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.

**Number:**MAFS.8.EE.1

**Title:**Work with radicals and integer exponents. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**8

**Domain-Subdomain:**Expressions & Equations

## Related Standards

## Related Access Points

## Access Points

^{8}).

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Student Center Activity

## Tutorials

## Video/Audio/Animations

## Student Resources

## Original Student Tutorials

Use scientific notation to compare the distances of planets and other objects from the Sun in this interactive tutorial.

Type: Original Student Tutorial

Use astronomical units to compare distances betweeen objects in our solar system in this interactive tutorial.

Type: Original Student Tutorial

Learn how to simplify radicals in this interactive tutorial.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Explore how to express large quantities using scientific notation in this interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.

Type: Problem-Solving Task

The student is asked to perform operations with numbers expressed in scientific notation to decide whether 7% of Americans really do eat at Giantburger every day.

Type: Problem-Solving Task

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

This video discusses exponent properties involving products.

Type: Tutorial

This video models how to use the Quotient of Powers property.

Type: Tutorial

This video demonstrates multiplying in scientific notation.

Type: Tutorial

This example demonstrates mathematical operations with scientific notation used to solve a word problem.

Type: Tutorial

This tutorial shows students the rule for negative exponents. Students will see, using variables, the pattern for negative exponents.

Type: Tutorial

This video demonstrates a scientific notation word problem involving division.

Type: Tutorial

This is an example showing how to simplify an expression into scientific notation.

Type: Tutorial

In this tutorial, students will learn about negative exponents. An emphasis is placed on multiplying by the reciprocal of a number.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

In this tutorial, you will apply what you know about multiplying negative numbers to determine how negative bases with exponents are affected and what patterns develop.

Type: Tutorial

This tutorial reviews the concept of exponents and powers and includes how to evaluate powers with negative signs.

Type: Tutorial

This tutorial demonstrates how to use the power of a power property with both numerals and variables.

Type: Tutorial

If a term raised to a power is enclosed in parentheses and then raised to another power, this expression can be simplified using the rules of multiplying exponents.

Type: Tutorial

Any expression consisting of multiplied and divide terms can be enclosed in parentheses and raised to a power. This can then be simplified using the rules for multiplying exponents.

Type: Tutorial

Scientific notation is used to conveniently write numbers that require many digits in their representations. How to convert between standard and scientific notation is explained in this tutorial.

Type: Tutorial

## Video/Audio/Animations

Exponentiation can be understood in terms of repeated multiplication much like multiplication can be understood in terms of repeated addition. Properties of multiplication and division of exponential expressions with the same base are derived.

Type: Video/Audio/Animation

Integer exponents greater than one represent the number of copies of the base which are multiplied together. hat if the exponent is one, zero, or negative? Using the rules of adding and subtracting exponents, we can see what the meaning must be.

Type: Video/Audio/Animation

Exponential expressions with multiplied terms can be simplified using the rules for adding exponents.

Type: Video/Audio/Animation

Exponential expressions with divided terms can be simplified using the rules for subtracting exponents.

Type: Video/Audio/Animation

Exponential expressions with multiplied and divided terms can be simplified using the rules of adding and subtracting exponents.

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies minted either in a single year or for the last century is phenomenally large and difficult to grasp. One way to assess how large this number is would be to consider how far all of these pennies would reach if we were able to stack them one on top of another: this is another phenomenally large number but just how large may well come as a surprise.

Type: Problem-Solving Task

In this problem students are comparing a very small quantity with a very large quantity using the metric system. The metric system is especially convenient when comparing measurements using scientific notations since different units within the system are related by powers of ten.

Type: Problem-Solving Task

This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass. The solution below converts the mass of humans into grams; however, we could just as easily converted the mass of ants into kilograms. Students are unable to go directly to a calculator without taking into account all of the considerations mentioned above. Even after converting units and decimals to scientific notation, students should be encouraged to use the structure of scientific notation to regroup the products by extending the properties of operations and then use the properties of exponents to more fluently perform the calculations involved rather than rely heavily on a calculator.

Type: Problem-Solving Task

The student is asked to perform operations with numbers expressed in scientific notation to decide whether 7% of Americans really do eat at Giantburger every day.

Type: Problem-Solving Task

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. It is good for students to learn the convention that negative time is simply any time before t=0.

Type: Problem-Solving Task

## Tutorials

This tutorial reviews the concept of exponents and powers and includes how to evaluate powers with negative signs.

Type: Tutorial

This tutorial demonstrates how to use the power of a power property with both numerals and variables.

Type: Tutorial