Cypher IV Mathematics Leadership Project

Teaching Student-Centered Mathematics Book Study 5-12 S3

Fraction Concepts & Computation

(Re)Introductions 5-12 Group Emily Macht (Grade 6, Whitehorse) Sheila Merkley (Grades 8-11, Whitehorse) Rea Postoloski (Grades 7-9, Teslin) Jean MacLean (Grades 8-12, Watson Lake) Rollie Comeau (Mathematics Teacher, Watson Lake) Nicholle Ingalls (Grades 5-6, Watson Lake) Camille Luks (Essential Skills Development, Whitehorse) Rob McGurk (Transitions Teacher, Whitehorse) Kalvin Beuerlein (Grades 3-9, Telegraph Creek) Amy Hes (Grades 6-9, Telegraph Creek) Sarah Baigent-Nixon (Grades 6-9 Teacher, Atlin) Trygve Sort (Grades 5-6, Dease Lake) Asa Berg (Stikine School District Local 87 Union President, Atlin) Bev Fairful (Principal, Atlin)

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 and computation Determine the meaning of the top and bottom

number in fractions Explore strategies to develop fraction number

sense Consider strategies to enhance a conceptual

understanding of equivalent fractions Develop a problem-based, number sense approach

to fraction computation• 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? (3-5, pp. 138-141, 5-8, pp. 67-69)

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

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) The Weird Number

http://www.guidanceassociates.com/weirnumfrac.html (Teaching Ideas)

http://www.ciese.org/ciesemath/number_town.html (Video in Quick Time)

http://letsplaymath.net/2011/03/13/the-weird-number/ (YouTube)

Fraction Number Sense (cont’d)

Work through the instructions in the Stop and Reflect box (3-5, p. 147, 5-8, p. 76).

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 (3-5, p. 147, 5-8, p. 76-77).

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 (3-5, p. 151, 5-8, p. 81) 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” (3-5, p. 151, 5-8, p. 81).

€

4

6=

2

3

A Problem-Based, Number Sense Approach to Fraction Computation

Review the four guidelines for developing computational strategies for fractions (p. 88). (2 minutes)

Divide into 3 rooms: Addition and Subtraction (pp. 89-93) Multiplication (pp. 93-98) Division (pp. 98-104)

• Review your groups section of the text and determine how you would teach the operation using the four guidelines. Be prepared to share with the larger group in 25 minutes. We will have 5-10 minutes of large group share time.

After

For 10 minutes 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.

3-5 Group - Read Chapter 7, Decimal and Percent Concepts and Decimal Computation (pp. 181-203)

5-12 Group - Read Chapter 4, Decimal and Percent Concepts and Decimal Computation (pp. 107-130)