit and use evidence of student thinking, expecting students to  justify operations related to both whole numbers and variables within radicals, and using their own thinking to guide them toward deeper understanding of the concept by looking for alternate routes to the same solution. rather than having students memorize a series of steps.

  • Create examples and pose questions that highlight what parts of a root change and what parts stay the same by asking students to compare equivalent representations of the same expression.

  • Facilitate meaningful mathematical discourse, as students and teachers discuss common errors and their processes concerning simplifying radicals and the use of proper mathematical notation.

  • Implement tasks that promote reasoning and problem solving by providing examples with common errors made and allowing students to examine and find the mistakes.

     

Key Understandings

Misconceptions

 

  • Produce the simplest form of square and cube roots including both whole numbers and variables, using knowledge of factoring

 Examples:

 

 

  • When taking the square root of a variable that results in an odd exponent, students need to remember to apply absolute value bars on the variable to keep it positive.

  •  Example:

 

 

  • Students will mistakenly square or cube a number, rather than finding its root.

i.e. = 16 rather than 

 

 rather than 

 

 

  • Students  confuse division and roots and divide by 2 or 3 rather than finding the root.

i.e.  = 50 rather than 

 

 rather than 

 

  • Students forget to apply absolute value bars on the variable that is simplified to an odd exponent outside the radical when using an even root.

OKMath Framework Introduction

Algebra 1 Introduction

 

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