### 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.

**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

## Related Access Points

## Related Resources

## Lesson Plan

## Perspectives Video: Experts

## Problem-Solving Tasks

## Student Resources

## 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

## Parent Resources

## Problem-Solving Tasks

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