Gr 3-5 A look at fractions

Fraction Understanding What do you notice about the strips of paper?

Fraction CharacteristicsDescription ExamplesNon-examples

Fraction Kits Cutting the fraction strips 1 whole unit 1/2 How can we cut the next strip so we know that it will be in three equal pieces?

1 whole unit 1/2 1/3 1/4 1/6 1/8

Questions What do you notice as we are cutting the strips? Are all one-fourth pieces in our life exactly the same size? Which is bigger ¾ or 5/6? How do you know. Who can ask another “Which is bigger” question? What fractions are the same length as a ½? Can you find other groups of fractions that are the same length?

Comparing Fractions Can you always tell which fraction is bigger if you compare two fractions with the same numerator? How about comparing fractions that have the same denominator?

Creating a numberline Add a triangular piece of construction paper to each end of another strip of paper to simulate a number line. Place the number line strip below the two half strips. Mark ½ on the number line Place the number line strip below each strip and mark on the number line hash marks to indicate 1/3, ¼, 1/6, 1/8

Game of Cover up The game is for 2 or more players. Each player starts with their whole strip. The goal is to cover up the whole strip completely with other pieces of their fraction strips. No overlapping is allowed. 1.Players take turns rolling the dice labeled with fractions 2.The fraction face up on the cube tells what size piece to place on the whole strip 3.When the games nears the end and a player needs only a small piece such as 1/8, rolling a ½ or ¼ won’t do. The student must roll exactly what is needed. 4.Keep going until all players cover their whole strip keeping track of who comes in first, second, etc. 5.Each player should record how they covered their whole. taken from About Teaching Math 3rd Edition by Marilyn Burns, pp

Introducing notation After the cover up game introduce the notation beyond unit fractions by having students report out how they covered their whole strip. Write the equation as dictated by the student. Ex. 1/8 + 1/8 + ¼ + 1/8 + ¼ + 1/8 = 1 Count up how many one eighths you have and how many one- fourths and shorten the equation to 4/8 + 2/4 = 1

Uncover Game Provides experience with equivalent fractions: 1.Before the game begins each player places their two ½ pieces on top of their whole piece 2.A player has 3 options on each turn/roll: 1.To remove a piece (only if he has a piece the size indicated by the fraction face-up on the cube), 2.to exchange any of the pieces left for equivalent pieces, 3.or to pass the cube to the next player. (A player may not exchange pieces and remove on the same turn, but can do one or the other. All players need to check that each other trades correctly. 4.The person to clear their whole strip first wins taken from About Teaching Math 3rd Edition by Marilyn Burns, pp

Doing operations using fraction strips The fraction strips (kit) can be used to illustrate operations. Have a discussion with your partner about how this might be done Fraction kits can be stored in a business size envelope. The whole unit strip can be folded in half and will fit perfectly in the envelope. It is recommended that students put their initials on the back of each of their pieces and their name on the envelope.

Let’s look at the CCSSM Turn to the 3-5 th grade Operations and Algebraic Thinking – Fractions in your CCSSM document Which of these standards did we experience in the activities just completed? Make record of them and check with your table mates.

Electronic versions of fraction strip activities Fraction Bar Applet Ahttp://ejad.best.vwh.net/java/fractions/fractions.html Fraction Tracks Game Fraction Tracks Game for two players taken from NCTMs Illuminations website

Multiple sticks – fraction sticks What patterns do you see in your Multiple Sticks handout? Cut strips apart Cover-up one of the strips. What number comes next? Before? What if we use two of them? Align Underlined numbers. What do you notice? ¾ and 5/6? Which is greater? How do you know? Compare fractions with same numerator, same denominator Multiple sticks created by Dr. Edna Bazik National Louis University

Reflections What were the big ideas in this session? How can I implement the ideas from this session? What do I still need?