Cypher IV Mathematics Leadership Project

Teaching Student-Centered Mathematics Book Study 3-5 S5

Developing Fraction Concepts

(Re)Introductions 3-5 Group

Kendra Haines (Grades 5&6, Ross River) Jane MacArthur (Grades 4-6, Carcross) Lois Moore (Grades 4-5 Whitehorse) Pam Harry (Grades 3-4 Whitehorse) Sherry MacInnis (Grades 3-5, Atlin) Kalvin Beuerlein (Gr. 3-9, Telegraph

Creek) Mike Emerick (Gr. 7-8, Dease Lake)

Group Norms Be Responsible For How

& What You Learn Everyone brings prior

experience & knowledge. Take ownership of your learning by being on time and staying, doing the reading & reflection to prepare for discussion, and be willing to try out new ideas in your classroom.

Encourage Risk-Taking and Accept All Ideas When learning and

discussing, everyone needs to feel safe& that ideas will be respected, even if there is disagreement. Discussion of new ideas allows everyone to ? their own beliefs & discover new ways of thinking – an essential focus of this book study.

Group Norms - cont’d Be Your Own

Watchdog Monitor and manage

your participation to prevent contributing too much or too little.

Be An Attentive Listener Listen to each other

during the discussion. Turn off your e-mail and refrain from surfing the net during the sessions.

Homework Review (Small Group) Based on the homework

assigned in the previous session, discuss the following questions in a small group: What have you tried in

your classroom as a result of the last session?

What role did you play in the teaching and learning of math?

What role did the students play in their learning?

What discoveries did you and your students make?

What misconceptions, if any, surfaced about the topic? How did you redirect the students?

What suggestions do you have for others when they try this?

Objectives Focus on the Big Ideas for developing fraction

concepts Determine the meaning of the top and bottom

number in fractions Investigate parts-and-whole tasks Explore strategies to develop fraction number

sense Consider strategies to enhance a conceptual

understanding of equivalent fractions• Use Elluminate Live! with increasing ease

Materials Grade 3 Math IRP Pages 56-57

• Grade 4 Math IRP Pages 52-54• Grade 5 Math IRP Pages 53-54

• Grade 6 Math IRP Page 51• Grade 7 Math IRP Pages 51-53

Evaluation & Self-Assessment Form Frayer Model/Chart - Completed examples for

Differentiated Instruction and Quadrilateral

Before Connecting Fractions to Real Life

In a small group, discuss the following question: “When and where do we use fractions in our lives?”

Be prepared to share your ideas with the large group in about 7 minutes.

During - Big Ideas Review the Big Ideas

for this chapter (p. 131) for a couple of minutes.

Using the portions of the grades 3-5 IRPs: What grade level do

students begin to explore fraction concepts and what methods, if any, are suggested to facilitate this understanding?

Top and Bottom Numbers

Get into two groups Room 1 will complete the Frayer Model for

numerator Room 2 will complete the Frayer Model for

denominator Be prepared to share with the large group and also

consider:• How would you introduce the terms numerator and

denominator to your students in such a way as to promote understanding and not just memorization? (pp. 138-141)

F r a y e r M o d e l

D e f i n i t i o n i n y o u r o w n w o r d s F a c t s / c h a r a c t e r i s t i c s

E x a m p l e s N o n e x a m p l e s

W o r d

Parts-and-Whole Tasks

One way to help students strengthen their understanding of fractional parts and the meaning of the top and bottom numbers in a fraction is through exploring parts-and-whole tasks.

Parts-and-Whole Tasks (cont’d)

Given the whole and the fraction, find the part. If this rectangle is one whole,

• find one-fourth• find two-thirds• find five-thirds

Parts-and-Whole Tasks (cont’d) Given the part and the fraction, find the

whole. If the red Cuisinaire rod is one-third, what rod

is the whole? If the dark green is two-thirds, what rod is the

whole? If yellow is five-fourths, what strip is one

whole?

QuickTime™ and a decompressor

are needed to see this picture.

Parts-and-Whole Tasks (cont’d)

Given the whole and the part, find the fraction. If 10 counters are the whole set, what

fraction of the set is 6 counters? 16 counters are what fraction of a whole set

of 12 counters?

Easter Egg Fractions

http://illuminations.nctm.org/LessonDetail.aspx?ID=U112

Parts-and-Whole Tasks (cont’d)

In groups of 3: How would you present questions such as

these to your students? Which questions are the most challenging?

Why? What other types of activities could you use

with students to further develop these relationships?

Fraction Number Sense

Students need to develop fluency and flexibility with fraction number sense just as they do with whole numbers. Number sense with fractions requires that students have a sense of the approximate size of fractions and be able to easily tell which of two fractions is larger.

Fraction Number Sense (cont’d)

Work through the instructions in the Stop and Reflect box (p. 147).

Do not use: equivalent fractions common denominators cross multiplication

to find answers.

In partners, share your explanations for each answer.

Fraction Number Sense (cont’d) As a large group, let us review the four

conceptual thought patterns for comparison (p. 147).

Be prepared to share how your reasoning for selecting the larger fraction compares to these four ideas. Remember that these four methods for comparing

fractions should not be taught to students directly, but should be developed through student exploration.

Fraction Number Sense (cont’d) In two groups, discuss the following questions:

How does an understanding of the meaning of the top and bottom numbers in a fraction help students to develop fraction number sense?

How do reference points of 0, half, and 1 help students to develop fraction number sense?

What activities could you use with students to develop these concepts?

Equivalent Fraction Concepts

Think of at least two different reasons for how you know that

Reread Concepts versus Rules (p. 151) to discuss: “All students should eventually be able to write an

equivalent fraction for a given fraction. At the same time, the rules should never be taught or used until the students understand what the result means” (p. 151).

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4

6=

2

3

After

In small groups, develop a Top Ten List for developing fractional concepts with students. Record you list and be prepared to share with the large group.

After - Round-table Sharing Reflect Stems

I feel good about… I used to… but now I… My goal is… I will know I am on my way when… One thing that worked today was… One question I have… Two things I remember are… If I could do something again differently, I would…

After - Evaluation & Self-Assessment Form

Please take a few minutes to complete the evaluation & self-assessment form at this time and e-mail it to me at Paula.Thompson@yesnet.yk.ca or fax to 867-393-6339.

After - Homework

Try some of the fraction activities from this chapter with your students and be ready to share your experiences at the next session.

Read Chapter 7, Decimal and Percent Concepts and Decimal Computation (pp. 181-203)