Third Grade Mathematics
Unit 5
Equivalence and Comparing Fractions

Printable Parent Letter

During Unit 5, your children will build the understanding that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Your children will use fractions to represent numbers equal to, less than, and greater than one.  They will solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.  Your children will apply their knowledge of fractions by using rulers to measure to the nearest fourth of an inch.  They will organize their measurement data on a line plot.
 

Students need to:

  • Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
     
  • Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
     
  • Recognize and generate simple equivalent fractions, e.g., ½=2/4, 4/6=2/3).  Explain why the fractions are equivalent, e.g., by using a visual fraction model.
     
  • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.  Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
     
  • Compare two fractions with the same numerator or the same denominator by reasoning about their size.  Recognize that comparisons are valid only when the two fractions refer to the same whole.  Record the results of comparisons with the symbols >,=, or <, and justify the conclusions, e.g., by using a visual fraction model.
     
  • Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
     
  • Show the data by making a line plot, where the horizontal scale is marked off inappropriate units- whole numbers, halves, or quarters.  (X’s or dots can be used to plot the data.)

Carroll County Public Schools Video Support


Equivalent Fractions


Express a Whole Numbers as a Fraction


Comparing Fractions with Number Lines


Comparing Different Size Wholes
 

Ways Parents Can Help

  • When cooking, explore the concept of equivalent fractions when measuring ingredients.  For example, use two one-fourth measurements to equal a one-half measurement or three one-third measurements to equal one whole measurement.
  • Explore the concept of equivalent fractions when measuring length with a ruler.  For example, two-eighths of an inch is equivalent to one-fourth of an inch.
  • Compare fractional amounts when they have the same numerator or the same denominator.  For example, one-fourth of an inch is less than three-fourths of an inch; one-half of a cup is greater than one-third of a cup.
  • Use chalk on the driveway to create the “key” on a basketball court or hopscotch board with specific measurements.  Simply draw some lines on the driveway for your child to measure to the nearest ½ inch.
  • Take weekly measurements of the plants/flowers that are beginning to grow in your garden. Record the measurements in a chart.
  • Ask your child to grab a handful of string beans, potatoes, or carrots.  Have him/her measure to the nearest ¼ inch and record the data on a line plot.

Some Support Sites

 

 

 

Key Vocabulary to Know

Fraction:  A number that represents one or more equal parts of a whole

Unit fraction: A fraction in which its numerator is 1 and its denominator is a whole number

Numerator:  The number of parts one selects from the whole

Denominator:  The number of parts the “whole” is partitioned into

Halves:  either of two equal parts into which a whole can be partitioned

Fourths:  one or more of four equal parts into which a whole can be partitioned

Sixths:  one or more of six equal parts into which a whole can be partitioned

Eighths:  one or more of eight equal parts into which a whole can be partitioned

Tenths:  one or more of ten equal parts into which a whole can be partitioned

Thirds:  one or more of three equal parts into which a whole can be partitioned

Equivalent: having the same value or amount

Compare:  to examine in order to note similarities and differences

Unit interval:  on a number line, it is the whole that is the interval from 0 to 1, as measured by length

Interval: distance between two points

Inch: customary unit for measuring length

Length: the measure of the greatest dimension of anything measured from end to end

Line Plot: A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line.