# MA.6.NSO.3.5

Rewrite positive rational numbers in different but equivalent forms including fractions, terminating decimals and percentages.

### Examples

The number can be written equivalently as 1.625 or 162.5%

### Clarifications

Clarification 1: Rational numbers include decimal equivalence up to the thousandths place.
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

• Dividend
• Divisor
• Rational Number

### Vertical Alignment

Previous Benchmarks

http://flbt5.floridaearlylearning.com/standards.html

Next Benchmarks

### Purpose and Instructional Strategies

In grades 4 and 5, students related the relationship between decimal values and fractions out of ten, one hundred or one thousand. Students also were taught that fractions show a division relationship. This understanding is being extended in grade 6 to re-write positive rational numbers into equivalent forms. This skill is extended in grade 7 to also include negative rational numbers.
• Instruction includes various methods and strategies to rewrite numbers into a percentage.
• Finding equivalent fractions with denominators of 10, 100 or 1000 to determine the equivalent percentage.
• Writing fractions and decimals as hundredths; the term percent can be substituted for the word hundredth.
• Multiplying the decimal by 100.
• Percent means “per 100,” so a whole is out of 100, or a whole is 100%. If converting the inverse relationship from a percent to a decimal, students divide the percent by 100 to find the equivalent decimal. Students should be encouraged to look for and discover the pattern that occurs (MTR.5.1).
• Instruction includes various methods and strategies to rewrite numbers from fraction to decimal or from decimal to fraction (MTR.3.1).
• Decimal grid models
• Dividing the numerator by the denominator. If the fraction is a fraction greater than one or a mixed number, there will be a whole number in the decimal equivalent and the percent will be greater than 100. Students can convert mixed numbers to fractions greater than one and then divide to help them see the pattern of where the whole number falls in relation to the decimal (MTR.5.1).
• Instruction focuses on relating fractions, decimals and percent equivalents to familiar real-world situations, like scores and grades on tests or coupons and sales offered by stores (MTR.5.1, MTR.7.1).
• Use questioning to help students determine their solution’s reasonableness (MTR.6.1).
• For example, is it reasonable for the percent to be more than 100? Is it reasonable for the percent to be less than 1?
• Instruction includes the understanding that percentages are a number and are worth specific amounts in contexts (MTR.7.1).
• Students should have practice with and without the use of technology to rewrite positive rational numbers in different but equivalent forms.

### Common Misconceptions or Errors

• Students may incorrectly think that, when dividing, the larger value is divided by the smaller value. This is a common overgeneralization because most of their experience in elementary school is dividing larger values by smaller values.
• Students may misplace the decimal when converting from fraction to decimal form because they forget to place the decimal after the whole number in the dividend if the numbers do not divide evenly or do not place the decimal in the aligned place value of the quotient. It is helpful for some students to use graph paper when dividing with decimals to help students keep place values accurately aligned.
• Students may incorrectly think that the decimal value and the percent are exactly the same, not realizing that the percent is 100 times the decimal value.
• Students may incorrectly convert from fraction to decimal form because of their lack of place value knowledge. Instruction includes students using expanded form of the numbers by adding a decimal and zeros in aligned place values until the decimal terminates. Practice includes multiple opportunities for students to work with fractions that require students to add zeros.
• Students may incorrectly move the decimal direction when converting between decimals and percentages because they do not understand what happens to the decimal when a number is multiplied or divided by a power of 10.

### Strategies to Support Tiered Instruction

• Instruction includes the use of estimation when converting fractions to decimal form to ensure the proper placement of the decimal point in the final quotient.
• Instruction includes the use of a 100 frame to review place value for tenths, hundredths, and if needed, thousandths and the connections for decimal and fractional forms.
• For example:
• Instruction includes providing multiple opportunities for students to work with fractions that require students to add zeros.

Kami told her mother that she answered 17 out of 25 questions correctly on her math test or 68%. Did Kami determine the correct percent score? Explain your reasoning.

Instructional Task 2 (MTR.2.1, MTR.4.1, MTR.5.1
Complete the table to identify equivalent forms of each number. Explain how you approached your solutions.

Convert each of the following to an equivalent form to compare their values.
$\frac{\text{1}}{\text{5}}$   0.4   65%   2$\frac{\text{3}}{\text{4}}$    5.75   $\frac{\text{9}}{\text{8}}$   123%

### Instructional Items

Instructional Item 1
How can $\frac{\text{3}}{\text{4}}$ be written as a decimal and as a percent?

Instructional Item 2
What is an equivalent fraction and decimal representation of 42%?

Instructional Item 3
Complete the following statement:
4$\frac{\text{2}}{\text{5}}$ is equivalent to ______ percent or can be written as the decimal _______.

*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.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 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))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.NSO.3.AP.5: Rewrite a positive rational number 3 or less, as a fraction, decimal or a percent.

## Related Resources

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

## 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

## 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

## Teaching Ideas

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

Calculating Sharks-SeaWorld Classroom Activity:

• Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems.
• Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph.
• Given the conversion factor, students will be able to convert from metric to English units.

Type: Teaching Idea

## Student Resources

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

## 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

## Parent Resources

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