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

### Examples

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.)

**Grade:**8

**Strand:**Number Sense and Operations

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### 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 × 10
^{28}and 6.7 × 10^{7}, students can highlight the 3.2 and 6.7 in one color and the 10^{28}and 10^{7}in another color for organizational purposes.

- For example, when multiply 3.2 × 10
- 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 × 10
^{5}) as 4.7 × 10^{8}.

- For example, students may miscalculate (1.3 × 10³) + (3.4 × 10
- Some students may incorrectly apply multiplication across a problem.
- For example, students may miscalculate (2 × 10
^{4})(3 × 10^{5}) as 6 × 10^{20}.

- For example, students may miscalculate (2 × 10
- Some students may incorrectly represent their final answer not in scientific notation.
- For example, students may write (2 × 10
^{4})(6 × 10^{5}) as 12 × 10^{9}instead of 1.2 × 10^{10}.

- For example, students may write (2 × 10

### 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 × 10
^{2}) and (4 × 10^{4}), students can rearrange the expression as (3 × 4)(10^{2}× 10^{4}) to determine 12 × 10^{6}which is equivalent to 1.2 × 10^{7}.

- For example, when multiplying (3 × 10
- 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.

### Instructional Tasks

*Instructional Task 1*

**(MTR.3.1, MTR.6.1)**A collection of meteorites includes three meteorites that weigh 1.1 × 10

^{2}grams, 6.8 × 10

^{2}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

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## Lesson Plan

## Perspectives Video: Experts

## Student Resources

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## Parent Resources

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