Cypher IV Mathematics Leadership Project

Teaching Student-Centered Math Book Study 3-5 Group Session 2

Number & Operation Sense

(Re)Introductions 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 (Grades 3-9, Telegraph

Creek) Mike Emerick (Grades 7-8, Dease Lake)

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 number and

operation sense Explore various number relationships Investigate problem structures and

models for multiplication and division Discuss important issues related to

solving story problems

Materials (Electronic Transfer) Evaluation Form Copy of the curriculum

(sent big poster) Grade 3, 4, 5, and/or

poster (smaller size) Ten-frames (BLM 1) Little ten-frame cards

(BLM 3,4) Hundreds Chart (BLM

5,6)

Graph Paper (BLM 7-13 & 16-19)

Thousand Chart Skip-by-Ten

How Bear Got A Short Tail Materials (Problem Structures)

What’s Your Number? Game Sheets

The Snowsnake Game

Number Sense (Partner) Discuss the following with a partner:

What does it mean for a student to have a good sense or intuition of numbers?

What implications does teaching to encourage number sense have on how we work with students and what we emphasize in our classrooms?

Be prepared to share a few of your ideas with the large group in 10 minutes. (If the breakout room whiteboard is used to record ideas, I can copy it into the main room.)

Big Ideas Look at the Big Ideas for this chapter (p.

39) Does the curriculum have a strong

emphasis on the key points about number sense that are articulated in the Big Ideas?

Consider ways that you can emphasize the Big Ideas of number sesne and provide number sense strengthening activities for individuals or groups of students.

Anchoring Numbers to 5 & 10 In grades K-3, the numbers 5 & 10 can

be used as anchors. They are especially useful when thinking about combinations of numbers. A key model to use with students to illustrate these relationships is the 10-frame.

Anchoring Numbers to 5 & 10 (cont’d) Here is a ten frame. To build the 7-frame:

Always fill the top row first, starting on the left - the same way that you read.

When the top row is full, counters can be placed in the bottom row, also starting on the left.

Anchoring Numbers to 5 & 10 (cont’d) Build 8

Share what you know about the number 8 from looking at the ten-frame.

How could you use ten-frames to help students develop 5 and 10 benchmark relationships?

Part-Part-Whole Relationships & Extending Number Relationships to Larger

Numbers - Lauren Resnick (1983) states: Probably the major conceptual achievement of the

early school years is the interpretation of numbers in terms of part and whole relationships. With the application of a Part-Whole schema to quantity, it becomes possible for children to think about numbers as compositions of other numbers. This enrichment of number understanding permits forms of math problem solving and interpretation that are not available to younger children.

Part-Part-Whole Relationships & Extending Number Relationships to

Larger Numbers (continued) Find as many ways as possible to

represent the following numbers (with the ten-frame cards):

80 35 67

Relative Magnitude Small Group Activity Complete Activity 2.6, Close, Far, and In

Between (p. 45) using 219, 364, & 457. Explain the thinking behind your responses to the

questions in the activity. Consider other trios of numbers that you could use

and the prompts you would use with students to get them thinking about the relative magnitude of numbers.

Thinking About Parts of #s To continue to build on part-part-whole ideas

together, and in particular to focus on the missing part, we will work through one or more of: Activity 2.17 50 and Some More (p. 54) Acitivity 2.18, The Other Part of 100 (p. 54) Activity 2.19, Compatible Pairs (p. 55)

Work with a partner to consider ways to use these activities in your class. Be prepared to share with the whole group.

Compatible Pairs - Make 50 37 41 28 9 31

12 38 19 22 13

Compatible Pairs - Make 1000 815 635 435 565 760 550

240 365 280 720 450 185

CP - Using 5s to Make 100 25 35 5 45 95

85 15 65 75 55

Compatible Pairs - Make 500 240 150 415 165 375

350 85 260 125 335

Thinking About Parts of #s To continue to build on part-part-whole ideas

together, and in particular to focus on the missing part, we will work through one or more of: Activity 2.17 50 and Some More (p. 54) Acitivity 2.18, The Other Part of 100 (p. 54) Activity 2.19, Compatible Pairs (p. 55)

Work with a partner to consider ways to use these activities in your class. Be prepared to share with the whole group.

Problem Structures for x and ÷ Multiplication and division problems can be

categorized according to the types of relationships involved. The two most common structures for multiplication and division are equal-group problems and multiplicative comparison problems.

Review Equal-Group Problems (pp. 58-59) & Multiplicative Comparison Problems (pp. 59-60)

Problem Structures (cont’d) In groups of 2 or 3, solve the problems

in the text as directed in the Stop and Reflect box (p. 60).

Create one of each type of problem with your partners.

Using Models For x and ÷ An important model for multiplication and

division is the array. An array is any arrangement of things in rows and columns, such as a rectangle of square tiles or blocks.

With a partner, represent the factors of 30 using arrays. Record your arrays on the grid paper and write the

multiplication expression that the array represents beside it.

Be prepared to share with the whole group.

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are needed to see this picture.

Using Models for x and ÷ Large group discussion:

How and why do arrays support students in their understanding of multiplication.

Share your ideas about how arrays could be used to support students in their understanding of division.

After Round table sharing

Impressions and/or questions that have surfaced as a result of the session/

Your responses to impressions and/or questions that have surfaced as a result of the session

What does it mean for a student to have a good sense or intuition of numbers?

What implications does teaching to encourage number sense have on how we work with students and what we emphasize in our classrooms?

Homework Try the two strategies for problem solving,

Think About the Answer Before Solving the Problem (p. 68) and Work a Simpler Problem (p. 69), with a small group of students in your class. Reflect on how your students solved problems and be ready to share your experiences at the next session.

Read Chapter 3, Helping Children Master the Basic Facts (pp. 74-99)

Evaluation Please consider completing the

evaluation form and e-mailing it to me after this session.