Math  201718
6.2abc and *6.2a  Fraction, Decimal, Percent Equivalence (No Calc)
6.2 The student will
a) investigate and describe fractions, decimals and percents as ratios;
b) identify a given fraction, decimal or percent from a representation;
c) demonstrate equivalent relationships among fractions, decimals, and percents (NO CALCULATOR);;
6.2 The student will (with NO CALCULATOR)
a) represent and determine equivalencies among fractions, mixed numbers, decimals, and percents;*
Bloom's Level: Remember, Understand, Analyze
BIG IDEAS
 I can determine the best buy when items are onethird off, 40% off or $50 off, find sale costs while shopping, create a budget, dilute mixtures, understand scales on maps, interpret probabilities and odds, and convert among metric units.
 I will be able to interchange fraction, decimal, and percent values to
interpret real world situations.
UNDERSTANDING THE STANDARD
 Percent
means “per 100” or how many “out of 100”; percent
is another name for hundredths.
 A number followed by a percent symbol (%) is
equivalent to that number with a denominator of 100 (e.g., 30% = 30/100 = 3/10 = 0.3).
 Percents can be expressed as fractions with a
denominator of 100 (e.g., 75% = 75/100 = 3/4).
 Percents can be expressed as decimal (e.g., 38% = 38/100 = 0.38).
 Some fractions can be rewritten as equivalent fractions with denominators of powers of 10, and can be represented as decimals or percents (e.g., 3/5 = 6/10 = 60/100 = 0.60 = 60%).
 Decimals, fractions, and percents can be
represented using concrete materials (e.g., Base10 blocks, number lines, decimal
squares, or grid paper).
 Percents can be represented by drawing shaded
regions on grids or by finding a location on number lines.
 Percents are used in real life for taxes, sales,
data description, and data comparison.
 Fractions, decimals and percents are equivalent
forms representing a given number.
 The decimal point is a symbol that separates the
whole number part from the fractional part of a number.
 The decimal point separates the whole number
amount from the part of a number that is less than one.
 The symbol can be used in Grade 6
in place of “x” to indicate multiplication.
 Strategies using 0, 1/2 and 1 as benchmarks
can be used to compare fractions.
 When comparing two fractions, use 1/2 as a benchmark.
Example: Which is greater, 4/7 or 3/9?
4/7 is greater than 1/2 because 4, the numerator, represents more than half of 7, the denominator. The denominator tells the number of parts that make the whole. 3/9 is less than 1/2 because 3, the numerator, is less than half of 9, the denominator, which tells the number of parts that make the whole. Therefore, 4/7 > 3/9.  When comparing two fractions close to 1, use
distance from 1 as your benchmark. Example: Which is greater, 6/7 or 8/9? 6/7 is 1/7 away from 1 whole. 8/9 is 1/9 away from 1 whole.
Since 1/7 > 1/9, then 6/7 is a greater distance
away from 1 whole than 8/9 so 8/9 > 6/7.
 Students should have experience with fractions such as 1/8, whose decimal representation is a terminating decimal (e. g., 1/8 = 0.125) and with fractions such as 2/9, whose decimal representation does not end but continues to repeat (e. g., 2/9 = 0.222…). The repeating decimal can be written with ellipses (three dots) as in 0.222… or denoted with a bar above the digits that repeat as in 0.2.
2016 VDOE Curriculum Framework  6.2 Understanding
 Example: The ratio of dogs to the total number of pets at a grooming salon is 5:8. This implies that 5 out of every 8 pets being groomed is a dog. This parttowhole ratio could be represented as the fraction ( of all pets are dogs), the decimal 0.625 (0.625 of the number of pets are dogs), or as the percent 62.5% (62.5% of the pets are dogs).
· Fractions, decimals, and percents are three different ways to express the same number. Any number that can be written as a fraction can be expressed as a terminating or repeating decimal or a percent.
· Equivalent relationships among fractions, decimals, and percents may be determined by using concrete materials and pictorial representations (e.g., fraction bars, base ten blocks, fraction circles, number lines, colored counters, cubes, decimal squares, shaded figures, shaded grids, or calculators).
· Percent means “per 100” or how many “out of 100”; percent is another name for hundredths.
· A number followed by a percent symbol (%) is equivalent to a fraction with that number as the numerator and with 100 as the denominator (e.g., 30% = = ; 139% = ).
· Percents can be expressed as decimals (e.g., 38% = = 0.38; 139% = = 1.39).
· Some fractions can be rewritten as equivalent fractions with denominators of powers of 10, and can be represented as decimals or percents (e.g., = = = 0.60 = 60%). Fractions, decimals, and percents can be represented by using an area model, a set model, or a measurement model. For example, the fraction is shown below using each of the three models.
· Percents are used to solve practical problems including sales, data description, and data comparison.
· The set of rational numbers includes the set of all numbers that can be expressed as fractions in the form where a and b are integers and b does not equal zero. The decimal form of a rational number can be expressed as a terminating or repeating decimal. A few examples of positive rational numbers are, , 82, 75%, .
· Students are not expected to know the names of the subsets of the real numbers until grade eight.
· Proper fractions, improper fractions, and mixed numbers are terms often used to describe fractions. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is equal to or greater than the denominator. An improper fraction may be expressed as a mixed number. A mixed number is written with two parts: a whole number and a proper fraction (e.g., 3 ).
· Strategies using 0, and 1 as benchmarks can be used to compare fractions.
 Example: Which is greater, or ? is greater than because 4, the numerator, represents more than half of 7, the denominator. The denominator tells the number of parts that make the whole. is less than because 3, the numerator, is less than half of 9, the denominator, which tells the number of parts that make the whole. Therefore, > .
· When comparing two fractions close to 1, use the distance from 1 as your benchmark.

Example:
Which is greater, or ? is away from 1 whole. is away from 1 whole. Since,
, then is a greater distance away
from 1 whole than . Therefore, .
·
Some
fractions such as , have a decimal representation that is a terminating decimal
(e. g., ) and some fractions such as , have a decimal representation that does not terminate but
continues to repeat (e. g., = 0.222…). The repeating
decimal can be written with ellipses (three dots) as in 0.222… or denoted with
a bar above the digits that repeat as in .
ESSENTIALS
 What
is the relationship among fractions, decimals and percents?
Fractions, decimals, and percents are three
different ways to express the same number.
A ratio can be written using fraction form ( ), a colon (2:3), or the word to (2 to 3). Any number that can be written as a fraction
can be expressed as a terminating or repeating decimal or a percent.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
6.2a_{1} Identify the decimal and percent equivalents for numbers written in fraction form including repeating decimals.
· 6.2a_{2 } Determine the decimal and percent equivalents for numbers written in fraction form (proper or improper) or as a mixed number, including repeating decimals.
6.2b_{1} Represent fractions, decimals, and percents on a number line.
6.2b_{2} Represent, by shading a grid, a fraction, decimal, and percent.
6.2b_{3} Represent in fraction, decimal, and percent form a given shaded region of a grid.
· 6.2a_{1} Represent ratios as fractions (proper or improper), mixed numbers, decimals, and/or percents.
6.2c_{1} Describe orally and in writing the (No Calc) equivalent relationships among decimals, percents, and fractions that have denominators that are factors of 100.
· 6.2a_{3} Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100.
KEY VOCABULARY
fraction, decimal, percent, numerator, denominator, equivalent, represent, compare, repeating decimal, terminating decimal, ascending, descending