6.N.1.4 Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.
In a Nutshell
Students have previous knowledge of converting between decimals, fractions and mixed numbers. Understanding that rational numbers can be written as a fraction or a decimal, and that both of these forms can be written as a percent (part of 100) is the basis of this objective. This is the first time students will work with percents. Decimals are the quotient of fractions (numerator divided by the denominator). Place value is used to convert a decimal to a fraction (Ex: 0.1 is “one tenth”, which is the fraction 1/10). By definition percents can be written as a fraction with 100 in the denominator and can then be converted to a decimal. Choosing the correct representation is key to solving problems involving fractions, decimals, and percents. For example, when asked to find a tip of 15% based on a total bill of $30.00, students would need to convert the percentage into a decimal before multiplying. Percents cannot be used in normal calculations and must be converted to an equivalent fraction or decimal first.
Student Actions

Teacher Actions


Develop the ability to communicate mathematically while representing decimal place values as fractions with denominators such as tenths, hundredths, thousandths.

Develop the ability to use various models to prove the equivalence of fraction, decimal, and percent representations of a single value.
 Develop accurate and appropriate procedural fluency by converting between any two representations of a rational number.


Use and connect mathematical representations (Ex: Hundredths grid or number line) to allow students to visually make the connection between the equivalencies among fractions, decimals, and percents.

Use evidence of student thinking of fractional division to convert fractions into decimals. Connect student understanding of percent as “out of 100” to fractions with a denominator of 100 (6.N.1.3).
 Pose purposeful questions about patterns and representations for equivalent fractions, decimals, and percents. (Ex: Which representation is most reasonable for an architect to use? Why?)

Key Understandings

Misconceptions


Understand equivalent decimals, fractions, and percents, and are able to fluently convert between each representation.

Identify benchmark fractions (Ex: halves, fourths, tenths,), decimals and percents without calculations.

Be able to choose the best representation to solve problems.


Think a percent represents a whole number.

Treat percents as whole numbers or may simply add a decimal point to the beginning or end of any percent. (Ex: Students may think 6%= .6 or 120%= 120.)

Get confused with mixed numbers when converting to percents or decimals.
 Not recognize that percents cannot be used in computations and must be converted first to a fraction or a decimal.

OKMath Framework Introduction
6th Grade Introduction
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