1. Overview of Class #5 Overview
Introduction to beansticks (second material for modeling place value)
Modeling conventional subtraction algorithm
Mathematical proficiency
Learning to see students through lens of mathematical proficiency
Wrap up
Overview: 1. New notebook collection process
2. Brief sharing about mini-problem

2. The Instructional Triangle

3. Principled Practice

4. Using Beansticks to Model Addition Algorithms
Use beansticks to model:
The standard algorithm
The column-addition method
What is similar and different about modeling these two algorithms?
How do these new materials compare with bundling sticks?

5. Bundling Sticks vs. Beansticks
Grouping model
Language: “bundling” loose sticks, “unbundling” bundles
Good up through 100s
Awkward for overhead or board
Easy to manipulate
Can be represented with drawings
Cheap, easy to maintain
BEANSTICKS
Trading model
Language: “trading” loose beans for (ten-)sticks
Good up to 100s
Easy for overhead and (magnetic) board
Small to manipulate
Can be represented with drawings
Cheap, but take work to make and maintain

6. Write a word problem that corresponds to this problem.
Shift to Subtraction
Write a word problem that corresponds to this problem.

7. Two Meanings for Subtraction
Take away
Compare

8. Mathematical Proficiency for All Students
Conceptual understanding - comprehension of mathematical concepts, operations, and relations
Procedural fluency - skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
Strategic competence - ability to formulate, represent, and solve mathematical problems
Adaptive reasoning - capacity for logical thought, reflection, explanation, and justification
Productive disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
Kilpatrick, J., J. Swafford, and B. Findell. (2001). Adding It Up: How Children Learn Mathematics. Washington, DC: National Academy Press.

9. Video Clip: November 6, 1989
Early in unit on addition and subtraction computation
Using beansticks, number line
Students have already learned conventional algorithm, but few or none know it well yet
Problem:
Joshua ate 16 peas on Monday and 32 peas on Tuesday. How many more peas did he eat on Tuesday than he did on Monday?
Students have already worked on problem, whole class discussion of solutions

10. Video Clip Analysis Focal Students Bernadette Lin & Rania
Christina & Shea
Proficiency Strands
Conceptual understanding
Procedural fluency
Strategic competence
Adaptive reasoning
Productive disposition

11. Wrap Up Assignments Those who wish, leave notebooks on your way out
Mini-problem - bring audio, player, artifacts, and 4 copies of question track form
Readings
Analyze common student errors
Practice modeling subtraction
Try to use Mathematical Proficiency framework in field
Those who wish, leave notebooks on your way out
Comment cards