Cluster 1: Work with radicals and integer exponents. (Major Cluster)Archived

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

Type: Formative Assessment

Students are given numerical expressions and asked to use properties of integer exponents to find equivalent expressions.

Type: Formative Assessment

Students are asked to complete a table of powers of three and provide an explanation of zero powers.

Type: Formative Assessment

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

Type: Formative Assessment

Students are asked to add and subtract numbers given in scientific notation in real-world contexts.

Type: Formative Assessment

Students are asked to multiply and divide numbers given in scientific notation in real-world contexts.

Type: Formative Assessment

Students are given word problems with numbers in both standard and scientific notation and asked to solve problems using various operations.

Type: Formative Assessment

This lesson unit is intended to help you assess how well students are able to:

• Estimate lengths of everyday objects.
• Convert between decimal and scientific notation.
• Make comparisons of the size of numbers expressed in both decimal and scientific notation.

Type: Formative Assessment

Students are asked to apply the properties of integer exponents to generate equivalent numerical expressions.

Type: Formative Assessment

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

Type: Formative Assessment

Students are asked to estimate an extremely large and an extremely small number by writing it in the form a x .

Type: Formative Assessment

Students are given pairs of numbers written in the form of an integer times a power of 10 and are asked to compare the numbers in each pair using the inequality symbols.

Type: Formative Assessment

Students are given pairs of numbers written in exponential form and are asked to compare them multiplicatively.

Type: Formative Assessment

Students are given pairs of numbers written in scientific notation and are asked to compare them multiplicatively.

Type: Formative Assessment

Students are given expressions with negative exponents and are asked to identify those that are equivalent from given sets of expressions.

Type: Formative Assessment

Students are given examples of calculator displays and asked to convert the notation in the display to both scientific notation and standard form.

Type: Formative Assessment

Students will create a working model of the solar system to scale. They will incorporate QR codes to present information on solar system objects, as well as compare the geocentric and heliocentric models of the solar system.

Type: Lesson Plan

In this discovery oriented lesson, students will explore the use of non-standard units of measurement. They will convert linear measurements within the metric system and convert measurements given in astronomical units (AU) into more familiar units, specifically meters and kilometers. The unit conversions will be completed with measurements that are expressed in scientific notation. Students will recall their prior knowledge of how to add and subtract numbers given in scientific notation. They will also use their knowledge of exponent rules to determine an efficient method for multiplying and dividing numbers expressed in scientific notation.

Type: Lesson Plan

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

This lesson unit is intended to help you assess how well students are able to estimate lengths of everyday objects, convert between decimal and scientific notation and make comparisons of the size of numbers expressed in both decimal and scientific notation.

Type: Lesson Plan

Students explore numerical examples involving multiplying exponential terms that have the same base. They generalize the property of exponents where, when multiplying terms with the same base, the base stays the same and the exponents are added together.

Type: Lesson Plan

Students will participate in a gallery walk in which they observe patterns in algebraic expressions. Students will apply the properties of integer exponents to simplify expressions.

Type: Lesson Plan

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

This low-tech lesson will have students stand up holding different exponent cards. This will help them write and justify an equivalent expression and see the pattern for expressions with the same base and descending exponents. What happens as you change from 2 to the fourth power to 2 to the third power; 2 to the second power; and so forth? This is an introductory lesson to two of the properties of exponents: and

Type: Lesson Plan

Get your students up and moving and interested in simplifying expressions with whole integer powers. After getting your students to figure out what it takes to multiply and divide powers with whole number exponents, have your students scurry about the room to find the questions and answers for scavenger hunt exercise. The lesson includes questions and answers for the hunt, directions for the hunt, printable cards for the hunt, and step by step directions on how to get your students to figure out what they need to do when multiplying and dividing powers with whole number exponents.

Type: Lesson Plan

The students will informally learn the rules for exponents: product of powers, powers of powers, zero and negative exponents. The activities provide the teacher with a progression of steps that help lead students to determine results without knowing the rules formally. The closing activity is hands-on to help reinforce all rules.

Type: Lesson Plan

This resource provides a Lesson Plan for teaching students how to apply the Product of Powers Property of exponents. They will be able to write equivalent exponential expressions and evaluate them when possible.

Type: Lesson Plan

In this lesson students will learn the properties of integer exponents and how to apply them to multiplication and division. Students will have the opportunity to work with concrete manipulatives to create an understanding of these properties and then apply them abstractly. The students will also develop the understanding of the value of any integer with a zero exponent.

Type: Lesson Plan

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

The students must rationalize how a Ponzi email could make money or fall apart. Using their knowledge of exponential growth, the students can estimate the potential gains, but then are asked to think about why these schemes are illegal and tend to collapse.

Type: Problem-Solving Task

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

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

We will look at examples of limits at infinity.

Type: Tutorial

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

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