# MAFS.8.EE.1.2Archived Standard

Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
General Information
Subject Area: Mathematics
Domain-Subdomain: Expressions & Equations
Cluster: Level 1: Recall
Cluster: Work with radicals and integer exponents. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
s Square roots and cube roots may be used to represent solutions to equations. Radicands may not include variables.
• Calculator :

Neutral

• Context :

Allowable

Sample Test Items (3)
• Test Item #: Sample Item 1
• Question:

What is the value of p in the equation shown? • Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question:

A square is cut in half on the diagonal, creating two equal triangles. Each triangle has an area of 0.32 square units.

What is the side length, in units, of the original square?

• Difficulty: N/A
• Type: EE: Equation Editor

## 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))
7912115: Fundamental Explorations in Mathematics 2 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

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

## Formative Assessments

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

Type: Formative Assessment

The Root of the Problem:

Students are asked to evaluate perfect square roots and perfect cube roots.

Type: Formative Assessment

Dimensions Needed:

Students are asked to solve problems involving square roots and cube roots.

Type: Formative Assessment

## Lesson Plans

Generalizing Patterns: The Difference of Two Squares:

This lesson is designed to help teachers assess how well students can work with square numbers. Upon completion of the lesson, students should be able to describe and explain their findings and why results are possible or impossible. This lesson is a bridge towards proofs. The materials required for this lesson are worksheets, plain paper, large sheets of paper for making posters, and felt-tip pens. The entire lesson requires 110 minutes, broken down into a 20-minute pre-lesson, an 80-minute lesson (or two 40-minute lessons), and a 10-minute follow-up lesson.

Type: Lesson Plan

Discovering Kepler's Law for the Periods of Planets:

Students listen to a video that describes Kepler's determination that planetary orbits are elliptical and then will use data for the solar distance and periods of several of the planets in the solar system, then investigate several hypotheses to determine which is supported by the data.

Type: Lesson Plan

## 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

## Tutorials

Finding the square root of a decimal:

Students will learn how to find the square root of a decimal number.

Type: Tutorial

Finding cube roots:

Learn how to find the cube root of -512 using prime factorization.

Type: Tutorial

Introduction to cube roots:

Students will learn the meaning of cube roots and how to find them. Students will also learn how to find the cube root of a negative number.

Type: Tutorial

Introduction to square roots:

Students will earn about the square root symbol (the principal root) and what it means to find a square root. Students will also learn how to solve simple square root equations.

Type: Tutorial

## MFAS Formative Assessments

Dimensions Needed:

Students are asked to solve problems involving square roots and cube roots.

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

The Root of the Problem:

Students are asked to evaluate perfect square roots and perfect cube roots.

## 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

## Tutorials

Finding the square root of a decimal:

Students will learn how to find the square root of a decimal number.

Type: Tutorial

Finding cube roots:

Learn how to find the cube root of -512 using prime factorization.

Type: Tutorial

Introduction to cube roots:

Students will learn the meaning of cube roots and how to find them. Students will also learn how to find the cube root of a negative number.

Type: Tutorial

Introduction to square roots:

Students will earn about the square root symbol (the principal root) and what it means to find a square root. Students will also learn how to solve simple square root equations.

Type: Tutorial

## Parent Resources

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