1. By: Ryan Killian and Therese Cibula
Teaching Fractions
By: Ryan Killian and Therese Cibula

2. Introduction to Fractions
Partitioning and Equivalence
Partitioning – sharing equally (ex: sharing a pizza among eight people means partitioning the pizza into eight pieces)
Equivalence – different representations of the same amount (ex: three-fourths is the same as six-eighths)
Decimals – a notation for fractions
Fractions can represent any partitioning
Decimals can represent partitions of only tenths and powers of tenths
Real World Application
Fractions are important in daily life and necessary for further study in mathematics =
Different representations of the same amount
Real World Use of Fractions

3. Three Meanings of Fractions
Part-Whole – a whole has been separated into equal parts (ex: the fraction 1/8 represents that a whole has been separated into 8 equal amounts)
Region
The region represents the whole – it is easiest to use a shape and best to use a variety of shapes
Length
Units of length can be partitioned into fractions (ex: students can fold paper into halves, fourths, eighths, and so on)
Set
Ex: Using a deck of cards divide a deck of cards equally among four students – students will see that all of their parts make a the complete set
1/4
1/4
1/4
1/4

4. Three Meanings of Fractions
Quotient
Result of a mathematical process
Ex) There are 200 M&Ms and 20 students how many M&Ms will each student have?
Ratio
Conceptually different from part-whole and quotient
Ex) There are 12 Boys and 8 Girls in a class (12:8) = (3:2)
There are 3 Boys to every 2 Girls
12/20 students are boys and 8/20 students are girls
3/5 of students are boys
2/5 of students are girls

5. Fractions
Partitioning – making equal shares by separating a whole into equal parts
Ex) Each student could be given a candy bar or a piece of paper in place of a candy bar. Have students break apart the candy bar or fold the piece of paper to represent how they would divide it so each student receives the same amount – this is partitioning
Words
Halves – 1/2
Thirds – 1/3
Fourths – 1/4
Fifths – 1/5
Sixths – 1/6
Sevenths – 1/7
Eighths – 1/8
Ninths – 1/9
Tenths – 1/10
Counting
After students learn fractional terms they can begin the counting process
This can lead to questions about ordering and equivalent fractions – Which is more 3/5 or 4/6?
Using fraction bars is another way to count fractions – fraction bars could consist of thirds, fourths, fifths, sixths, etc. If using a fourths bar, students would label each box and count one-fourth, two-fourth, three- fourths, etc.
Using a ruler could be an excellent way to fractions in comparison with each other

6. Ordering Fractions
Number Lines

7. Mixed Numbers and Improper Fractions
Mixed Number – a whole number and a fraction – Ex) 4¾
Improper Fractions – a fraction greater than one – Ex) 9/6
The picture below will help students see that 2 2/3 is equivalent to 8/3
Models should be used as much and students should write both the improper fraction and the mixed number

8. Addition and Subtraction
Allow students to see that adding fractions is similar to adding whole numbers. Ex) ¼ + 2/4 = ¾
Give students the opportunity to see why it is necessary to add with a common denominator
Step 1 – Find a common denominator – the denominator must be the same before adding fractions – Ex) 1/3 + 2/4
Step 2 – Add the top number the numerators: 4/12 +6/12
Step 3 - Simplify the fraction: 10/12 – is simplified to 5/6

9. Addition and Subtraction
Similar to addition subtracting fractions is similar to subtracting whole numbers
Must have a common denominator
There are 3 simple steps to subtract fractions
Step 1. Make sure the bottom numbers (the denominators) are the same
Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator.
Step 3. Simplify the fraction.

10. Multiplication There are 3 simple steps to multiply fractions
1. Multiply the top numbers (the numerators).
2. Multiply the bottom numbers (the denominators).
3. Simplify the fraction if needed

11. Division There are 3 Simple Steps to Divide Fractions:
Step 1. Turn the second fraction (the one you want to divide by) upside-down (this is now a reciprocal).
Step 2. Multiply he first fraction by that reciprocal
Step 3. Simplify the fraction (if needed)

12. Decimals
Students must identify that .3 and 3/10 are the same number and are pronounced three-tenths