1. Developing Fractions Concepts
Chapter 15
Developing Fractions Concepts

2. Fractions structures There are several types of fractions structures
Part-Whole – Most Common
Example: 3/5 of the class went to the movies
Measurement – Identifying a length and then using that length as a measurement piece to determine the length of an object
Example: Use a ¼ cup scoop and measure that a container is about 5 scoops or 5/8 of a cup.
Division – Where the fraction is directly tied to the division operation
Suppose you have 12 dollars and you are going to share equally among 5 friends. Each friend gets 12/5 dollars or 2 and 2/5 dollars = $2.40.
Operator – Where fractions are directly tied to a multiplication like operation on the given unit
Example: I will leave 2/5 of my salary to my oldest daughter. Here the 2/5 is operating on my salary. Lucky daughter.
Ratio – Ratios can be part-part or part-whole
Example: ¾ could represent 3 people wear a jacket for every 4 that don’t or it could represent 3 people wear a jacket for every 4 people. You should probably run through the first example in your mind several times to verify it “clicks.”

3. Fractions
Make sure you read the section “Why Fractions Are So Difficult” in Chapter 15.
Note that fractions do not say anything about the size of the parts or the size of the whole.
They only tell us about the relationship between the part and the whole.
Question: What is 2/5 really?
Mark gets 1/2 of a pizza and Jane gets 1/3 of a pizza. He chooses ½ because he likes pizza, but is upset when he learns that Jane received more pizza. What happened?

4. Fractions
One must understand that fractions require an understanding of 3 key ingredients
1. The numerator indicates the counting number. It tells how many shares or parts we have or are considering.
2. The denominator indicates what exactly is being counted. More specifically, it tells us how many shares or parts make up the whole.
3. IMPORTANT: The first two items are no enough to define a fraction. One must also specify whole or unit. Connect this back to the pizza example.
Activity: Use the pattern blocks to represent 2/3 where one representation of 2/3 is necessarily different than the other representation of 2/3. What must have changed? Then do the same activity with 5/3.