NCTM JournalsPlease browse the copies of Teaching

Children Mathematics and/or Mathematics Teaching in the Middle School.

• What articles or features do you find interesting or helpful?

• How might you use these resources in your teaching?

NCTM

National Council of Teachers of Mathematics(www.nctm.org)

• 4 major journals• Principles and Standards for School

Mathematics• variety of publications, newsletters, and

other resources• conferences and professional development

Overview of Class #12

• NCTM journals• Announcements, questions• Introduction to division (part 1)• Remodeling textbook exercises to

accommodate diversity and also increase intellectual complexity

• Assignments & Wrap Up

Announcements• Write-up for Part 3 of Project #2• Final exam• Notebooks• Questions?

Division

Use color tiles to show

in two different ways.

What is the same? What is different?

12 ÷ 6

12 ÷ 6 = 2dividend

divisor quotient

1262

dividenddivisor

quotient

Division Notation

Two Different Interpretations of the Meaning of Division

• Partitive:– a ÷ b means a divided into b equal groups – the divisor tells you how many equal groups to

make– the quotient tells you the size of each group

• Measurement: – a ÷ b means a divided into groups of b– the divisor tells you the size of each group– the quotient tells you how many equal groups you

can make of that size

12 ÷ 2 = 6Partitive? Measurement?

Writing Division Story Problems

Write as many different stories as you can that correspond to this division expression and that represent different interpretations of the meaning of division or what it means in specific situations.

38 ÷4

Sharing Division Story Problems

Take turns sharing your problems with a partner:•First person reads one of their problems.•Partner tells what the answer is, and whether it’s partitive or measurement.•Discuss – did you agree?•Switch roles, choosing a problem that represents a different interpretation or gives a different answer.

38 ÷4

Practice with Meaning of Division –– Fraction Division

134 ÷

12

1. Calculate the answer.

2. Write a story problem, or describe a situation, that corresponds to 1 3/4 ÷ 1/2.

I have two pizzas. My friend eats one quarter of one of the pizzas. I have one and three quarters pizzasleft. Then I split it evenly between two of my other friends.Each person gets three and a half pieces of pizza.

D D

D H

H

H HD

1. What is wrong with this?

2. Write a story problem that correctly represents the division.

• To deepen the mathematical challenge of the work

• To “layer” the tasks so that more mathematical goals are served by one problem (Lampert)

• To manage diversity of students’ levels and skills (e.g., providing multiple entry points and opportunities for extension)

Remodeling Textbook Problems

Grade 4 Lesson on Place Value

• One hour• Modeling numbers with base ten blocks;

using place value to increase numbers by ones, tens, hundreds mentally; broken calculator problems

• “What is ten more than 109?”1 2 3

4 5 6

7 8 9

0

+

x

÷= .

-

Teaching the Whole GroupWhile Leading a Whole-Class

DiscussionAttention to equity: Holding and enacting high expectations of students to learn significant mathematics

1. What specific types and difficulties of mathematical questions can you identify in this segment?

2. What methods of getting student participation can you name in this segment?

3. How does the teacher manage errors?

4. Other observations or critique

Wrap Up• Assignments• Collect notebooks• Other?

Assignments• Due on November 26:

– Part 3 of Project #2• For December 4:

– Read Lester article– Browse two NCTM journals– 1 ¾ ÷ ½ – Division Computation