1. Overview of Class #5 Mini-problem
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

2. 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?

3. Bundling Sticks vs. Beansticks
Grouping model
Language of “bundling” and “unbundling” loose sticks and 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 of “trading” loose beans for ten-sticks
Good up to 100s
Easy for overhead
Can be represented with drawings
Small to manipulate
Cheap, but take work to make and maintain

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

5. Two Meanings for Subtraction
Take away
Compare

6. 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.

7. 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

8. Focal Students for Video Clip Analysis
Bernadette
Lin & Rania
Christina & Shea

9. Wrap Up Assignments Please leave notebooks on your way out
Finish mini-problem
Be sure to send me your plan two days before you teach
Readings
Try to use Mathematical Proficiency framework in field
Please leave notebooks on your way out