# MA.8.NSO.1.5

Add, subtract, multiply and divide numbers expressed in scientific notation with procedural fluency.

The sum of .

### Clarifications

Clarification 1: Within this benchmark, for addition and subtraction with numbers expressed in scientific notation, exponents are limited to within 2 of each other.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Scientific Notation

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students developed an understanding of Laws of Exponents (Appendix E) with numerical expressions. They focused on generating equivalent numerical expressions with whole-number exponents and rational number bases. In grade 8, students use the knowledge of Laws of Exponents to work with scientific notation. In Geometry, students will solve problems involving density in terms of area and volume which can be represented using scientific notation when the numbers are large. Additionally, students can apply their scientific notation knowledge in science courses.
• Instruction connects the work of scientific notation with the Laws of Exponents with integer exponents.
• Instruction includes having students color code or use a highlighter to help keep the numbers together.
• For example, when multiply 3.2 × 1028 and 6.7 × 107, students can highlight the 3.2 and 6.7 in one color and the 1028 and 107 in another color for organizational purposes.
• Students should develop fluency with and without the use of a calculator when performing operations with numbers expressed in scientific notation.
• It is helpful to include contextual problems to compare numbers written in scientific notation, including cross-curricular examples from science.

### Common Misconceptions or Errors

• Some students may incorrectly apply addition and subtraction across a problem.
• For example, students may miscalculate (1.3 × 10³) + (3.4 × 105) as 4.7 × 108.
• Some students may incorrectly apply multiplication across a problem.
• For example, students may miscalculate (2 × 104)(3 × 105) as 6 × 1020.
• Some students may incorrectly represent their final answer not in scientific notation.
• For example, students may write (2 × 104)(6 × 105) as 12 × 109 instead of 1.2 × 1010.

### Strategies to Support Tiered Instruction

• Instruction includes making connections to the use of place values when adding and subtracting numbers written in standard form to place values with scientific notation.
• Teacher demonstrates how rewriting numbers in scientific notation utilizing the same power of 10 represents numbers with the same place value.
• Instruction includes correct use of operations and laws of exponents when finding the products and quotients of numbers represented in scientific notation, paying close attention to the solution to ensure it is in scientific notation.
• For example, when multiplying (3 × 102) and (4 × 104), students can rearrange the expression as (3 × 4)(102 × 104) to determine 12 × 106 which is equivalent to 1.2 × 107.
• Teacher provides opportunities for students to complete problems using scientific notation and standard form in order to check for the reasonableness of their solutions and build on connections between the two.

A collection of meteorites includes three meteorites that weigh 1.1 × 102 grams, 6.8 × 102 grams, and 8.4 × 10−2 grams.
• Part A. Why would a scientist represent the weights using scientific notation? Are all the meteorites approximately the same size?
• Part B. What is the difference between the mass of the heaviest meteorite and the mass of the lightest meteorite? Write your answer in standard notation.

### Instructional Items

Instructional Item 1
What is the sum of 7 × 10−8 and 6 × 10−8?

Instructional Item 2
Write the expression shown as a number in scientific number.

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## 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))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.NSO.1.AP.5: Perform operations with numbers expressed in scientific notation using a calculator.

## Related Resources

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

## Lesson Plan

How Many Smoots Does It Take to Reach the Moon?:

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

## Perspectives Video: Experts

Fluency vs. Automaticity:

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What is Fluency?:

What is fluency? What are the ingredients required to become procedurally fluent in mathematics? Dr. Lawrence Gray explores what it means for students to be fluent in mathematics in this Expert Perspectives video.

Type: Perspectives Video: Expert

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.

Giantburgers:

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.

## Student Resources

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

Giantburgers:

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.

## Parent Resources

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