Cypher IV Mathematics Leadership Project

Teaching Student-Centered Math Book Study 5-12 Session 5

Extending The Number System

(Re)Introductions 5-12 Group

• Kalvin Beuerlein (Gr. 3-9, Telegraph Creek)• Emily Macht (Gr. 6, Whitehorse)• Sheila Merkley (Gr. 8-11, Whitehorse)• Amy Hes (Grades 6-9, Telegraph Creek)• Sarah Baigent-Nixon (Gr. 6-9 Teacher, Atlin)• Trygve Sort (Grades 5-6, Dease Lake)• Asa Berg (Local 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

• Based on the homework assigned in the previous session, discuss the following questions:• 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 of extending the number system

• Investigate the use of calculators as a tool for exploring scientific notation

• Examine two models for integer operations• Explore rational numbers and real numbers• Use “Elluminate Live!” as a tool for collaborations and

extending the boundaries of community with increasing ease

Materials

• Calculator• NCTM Families Ask Calcultors in the Classroom• Folded Frayer Chart Instructions• Integers

• Grade 7 Greatest Sum & Master 2.6• Grade 7 Magic Squares & Master 2.7• Grade 7 Integer Alphabet & Master 2.8• Grade 7 What’s The Temperature & Master 2.9• Grade 8 Master 2.6 Salute• Grade 8 Master 2.7a & Master 2.7b Integer Racing• Grade 8 Master 2.8a & Master 2.8b Integer Bingo• Grade 8 Master 2.9a & Master 2.9b One to Ten

• Evaluation Form

Before - Defining the Concepts

• Divide up into 4 breakout rooms to complete a Frayer Model on one of the following:• Exponents• Scientific Notation• Integers• Rational Numbers

• Be prepared to share in about 12 min.• Other graphic organizer resources:

• http://yukon-math-differentiated-instruction.wikispaces.com/Graphic+Organizers

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

During - Big Ideas

• Refer to the Big Ideas for this chapter (p. 131) and reflect upon whether you acquired these ideas about the number system through exploration or direct teacher instruction.

• Discuss the similarities and differences between how “Teaching Student-Centered Mathematics” approaches the teaching of these concepts and your own experiences while completing the Integer Alphabet activity.

Integer Alphabet

A -1 N +7B +1 O -8C -2 P +8D +2 Q -9E -3 R +9F +3 S -10G -4 T +10H +4 U -11I -5 V +11J +5 W -12K -6 X +12L +6 Y -13M -7 Z +13

• The “value” of a word is the sum of the individual letters.

• Find the value of Vancouver Canucks, field trip, Yukon, or Stikine.

• Whose last name has the least value?

• Write an 8-letter word with a value > +15.

• Whose town’s name has the greatest value?

During - Exponents and Scientific Notation

• With a calculator, do Activity 5.2, Exploring Powers of 10 (p. 135).

• Once you have completed the activity, move to a breakout room to indicate that you are ready to work with a partner to discuss the activity. • Consider how the use of a calculator facilitated

learning• NCTM journal article: “Families Ask Calculators in

the Classroom”

Other Resources - Exponents & Scientific Notation

• http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

• http://yukon-education-math-grade-7.wikispaces.com/Shape+%26+Space+-+Measurement

During - Integers

• Review the following two activities with a partner:• Operations with Integers (pp. 139-141)• A Problem-Solving Approach for Integers

(pp. 141-146)• How would you present each of the operations

with integers in the classroom?• Work together to create an activity for integer

operations that you would use in the classroom.

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Other Integer Resources

• The Yukon Education Gr. 7 Mathematics Wiki• http://yukon-education-math-grade-7.wikispaces.com/

Number• http://yukon-education-math-grade-7.wikispaces.com/

Home#Curriculum-Wide%20Resources• Numeracy Nets Grade 7

• The Yukon Education Gr. 8 Mathematics Wiki• http://yukon-education-math-grade-8.wikispaces.com/

Number• http://yukon-education-math-grade-8.wikispaces.com/

home#Curriculum-Wide%20Resources• Numeracy Nets Grade 8

During - Rational Numbers

• Work in a small group on Activity 5.5, How Close Is Close? (p. 149). Use two fractions that you think are really close rather than two decimals.

• Be prepared to share the fractions that you identified with the large group, highlighting different strategies that you used to find them. As a large group, we will discuss how this activity helps students develop a sense of rational numbers.

During - Real Numbers

• In small groups:• Discuss how would you explain the

difference between a rational and irrational number to a grade 8 student?

• Create a visual representation that would accompany the explanation.

• Be prepared to share with the large group

After - Round-table Sharing

• Reflect Stems• I learned ___ about extending the number system in the mathematics

classroom.• 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…• Our discussions tonight have made me realize that …• One thing that I will try in my classroom after this session is …

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

• If it is appropriate for your grade, explore both models of integer operations with your class. Gather student samples and ask students to reflect upon which method they prefer when exploring the operations with integers. Be prepared to share your discoveries with the large group at the next session.

• Read Chapter 6, Developing Concepts of Ratio and Proportion (pp. 154-178).