Standard 1: Rewrite numbers in equivalent forms.

loading spinner
Export Print
General Information
Number: MA.7.NSO.1
Title: Rewrite numbers in equivalent forms.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 7
Strand: Number Sense and Operations

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.7.NSO.1.AP.1
Use properties of whole number exponents to produce equivalent expressions.
MA.7.NSO.1.AP.2
Rewrite positive rational numbers in different but equivalent forms such as fractions, mixed numbers, repeating decimals and/or percentages to solve problems.

Related Resources

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

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Formative Assessments

Find Decimal Using Long Division:

Students are asked to use long division to convert four different fractions to equivalent decimals and to identify those that are rational.

Type: Formative Assessment

Quotients of Integers:

Students are given an integer division problem and asked to identify fractions which are equivalent to the division problem.

Type: Formative Assessment

Fraction to Decimal Conversion:

Students are given a fraction to convert to a decimal and are asked to determine if the decimal repeats.

Type: Formative Assessment

Lesson Plans

The Watergate Effect part 3:

Students will create a circle graph to display categorical data of the public presidential approval rates after the Supreme Court Case United States v. Nixon. Students will graph results independently and compare them to the circle graphs created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926) and the Watergate Effect Part 2 Lesson (Resource ID#: 210122) to discuss the trend of the data over the entirety of the Supreme Court case.

Type: Lesson Plan

The Watergate Effect part 2:

Students will create a circle graph to display categorical data of the public presidential approval rates during the Supreme Court Case United States v. Nixon. Students will graph results in pairs/groups and compare them to the circle graph created during the Watergate Effect Part 1 Lesson (Resource ID#: 208926).

Type: Lesson Plan

Generating Equivalent Forms of Numbers Using the Legislative Branch of the Government:

Students will rewrite fractions, decimals, and percentages in equivalent forms to compare the number of seats that each state has in the U.S. House of Representatives to the total number of seats in the House of Representatives, in this integrated lesson plan.

 

Type: Lesson Plan

The Watergate Effect Part 1:

Students will create a circle graph to display categorical data of the public presidential approval rates of Richard Nixon before the Supreme Court Case United States v. Nixon. Students will calculate percentages and central angle degrees to graph results in pairs/groups and analyze the results in this integrated lesson plan.

 

Type: Lesson Plan

Fractions and Percentages of the Legislative Branch:

Students will use fractions, decimals, and percentages to compare the number of seats that Florida (as well as other states) has in the U.S. House of Representatives to the total amount of seats in the House of Representatives in this integrated lesson plan.  

 

Type: Lesson Plan

Rewriting Rational Numbers to Analyze International Organizations (Part 1: United Nations):

Students will analyze regional membership of the United Nations to represent the part to a whole relationship as a fraction. Students will rewrite rational numbers in equivalent forms while examining the purpose of the United Nations and the United States’ role as a member in this integrated lesson plan.

Type: Lesson Plan

Independent Compound Probability:

During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.

Type: Lesson Plan

Fast Food Frenzy:

In this activity, students will engage critically with nutritional information and macronutrient content of several fast food meals. This is an MEA that requires students to build on prior knowledge of nutrition and working with percentages.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Multiplying terms that have the same base:

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

Who's Being Irrational?:

In this lesson, students will learn how irrational numbers differ from rational numbers. The students will complete a graphic organizer that categorizes rational and irrational numbers. Students will also be able to identify irrational numbers found in the real world.

Type: Lesson Plan

Scavenger Hunt for Multiplying and Dividing Powers:

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

Rational vs Irrational:

Students will organize the set of real numbers and be able to identify when a number is rational or irrational. They will also learn the process of how to change a repeating decimal to its equivalent fraction.

Type: Lesson Plan

Predicting the decimal equivalent for a fraction - terminating or repeating?:

This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization.

Type: Lesson Plan

Beads in a Bowl:

This activity will allow students to explore the concept of simple probability using a random selection of multi-colored beads.

Type: Lesson Plan

Really! I'm Rational!:

In this lesson students will gain an understanding of how repeating decimals are converted into a ratio in the form of a over b by completing an exploration worksheet. They will conclude that any number which can be written in this form is called a rational number.

Type: Lesson Plan

Problem-Solving Tasks

Equivalent fractions approach to non-repeating decimals:

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

Type: Problem-Solving Task

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Type: Problem-Solving Task

Ants versus humans:

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

Estimating Square Roots:

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Type: Problem-Solving Task

Converting Decimal Representations of Rational Numbers to Fraction Representations:

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

Type: Problem-Solving Task

Calculating and Rounding Numbers:

In this task, students explore some important mathematical implications of using a calculator. Specifically, they experiment with the approximation of common irrational numbers such as pi (p) and the square root of 2 (v2) and discover how to properly use the calculator for best accuracy. Other related activities involve converting fractions to decimal form and a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

Type: Problem-Solving Task

Tutorial

Powers of Zero:

Students will learn that non-zero numbers to the zero power equal one. They will also learn that zero to any positive exponent equals zero.

Type: Tutorial

Student Resources

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

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Problem-Solving Tasks

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Type: Problem-Solving Task

Estimating Square Roots:

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Type: Problem-Solving Task

Converting Decimal Representations of Rational Numbers to Fraction Representations:

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

Type: Problem-Solving Task

Tutorial

Powers of Zero:

Students will learn that non-zero numbers to the zero power equal one. They will also learn that zero to any positive exponent equals zero.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Type: Problem-Solving Task

Ants versus humans:

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

Estimating Square Roots:

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Type: Problem-Solving Task

Converting Decimal Representations of Rational Numbers to Fraction Representations:

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

Type: Problem-Solving Task

Calculating and Rounding Numbers:

In this task, students explore some important mathematical implications of using a calculator. Specifically, they experiment with the approximation of common irrational numbers such as pi (p) and the square root of 2 (v2) and discover how to properly use the calculator for best accuracy. Other related activities involve converting fractions to decimal form and a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

Type: Problem-Solving Task