Overview

1. Overview • Sharing practice • Entry and exit moves • Anecdotal note-taking strategies • Contextualized mathematics problems • Textbook lesson analysis: Two interpretations of division • Planning lesson enactment: Lesson structure • Evaluating the context of a lesson • Wrap up

2. Sharing Practice • On a separate piece of paper, compile a list of entry and exit moves that worked well. • Anecdotal note-taking: What went well? What didn’t go as well?

3. Evaluating the Context of a Mathematics Lesson or Task • Reasons for and functions of context • Hazards of contexts

4. Evaluating Lesson Context Is there a non-mathematical context? 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

5. Making Context Accessible and Functional - Video Clip

6. Division Use tiles to show 14 2 in two different ways What is the same? What is different?

7. Two Different Interpretations of the Meaning of Division • Partitive: • a ÷ b means a divided into b (equal) groups (or parts) • 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 size b • the divisor tells you the size (or measure) of each group • the quotient tells you how many equal groups you can make of that size

8. 12 ÷ 2 = 6 12 ÷ 6 = 2 Partitive? Measurement? Partitive picture of a ÷ b = c || Measurement picture of a ÷ c = b

9. Division Notation

10. Writing Division Story Problems Possible answers to 45÷7. A) 6 B) 7 C) 6.43 D) 6 r.3 E) Friday What is the question? • A ticket to the movie costs $7. How many tickets can you buy with $45? • A mini van can carry 7 students. How many mini vans would be needed to carry 45? • Dayo was paid $45 for 7 hours of work. How much did she make per hour? • 45 cookies are to be put in boxes that hold 7 cookies each. How many boxes can be filled? • A pool needs to be cleaned every 45 days. If it was just cleaned Tuesday, what day of the week should the next cleaning be scheduled for? Write stories that correspond to this division expression and the different answers shown. Craft problems that represent different interpretations of the meaning of division. F) It depends on context (any of the above)

11. “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 • 45 ÷ 12 : It is 3 o’clock, what time is it 45 hours later?

12. Lesson Structure Beginning Middle End

13. Lesson Structure 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

14. Planning the Implementation(Lesson from EM on Division) • 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 are two different ways you can tie up this lesson?

15. Wrap Up • Sign up for a meeting about your lesson. I’ll post the available times. • Assignments • Reading • Long division warm-up ENJOY YOUR THANKSGIVING BREAK!