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

The Instructional Triangle

Principled Practice

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?

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

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

Two Meanings for Subtraction Take away Compare

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.

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

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

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