Fractions, Decimals and Percents Mini-course Session Four

Objectives To use Cuisenaire Rods as a manipulative for illustrating fraction concepts. To explore the fraction concepts of equivalence, unit and non – unit fractions, and reciprocals. To introduce the NCTM Communication Standard.

NCTM Communication Standard Instructional programs P-12 should enable all participants to: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Analyze and evaluate the mathematical thinking and strategies of others.

Homework Discussion Each group should write a solution to one problem on a flip chart. Volunteers can share the solutions with the class. Hmm, does that mean we’re using the NCTM standard from previous slide?

Cuisenaire Rods Cuisenaire rods are another manipulative we can use to develop understanding of fractions. With a partner figure out one way you might use Cuisenaire rods to represent fractions. Share your ideas with the group.

Measuring Map Activity The relative rods build a stair step pattern. Use the Cuisenaire rods to measure relative distances. If brown rods are placed along the entire route, then the police station is 1/3 of the way from my house to my school and the Burger Barn is 2/3 of the way from my house to my school. Write these fractions next to their place names on your list. Work with a partner to complete BLM 21 & 22

BLM 22

Defining Fractional Rod Relationships Work with a partner and find as many fractional relationships as possible using the Cuisenaire rods. e.g. red is ½ of purple. _________ is ½ of__________ _________ is 1/3 of _________ _________ is ¼ of___________

Fractional Rod Relationships When the smaller lengths fit evenly into the larger lengths, these are considered unit fractions. Now consider: Light green is________ of brown Find rods that divide brown and green evenly to solve this relationship. Purple is __________ of orange. Can you think of two different ways (equivalent fractions) to express the purple vs orange?

Challenge your partner Have one partner to take out any two different rods. Have other partner compare rods and describe what fraction the smaller rod is of the larger one. Trade roles a few times back & forth.

Volunteers to demonstrate solutions? BLM 23 Volunteers to demonstrate solutions?

A new challenge What happens when a LARGER rod is compared to a SMALLER rod? Recall that yellow is ½ of orange. => Orange is ________ of yellow. Recall purple is 2/5 of orange. => Orange is _______ of purple.

Challenge your partner, AGAIN Have one partner to take out any two different rods. Have other partner compare rods and describe what fraction the smaller rod is of the larger one, AND what fraction the larger rod is to the smaller one! Trade roles a few times back & forth. This activity demonstrates the term Reciprocal.

Reflection Reflect on the experience of learning or re- learning fractions using manipulatives. Discuss with a partner how your children might benefit by learning fractions through manipulatives and group work. Share your reflection with the class. Bringing it Home Activity 4 & Fraction III