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Chapter 12 - Exploring Fraction Concepts (Teaching Considerations for…
Chapter 12 - Exploring Fraction Concepts
Meanings of Fractions
Fraction Interpretations
The unit must be thought about to interpret all the possible concepts that fractions represent
Part-whole is effective starting point for building meaning of fractions. Circle is effective in illustrating part-whole relationship
Measurement involves identifying an amount of a continuous unit (length, area, volume or time) then comparing to a whole unit equal to 1
Division links directly to equal shares. Division is often not connected with fractions which is unfortunate
Fractions can be used to indicate an operation. the operation changes the scale or scale through multiplication
Ratios come into play during grade 6. a ratio expresses a relationship between 2 quantities and compares their relative measures or counts
Why Fractions Are Difficult
Fractions are difficult when students misapply whole-number thinking to solve fraction situations.
Models for Fractions
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
Fractional Parts of a Whole
Fraction size is relative
A fractional tells only about the relationship between the part and the whole
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
Equivalent Fractions
Equivalent-Fraction Models
start with a context and physical models is a perfect starting point helping students create an understanding of equivalent fractions
Area models for equivalent fractions are useful when dot paper is used
Developing an Equivalent-Fraction Algorithm
when students understand that fractions can have different but equivalent, they are ready to develop a method for finding equivalent names for a particular value
Comparing Fractions
Using Number Sense - "how students can work meaningfully with fractions if they do not have a sense of the relative size of the fractions is difficult to imagine
when students are examining whether two fractions are equivalent, they are comparing them
Students often have misconceptions about fractions and therefore aren't able to accurately compare
Find common denominators and use cross-multiplication
Teaching Considerations for Fraction Concepts
1 - Give greater emphasis to number sense & meaning of the fractions, rather than procedures for manipulating them
2 - Provide a variety of physical models & contexts to represent fractions
3 - Emphasize fractions are numbers, making use of number lines to represent fractions
4 - Spend whatever time is needed for students to understand equivalences
5 - Link fractions to key benchmarks & encourage estimation