Cypher IV Mathematics Leadership Project
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Transcript of Cypher IV Mathematics Leadership Project
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Cypher IV Mathematics Leadership Project
Teaching Student-Centered Mathematics Book Study 3-5 S5
Developing Fraction Concepts
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(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)
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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.
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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.
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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?
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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
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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
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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.
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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?
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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)
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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
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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.
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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
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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?
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QuickTime™ and a decompressor
are needed to see this picture.
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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?
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Easter Egg Fractions
http://illuminations.nctm.org/LessonDetail.aspx?ID=U112
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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?
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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.
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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.
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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.
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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?
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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).
€
4
6=
2
3
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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.
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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…
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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 [email protected] or fax to 867-393-6339.
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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)