1. Please sit in grade level groups. Grade 1 Grade 2 Grade 3Grade 4 Grade 5 Grade 6

2. Overview of Class Comments about notebooks Introduction to algorithms Modeling standard addition algorithm with bundling sticks Planning for teaching of mini-problem Wrap up

3. Comments About Notebooks Different methods of organization –Sections, typing & gluing things in To keep doing: –Making connections to work in field Curriculum Influences of work structures –Revising your previous ideas (rereading and annotating) To try more of: –Care when developing and using representations (e.g. superbundles) –Keeping track of other’s ideas –Recording questions or “wonderings” –Goal setting in relation to particular pieces of practice, principles,… –Learning from others about approaches to the notebook l = llll llll llll 1 super bundle 10100

4. Using Different Approaches to Add 49 + 37 = 9879 + 3958 = Which method was easiest for you to use on each calculation?

5. Algorithms for Adding and Subtracting Multi-Digit Numbers Algorithm: A step-by-step problem- solving procedure, especially an established, recursive computational procedure for solving a class of problems in a finite number of steps.

6. Different Kinds of Algorithms “Conventional” or “standard” algorithms –Traditionally taught in school –May vary across countries, times –Efficient, general “Alternative” algorithms –Transitional –Useful for particular computations –Make process more transparent

7. Conventional algorithmAlternative algorithm

8. Mini-Problem Assignment Send me an email with problem and date you will be teaching Start planning for mini-problem in class today At least two days before you teach, send me your completed discussion planning table for feedback Teach mini-problem –Practice moves/questions we have been working on –Make a digital audio record & collect any artifacts Analyze your questions –Choose a 3-5 minute segment of tape where you try moves/questions we have been working on –Complete “question track” form On October 12 bring: digital audio recording, artifacts, 4 copies of question track form

9. What is the mathematics that students are supposed to be working on in this problem? What methods are students likely to use? What misconceptions might students have? What fraction of the big rectangle is the blue region? What fraction of the big rectangle is the green region?

10. Leading a Discussion 1.Setting up the problem 2.Monitoring student work 3.Launching the discussion 4.Orchestrating the discussion 5.Concluding the discussion

11. Video Context Summer class for 21 incoming fifth graders (part of a larger mathematics institute) Wide range of mathematical achievement and dispositions 6 days of instruction (2.25 hours per day) This problem was given on Day 4

12. Viewing Focus Mathematical and instructional purpose of problem: To review & practice central ideas about fractions: –interpreting fractions as parts of wholes, and the importance of the “whole” –equal partitioning and naming of fractions with reference to the number of equal partitions Clip #1: Setting up the problem & monitoring student work Clip #2: Launching & orchestrating the discussion Clip #3: Orchestrating & concluding the discussion

13. Plan to Teach Your Mini-Problem Analyze your problem: 1.Identify the mathematical content and instructional purpose 2.Anticipate student thinking Plan its enactment: 1.Setting up the problem 2.Monitoring student work 3.Launching the discussion 4.Orchestrating the discussion 5.Concluding the discussion

14. Wrap Up Final- Wednesday, December 13 6-9 PM Assignments –Finish planning mini-problem, get feedback on your plan, and teach it on scheduled date –Reading: Strands of Mathematical Proficiency from Adding It Up (link to this through the course website) –Try to model an alternative algorithm (from Everyday Math) using bundling sticks Comment cards What stands out about the work on algorithms so far? Any important mathematical issues? Any teaching ideas? How does the work we are doing in Ed 411 build on what you learned in Math 385?