1. Overview Discuss anecdotal note-taking strategies
Two interpretations of division
Culminating performance assessments
Textbook lesson analysis
Discuss Everyday Math lesson
Evaluating the context of a lesson
Planning lesson enactment: Lesson structure
Wrap up

2. Anecdotal Note-Taking
What methods did you try?
What were you trying to document?
How well did it work?

3. Division Use tiles to show in two different ways What is the same?
What is different?

4. Division Notation

5. Two Different Interpretations of the Meaning of Division
Partitive:
a ÷ b means a divided into b 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

6. 12 ÷ 2 = 6 Partitive? Measurement?

7. 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.

8. “Remainders”
With whole numbers, the amount left after dividing –– expressed as R (some number) (e.g., R4)
With rational numbers, not really a “remainder,” can divide all the way; fractional part expressed as decimal or as fraction

9. one for each interpretation of division.
Draw two pictures of
15 ÷ 3 = 5,
one for each interpretation of division.
Label each drawing with the interpretation it represents:
partitive or measurement

10. Lesson-Based Culminating Performance Assessments
Lesson Analysis Conference
Leading a Discussion in a Mathematics Lesson
Assessing Students Through an End-of-Class Check

11. Lesson Analysis Conference
20-minute meeting with instructor to discuss textbook lesson analysis table -- at least one day before you teach
or drop off (at Tim’s office) the following materials at least 48 hours before meeting:
Completed textbook analysis table
Copy of textbook lesson and any modifications
Draft of end-of-class check prompt

12. Leading a Discussion in a Mathematics Lesson
Video or audio record the discussion portion of your lesson
Your discussion will be evaluated for elements such as soliciting broad participation and using a variety of moves
Write an explanation of how the discussion reflects your ability to skillfully perform one of the items on list
Turn in by Friday, December 15, at 5 pm:
Recording of discussion
Written analysis
Other relevant materials (e.g., student work, lesson plan, etc.)

13. Assessing Students Through an End-of-Class Check
Administer an end-of-class check prompt that assesses students’ understanding of the mathematics content of the lesson (Type 1)
Review student responses and make a class performance record
Write a reflection: Describe your prompt and three insights you learned (one about an individual; one about the class)
Turn in by Friday, December 15, at 5 pm:
Class performance record
Written reflection
Copies of student work

14. Evaluating Lesson Context
Is there a context for the mathematical work?
If YES: Does the context maintain the integrity of the mathematics?
If NO: Revise or eliminate context.
If YES: Is the context familiar to all students?
Free of barriers
Creates barriers
Mediated

15. Lesson Structure
Beginning
Middle
End

16. Lesson Structure Beginning Middle End Warm up Introduction
Launch of content
Set up of task(s)
Sparking student interest
Making connections to students’ prior knowledge
Beginning
Sequencing of task(s)
Students working (individually, in groups, whole class)
Teacher observes, listens, questions, scaffolds, explains
Teacher or student presentation
Whole class discussion
Middle
Summarizing: making the mathematical point
Tying up
Assessment
Assignment
End

17. End-of-Class Check
A short question or prompt to assess students at the end of a lesson
Purposes:
to check on students’ understanding of content
to help students reflect on their learning
to see what students think about their work that day
to reinforce skills or concepts
to help plan for the next day’s instruction
A single end-of-class check won’t satisfy all of these purposes.

18. Two Types of End-of-Class Checks
Type 1: Pose a question about the mathematical content of that day’s lesson and ask students to respond. This could be a carefully chosen problem from the text or one you generate yourself.
Type 2: Provide a general prompt that allows students to share information about their learning or disposition toward mathematical work.
A single end-of-class check won’t satisfy all of these purposes.
What prompts could you use as an end-of-class check for the Everyday Math lesson?
What would be your purpose for each prompt?

19. Planning the Implementation
Beginning: How are you going to introduce this lesson with your students?
Middle: How will you sequence the tasks? How will you launch, orchestrate, and close the discussion? What questions or examples could you use as students work independently?
End: What would be two different ways you could end this lesson?

20. Wrap Up Please leave notebook -- pick up Monday
Sign up for a lesson conference
Assignments
Teaching While Students are Working Independently
Reading
Long division warm-up
ENJOY YOUR
THANKSGIVING BREAK!