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.

A) _________ is ½ of__________

B) _________ is 1/3 of _________

C) _________ 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.

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