Using Fraction Tiles www floridaipdae org 2015 The

Using Fraction Tiles www. floridaipdae. org 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles A linear model gives an overview and shows relationships. 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles How many fourths in a whole? How many sixths? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles What is more, 1/4 or 1/3? What is more, 1/9 or 1/10? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles What is more, 1/4 or 1/3? What is more, 1/9 or 1/10? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles Which is more, 3/4 or 4/5? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles Which is more, 3/4 or 4/5? Which is more, 7/8 or 8/9? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles The pattern of 1/2, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10. 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles How many fourths equal a half? Eighths? Sevenths? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles How many fourths equal a half? Eighths? Sevenths? 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles What is half of a half? That’s multiplying fractions. 2015 The Institute for the Professional Development of Adult Educators

What is a fraction? A fraction is part of a set or part of a whole. textbook definition What about 3 2 ? Another common meaning of fraction is fragment or a small part. 2015 The Institute for the Professional Development of Adult Educators

What is a fraction? 3 means three 2 1 1 s or 3 ÷ 2. 2 1 2 1 1 2015 The Institute for the Professional Development of Adult Educators

Fraction Tiles 9/8 is 1 plus 1/8 2015 The Institute for the Professional Development of Adult Educators *

Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 23 4 11 two 4 s + 3 = 11 How did you find the 11? 2015 The Institute for the Professional Development of Adult Educators

Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 23 4 11 two 4 s + 3 = 11 four 3 s + 2 = 14 2015 The Institute for the Professional Development of Adult Educators

Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 23 4 11 four 5 s + 3 = 23 two 4 s + 3 = 11 four 3 s + 2 = 14 2015 The Institute for the Professional Development of Adult Educators

Improper to Mixed Fractions Circle the wholes and write each quantity as an improper fraction and as a mixed number. 2015 The Institute for the Professional Development of Adult Educators

Improper to Mixed Fractions Circle the wholes and write each quantity as an improper fraction and as a mixed number. The correlation to division becomes obvious here. 2015 The Institute for the Professional Development of Adult Educators

Improper to Mixed Fractions Circle the wholes and write each quantity as an improper fraction and as a mixed number. The correlation to division becomes obvious here. 2015 The Institute for the Professional Development of Adult Educators

Fractional Parts of Geometric Figures 1 2 2 3 1 4 2015 The Institute for the Professional Development of Adult Educators

Fractional Parts of Geometric Figures 1 2 2 3 1 4 2015 The Institute for the Professional Development of Adult Educators

Fractional Parts of Geometric Figures 1 2 2 3 1 4 2015 The Institute for the Professional Development of Adult Educators

Fractional Parts of Geometric Figures 1 2 2 3 1 4 A study showed that many students and adults thought this was impossible. 2015 The Institute for the Professional Development of Adult Educators

Dividing 100 3313 25 100 50 25 3313 25 50 3313 25 1212 1212 10 10 10 2015 The Institute for the Professional Development of Adult Educators *

Simplifying Fractions 1 2 2015 The Institute for the Professional Development of Adult Educators

Simplifying Fractions 3=1 6 2 2015 The Institute for the Professional Development of Adult Educators

Simplifying Fractions 4=1 8 2 2015 The Institute for the Professional Development of Adult Educators

Simplifying Fractions 9 3 = 12 3 4 Writing the common multiple in a circle, in this example, 3, helps students remember what they’re dividing by. 2015 The Institute for the Professional Development of Adult Educators

Simplifying Fractions 21 28 45 72 The fraction 4/8 can be reduced on the multiplication table as 1/2. 2015 The Institute for the Professional Development of Adult Educators

Simplifying Fractions 12 16 2015 The Institute for the Professional Development of Adult Educators *

Subtracting Fractions 4 3 – 5 2 35 – – 1 57 5 27 3 4 7 3 27 2015 The Institute for the Professional Development of Adult Educators *

Multiplying Fractions 1 x 1 = 2 2 The square represents 1. 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 1 x 1 = 2 2 We are thinking 1/2 of 1/2. First find 1/2 of it vertically. 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 1 x 1 =1 2 2 4 Now find 1/2 of it horizontally. The solution is the double crosshatched area. 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 2 x 3 = 3 4 Another example. 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 2 x 3 = 3 4 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 2 x 3 = 3 4 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 2 x 3 =6 =1 3 4 12 2 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 2 x 3 = 3 4 The total number of of rectangles is 3 x 4. 2015 The Institute for the Professional Development of Adult Educators

Multiplying Fractions 2 x 3 = 3 4 The total number of rectangles is 3 x 4. The number of double crosshatched rectangles is 2 x 3. That’s why to multiply fractions, we multiply the numerators and the denominators. 2015 The Institute for the Professional Development of Adult Educators

Dividing Fractions 1 ÷ 12 = 2 2 sets of ½ = 1 1 ÷ 13 = 3 3 sets of 1/3 = 1 1 ÷ 23 = 32 1 set of 2/3 plus 1/2 of another set of 2/3 = 1 The third problem can be thought of as how many 2/3 s are in 1 or half of 1 ÷ 1/3. 2015 The Institute for the Professional Development of Adult Educators

Dividing Fractions 1 ÷ 12 = 2 1 ÷ 3 = 13 1 ÷ 13 = 3 1 ÷ 4 = 14 1 ÷ 23 = 32 1 ÷ 43 = 34 1 3 1 ÷ 3 is simply the definition of a fraction. Notice the pattern. 2015 The Institute for the Professional Development of Adult Educators

Dividing Fractions Find 2 ÷ 34 = __ 1 1 1 4 1 4 2 sets of ¾ plus 2 of the 3 needed for the next set = 2 2/3 2015 The Institute for the Professional Development of Adult Educators 1 4

Dividing Fractions To find 2 3 3 ÷ 4 = __ (Is the answer more or less than 1? ) Another example: How many 3/4 s are in 2/3? 2015 The Institute for the Professional Development of Adult Educators

IPDAE 2015 The Institute for the Professional Development of Adult Educators