# Standard 1: Solve problems involving rational numbers, including numbers in scientific notation, and extend the understanding of rational numbers to irrational numbers. Export Print
General Information
Number: MA.8.NSO.1
Title: Solve problems involving rational numbers, including numbers in scientific notation, and extend the understanding of rational numbers to irrational numbers.
Type: Standard
Subject: Mathematics (B.E.S.T.)
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.8.NSO.1.AP.1
Locate approximations of irrational numbers on a number line.
MA.8.NSO.1.AP.2
Use appropriate tools to plot, order, and compare simple square roots and cube roots for quantities less than 100.
MA.8.NSO.1.AP.3
Use the properties of integer exponents and product/quotient of powers with like bases to produce equivalent expressions.
MA.8.NSO.1.AP.4
Multiply a single-digit number by the power of 10 using a calculator. Identify whether the number in scientific notation represents a very large or very small quantity.
MA.8.NSO.1.AP.5
Perform operations with numbers expressed in scientific notation using a calculator.
MA.8.NSO.1.AP.6
Given a real-world problem, perform operations with numbers expressed in scientific notation using a calculator and interpret the answer in context.
MA.8.NSO.1.AP.7
Use tools to solve multi-step mathematical problems, with four or fewer steps, involving the order of operations with rational numbers including exponents and perfect squares and/or square roots.

## Related Resources

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

## Formative Assessments

Sum of Rational Numbers:

Students are asked to define a rational number and then explain why the sum of two rational numbers is rational.

Type: Formative Assessment

Sum of Rational and Irrational Numbers:

Students are asked to describe the difference between rational and irrational numbers and then explain why the sum of a rational and an irrational number is irrational.

Type: Formative Assessment

Product of Non-Zero Rational and Irrational Numbers:

Students are asked to describe the difference between rational and irrational numbers, and then explain why the product of a non-zero rational and an irrational number is irrational.

Type: Formative Assessment

Equivalent Powers Expressions:

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

Type: Formative Assessment

Exponents Tabled:

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

Type: Formative Assessment

The Root of the Problem:

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

Type: Formative Assessment

Sums and Differences in Scientific Notation:

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

Type: Formative Assessment

Scientific Multiplication and Division:

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

Type: Formative Assessment

Mixed Form Operations:

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

Type: Formative Assessment

Multiplying and Dividing Integer Exponents:

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

Type: Formative Assessment

Dimensions Needed:

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

Type: Formative Assessment

Estimating Extreme Values:

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

Type: Formative Assessment

Rational Numbers:

Students are asked to identify rational numbers from a list of real numbers, explain how to identify rational numbers, and to identify the number system that contains numbers that are not rational.

Type: Formative Assessment

Order Matters:

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

How Many Times?:

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

Type: Formative Assessment

Compare Numbers:

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

Type: Formative Assessment

Decimal to Fraction Conversion:

Students are given several terminating and repeating decimals and asked to convert them to fractions.

Type: Formative Assessment

Negative Exponential Expressions:

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

Type: Formative Assessment

Scientific Calculator Display:

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

The Irrational Beauty of the Golden Ratio:

Students are asked to find and interpret lower and upper bounds of an irrational expression using a calculator.

Type: Formative Assessment

Approximating Irrational Numbers:

Students are asked to plot the square root of eight on three number lines, scaled to progressively more precision.

Type: Formative Assessment

Locating Irrational Numbers:

Students are asked to graph three different irrational numbers on number lines.

Type: Formative Assessment

Comparing Irrational Numbers:

Students are asked to estimate the value of several irrational numbers using a calculator and order them on a number line.

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

Scientific Notation: Expressing Large Quantities:

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

Type: Original Student Tutorial

Applying the Pythagorean Theorem to Solve Mathematical and Real-World problems:

Apply the Pythagorean Theorem to solve mathematical and real-rorld problems in this interactive tutorial.

Type: Original Student Tutorial

## Video/Audio/Animation

Exponentiation:

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

## Student Resources

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

## Original Student Tutorials

Square Root Part 3: Simplifying Radicals:

Learn how to simplify radicals in this interactive tutorial.

Type: Original Student Tutorial

Scientific Notation: Expressing Large Quantities:

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

Type: Original Student Tutorial

Applying the Pythagorean Theorem to Solve Mathematical and Real-World problems:

Apply the Pythagorean Theorem to solve mathematical and real-rorld problems in this interactive tutorial.

Type: Original Student Tutorial

## Video/Audio/Animation

Exponentiation:

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

## Parent Resources

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