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

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

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

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

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

Ordering Fractions Number Lines

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

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

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.

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

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)

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