Cypher IV Mathematics Leadership Project

Cypher IV Mathematics Leadership Project

Teaching Student-Centered Math Book Study K-3 Session 5 Base-

10 Concepts & Place Value

(Re)Introductions

• Kim Ramsay (Grade 2, Whitehorse)• Cathy Hines (Grade 3, Whitehorse)• Kathryn Lewis (Kindergarten, Old Crow)

– Sends her regrets this week - Out of her town working for the last six days

• Shari Heal (Grade 3 FI, Whitehorse)• Bernadette Roy (Grade 3 French, Whitehorse)

– Sends her regrets this week - Overnight trip with students

• Jenna Sawkins (Grades K-1, Dease Lake)• Nita Connolly (Grades K-2, Atlin)• Dana Caljouw (Grades K-3, Telegraph Creek)

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.

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Other Resource Ideas From Carole Fullerton’s Blog

• http://mindfull.wordpress.com/2008/11/24/place-value-materials/ (Carole Fullerton’s Blog)– Place Value Tents (100s, 10s, 1s)

• Consider printing the files onto heavy paper, cut them out, and fold them into tent shapes. They support children in understanding larger numbers and really making sense of the digits.

– Some Online Place Value Games• 100 Hunt• Give the Dog a Bone• Woodcards• The Adding 9 Fairy

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 base-10 concepts and place value

• Determine the goals of place value development

• Discuss and explore models for place value• Examine how place-value concepts develop• Extend place-value concepts to flexible

thinking activities

Materials

• Place-value tents• 1000 Chart (by 10s)• Base-10 models (pics)• Non-proportional

models (online)• Calculators• 100 chart materials

(BLMs 9,10 & 16)• Number Words Poster• Little 10-frames (BLMs

17-18 in pics.)

• Other BLMs in ch. not using tonight:– BLMs 13-14 Base-10

Materials & Bean Sticks– BLM 15 Place Value Mat

with 10-frames

• In TPL:– Can You Count to A

Googol? K3884– How Much, How Many,

How Far, How Heavy, How Long, How Tall is 1000?

Before

• Patterns in the Hundreds Chart– Work with a small group in a breakout room for 10

minutes.– Brainstorm how you might use the patterns in the

hundreds chart to help students develop base-ten and place-value concepts.

– (Blank 100s charts will be in breakout rooms.)• Online materials

– http://www.nctm.org/standards/content.aspx?id=25088– http://mindfull.wordpress.com/2009/09/27/hello-maple-

ridge/ (Carole Fullerton’s Blog)



During - Big Ideas

• Review the Big Ideas for this chapter (p. 122) for a couple of minutes.

• Share your thoughts about the Big Ideas with the large group for about 8 minutes.– Are any of the ideas

new to you or make you think about place value in a different way?

Children’s Pre-Base-10 Concepts

• Reread the section of the text on Children’s Pre-Base-10 Concepts (pp. 123-124) and paraphrase it in a maximum of two or three sentences. (5 minutes)

• Share your sentences with a partner in a breakout room. – Combine your work to paraphrase the section,

again using a maximum of two or three sentences. (5 minutes)

Goals of Place-Value Development

• Integration of Base-10 Groupings with Counts by Ones (pp. 124-125)

• The Role of Counting in Constructing Base-Ten Ideas (pp. 125-126)

• Integration of Grouping with Words (p. 126)

• Integration of Grouping with Place-Value Notation (pp. 126-127)

• Move into four breakout rooms. (Rm. 1 is Integration of Base-10 Groupings with Counts by Ones etc.)– Paraphrase the section

for the large group. (8 minutes)

– Be prepared to share with the large group.







Models for Place Value

• Consider the base-10 models (8 min.):– Discuss each of the

base-10 models (including how the models are alike and different)

– Why is it important to provide students with a variety of base-10 models?

– Share ideas of how you have used the models.

Models for Place Value

• Explore the base-10 models at http://nlvm.usu.edu/en/nav/vlibrary.html - in Number & Operations, find Base-10 Blocks or http://www.kyrene.org/mathtools/pvb/index.html (the other reference on p. 128 - 5 min.)– What are the advantages and disadvantages of

virtual models compared to physical models?– Do you think virtual manipulatives are appropriate

to use with primary students?– How have you used these virtual models or how

might you use them?

Non-proportional Models For Place Value

• Coloured counters, abacuses, & $ are not used to model base-10 ideas since these materials do not develop these relationships.

• Check out the abacuses at http://nlvm.usu.edu/en/nav/search.html?qt=abacus. (2 min.)– With some abacuses, 10 beads in one column are

exchanged for 1 bead in the next column. There is nothing in the representation that illustrates the relationship between the 10 beads and the single beads. The exchange is simply an arbitrary rule.

http://nlvm.usu.edu/en/nav/search.html?qt=abacus







Developing Place-Value Concepts & Procedures

• (10 min.) In a small group, answer the following (Grouping Activities pp. 129-133):– Why do students need to construct the idea for

themselves that counting by 10s is a good way to count? How do we help them to develop this idea?

– How does the vocabulary that we use for place value affect our students’ understanding of the concept?

– What would you do to determine whether students truly understand what they are doing when they trade one ten for ten ones?

Activities for Developing Place-Value Concepts (20 minutes)

• Poll to choose two activities:– Activity 5.8, Counting with

Base-10 Models (p. 135)– Activity 5.11, More or

Less on the Hundreds Chart (p. 139)

– Activity 5.12, Model with the Hundreds Chart (p. 139)

– Activity 5.16, Digit Change (p. 140) - Calculator

• What kind of mathematical thinking do these activities promote?

• What teaching strategies can we use to support this kind of thinking?

• What would parents learn about math if they were exposed to these kinds of activities?



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13, 15, 1823, 26

Activity 5.16, Digit Change (p. 140)

• Enter 48 on your calculator. Change it to 78. – The change must be made by adding or

subtracting an appropriate amount.– Write and discuss explanations for your

solution.

• Repeat the activity by changing 315 to 305.

Activities for Flexible Thinking

• Work with a partner in a breakout room for 15 min. to:– Do Activity 5.26, Little 10-

Frame + & - (p. 149)– Avoid using traditional

algorithms (i.e., no borrowing or carrying). Focus on bridging 10s rather than regrouping.

– Solve several + & - probs, prepare to share your strategies with the large group for 5 min

• Each person makes a # with their cards. Try to be the 1st to tell the sum.

• For the - version, one student makes a # > 50, the other writes a # < 50. The written # should be - from the modeled #. Share strategies to see how fast both of you can get it.





























After - Round-table Sharing

Round-table sharing in 2 min. on:

• Reflect on how you have taught place value in the past. After reading this chapter, what would you like to do differently when teaching the concept?

and/or

• 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 [email protected] or fax to 867-393-6339.

After - Homework

• Choose one of the Assessment Notes from the chapter to complete with two students. Record your findings and be prepared to share them at the next session.

• Read Chapter 6, Strategies for Whole-Number Computation (pp. 157-185).

Documents

Cypher IV Mathematics Leadership Project