MA.8.AR.2.3

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Given an equation in the form of x²=p and x³=q, where p is a whole number and q is an integer, determine the real solutions.

Clarifications

Clarification 1: Instruction focuses on understanding that when solving x²=p, there is both a positive and negative solution.

Clarification 2: Within this benchmark, the expectation is to calculate square roots of perfect squares up to 225 and cube roots of perfect cubes from -125 to 125.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 8
Strand: Algebraic Reasoning
Standard: Solve multi-step one-variable equations and inequalities.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.AR.2.AP.3:

Given an equation in the form of x²= p and x³= q, use tools to determine real solutions where p is a perfect square up to 144 and q is a perfect cube from –125 to 125.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessment

Roots and Radicals:

Students are asked to solve simple quadratic and cubic equations and represent solutions using square root and cube root symbols.

Type: Formative Assessment

Original Student Tutorials

Square Root Part 3: Simplifying Radicals:

Learn how to simplify radicals in this interactive tutorial.

Type: Original Student Tutorial

Square Root Part 2: Non-Perfect Squares:

Learn what non-perfect squares are and find the decimal approximation of their square roots in this interactive tutorial.

Type: Original Student Tutorial

Square Root Part 1: Perfect Squares:

Learn what perfect squares are and find their square roots in this interactive tutorial.

Type: Original Student Tutorial

MFAS Formative Assessments

Roots and Radicals:

Students are asked to solve simple quadratic and cubic equations and represent solutions using square root and cube root symbols.

Original Student Tutorials Mathematics - Grades 6-8

Square Root Part 1: Perfect Squares:

Learn what perfect squares are and find their square roots in this interactive tutorial.

Square Root Part 2: Non-Perfect Squares:

Learn what non-perfect squares are and find the decimal approximation of their square roots in this interactive tutorial.

Square Root Part 3: Simplifying Radicals:

Learn how to simplify radicals in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Square Root Part 3: Simplifying Radicals:

Learn how to simplify radicals in this interactive tutorial.

Type: Original Student Tutorial

Square Root Part 2: Non-Perfect Squares:

Learn what non-perfect squares are and find the decimal approximation of their square roots in this interactive tutorial.

Type: Original Student Tutorial

Square Root Part 1: Perfect Squares:

Learn what perfect squares are and find their square roots in this interactive tutorial.

Type: Original Student Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.