Cypher IV Mathematics Leadership Project Teaching Student-Centered Math Book Study K-3 S6, 3-5 S4, 5-12 S2 Strategies for Whole-Number Computation

(Re)Introductions K-3 & 3-5 Groups Kim Ramsay (Grade 2, Whitehorse) Cathy Hines (Grade 3, Whitehorse) Kathryn Lewis (K, Old Crow) Shari Heal (Grade 3 FI, Whitehorse) Bernadette Roy (Grade 3 French, Whitehorse) Jenna Sawkins (Grades K-1, Dease Lake) Nita Connolly (Gr. K-2, Atlin) 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)

(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 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 of strategies for whole-number computation Compare invented strategies to traditional algorithms Explore invented strategies for addition, subtraction, multiplication, and division –Use Elluminate Live! with increasing ease

Before Using Invented Strategies –Solve using any method other than the traditional algorithm and be prepared to share your strategy. –Volunteers to share? (On the whiteboard, record each step as you share, being sure to represent each step seperately.)

During - Big Ideas Review the Big Ideas for this chapter (K-3, p. 157; 3-5, p. 100; 5-12, p. 37) for a couple of minutes. Share your thoughts about the Big Ideas with the large group for about 8 minutes. –Discuss key messages within the Big Ideas and how they fit with a constructivist approach to teaching and learning math.

Comparison of Invented Strategies & Traditional Algorithms There is an emphasis in this chapter on having students develop their own meaningful and efficient methods to perform calculations. Sometimes these strategies are “invented.” –Using the info in the chapter (K-3, pp ; 3- 5, pp ; 5-8, pp ), work in small groups to create a T-Chart on the whiteboard to compare and contrast invented strategies and traditional algorithms. –Be prepared to share one of your ideas with the large group in about 8 minutes.

Invented Strategies for Addition Solve: –Two classes went on a field trip. There were 26 students in one class and 18 students in the other class. How many students went on the trip?

Invented Strategies for Addition (cont’d) Refer to the figure, Invented Strategies for Addition with Two-Digit Numbers (K-3, Figure 6.4; 3-5, Figure 4.4; 5-12, Figure 2.2). –Be prepared to discuss the following with the large group in about 5 minutes: Consider the strategy that you used. Were all four of the strategies in the figure helpful? When were certain strategies more helpful than others?

Invented Strategies for Addition (cont’d) For 10 minutes in a small group, try adding the following in as many different ways as you can. Record your work. – – – Discuss each question as a small group and highlight the strategies utilized. Consider the various ways that strategies were recorded as it is important to model ways to record the methods with students.

Invented Strategies for Subtraction Consider the following problems: –Greg has 45 hockey cards. He went to a card show and got some more cards for his collection. Now he has 72 cards. How many cards did Greg buy at the show? –Cathy counted all of her crayons. Some were broken and some were not. She had 50 crayons in all. 17 were not broken. How many were broken? –There were 75 children on the playground. The 24 grade two students came in first. How many students were still outside? –Work with a partner to solve the problems using some of the “counting up” and “take away” strategies provided in this chapter (K-3, pp ; 3-5, pp ; 5-8, pp ). Be prepared to share with the large group in about 10 min.

Invented Strategies for Multiplication Mentally multiply 26 x 6 and be prepared to share. From the shared examples, find examples of complete-number strategies, partioning strategies, or compensation strategies (K-3, pp ; 3-5, pp ; 5-12, pp ). Solve 38 x 4 using all three types of multiplication strategies. Share and discuss as a large group.

Invented Strategies for Division For 10 minutes with a partner: –One person check out Invented Strategies for Division (K-3, pp ; 3-5, pp ; 5-12, pp ) –The other check out The Traditional Algorithm for Division (K-3, pp ; 3- 5, pp ; 5-12, pp ) –Review your section and establish a list of key points and share with your partner.

After Refer to the section on Benefits of Invented Strategies (K-3, pp ; 3-5, p. 103; 5-8, p. 40). For ten minutes, consider the list of benefits and then think about your experiences in teaching the traditional algorithm to students.

After For 10 minutes, discuss the following questions in small groups of about four: –When is it appropriate to introduce the traditional algorithm for each operation. Is it necessary at all? –When students share their strategies, how can you manage them & highlight the most efficient ones? –How do teachers and students judge if an invented strategy is effective? –What should you do if a student utilizes a specific invented strategy (e.g., repeated + for x) & does not wish to adopt a more efficient one?

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 or fax to

After - Homework Introduce invented strategies for one of the operations being explored in your class. Gather samples and record anecdotal comments to share at the next session. K-3 –Look through the remainder of the text and identify any areas of learning that you would like to explore. Reflect on the book study experience and be prepared to share at the next session.

After - Homework Introduce cluster problems (3-5, pp ) to your students. Send in work samples to share with the group. Read Chapter 5, Developing Fraction Concepts (pp ) Introduce cluster problems (5-12, pp ) to your students. Send in work samples to share with the group. Read Chapter 3, Fraction Concepts and Computation (pp )