Chapter 14 - Exploring Early Fraction Concepts
Meanings of Fractions for PreK-2 Children
Part-Whole
ONe of the most commonly used meanings of fractions
Early childhood classrooms, typically represented by shading part of a whole that been partitioned into equal parts
Can be effective starting point for building meaning of fractions
Equal Sharing
Idea that young children understand intuitively because o thief experiences sharing things with brothers, sisters, friends, and so on
Can involve continuous or discrete quantities
It is best to use story problems that have whole-number solutions with no remainders when using discrete quantities
Measurement
Linear measurement involves identifiying a length and then using that length as a measurement piece to determine the length of an object
Measurement also includes time; most obvious place to relate is when telling time to the half hour and quarter hour
By their very nature consist of measuring a quantity that we could cut into as many equal-sized pieces as we need and so solve continuous quantities
Introducing Fraction Language
Faction symbolism represents a fairly complex convention that can be misleading to children
A good time to introduce the vocabulary of factional parts is during the discussions of children’s solutions to story problems and not before
Two aspects of fractional parts: the number of parts and the equality of the parts
Medals for Fractions
The effective use of visuals in fraction tasks is important in building children’s understanding
Area Models
One advantage of the circular model is that is emphasizes the part-whole concept of fractions and so are good for intro activities
What is being compared is the area of the part to the area of the whole
Length Models
With length models, lengths or linear measurements are compared instead of areas
Set Models
Whole in a set model is understood to be group of objects, and subsets of the whole make up fractional parts
A challenge with set models is that children may focus on the size of the subset rather that the number of equal-sized subsets in the whole
Building Fractional Parts through Partiting and Iterating
Partitioning
Can be thought of as splitting or cutting a quantity equally
Sharing tasks are a good place to begin the development of fractions
Allows children to develop concepts of fractions from an activity that make as sense to them
Iterating
Children should come to think of counting fractional parts in much the same way they might count apples or any other objects
Counting fractional parts to see how multiple parts compare to the whole helps children to understand the relationship between the parts and the whole
Children should engage in counting by fractional amounts to reinforce that fractions are numbers
Fraction Size is Relative
A fractional tells only about the relationship between the part and the whole
Fraction Equivalence and Comparison
Look for opportunities when children are solving equal-sharing story problems in which they have what appear to be different answers but which are actually equivalent amounts
Once children are successful with equal sharing problems over an extended period of time (months, not days), you can pose situations where children compare fractional amounts
From Fracition Words to Symbols
The way we write fractions symbolicallys is a convention— an arbitrary agreement for how to represent frations
Write fractions with a horizontal bar, not a slanted one. It is easier for children to ell which is the numerator and which is the denominator
Teaching Comnsiderations for Fraction Concepts
ONe reason fractions are not well understood is that there is a lot to know about them
Give greater emphasis to variety of meaning of fractions, moving beyond part-whole understanding
Incorporate a variety of models and contexts to represent fractions
Emphasize that fractions are numbers, making use of measurement contexts and number lines in representing fractions
Spend whatever time is needed for children to understand equivalences, inflicting flexible naming of fractions
Iterating and portioning must be significant aspect of Fraction instruction