Computational Fluency: Connecting Place Value Ideas to Addition Algorithms Math Alliance March 16, 2009 DeAnn Huinker and Beth Schefelker

Thinking About Fluency Jot down your thoughts to the following question… What does mean to have computational fluency? Turn and share with a table partner.

Mental Math

Understanding Mental Math Strategies An understanding of the basic number combinations for addition. Structure of the base-ten number system. Knowledge of quantity and magnitude of number. Recognize and use related problems. Understanding and use of properties of addition (commutative and associative)

WALT We Are Learning To… Develop an understanding of computational fluency for addition. We will know we are successful when… Solve addition problems with 3-digit numbers using strategies other than the traditional algorithm.

Computational Fluency  Flexibility  Comfortable with more than one approach.  Able to choose an appropriate strategy for the numbers in the problem.  Efficiency  Can easily carry out the strategy making use of intermediate results.  Doesn’t get bogged down in too many steps or lose track of the logic of the strategy.  Accuracy  Can judge the reasonableness of results  Has a clear way to record and keep track  Concerned about double-checking results. Source: Russell, S.J. (2000). Developing computational fluency with whole numbers. Teaching Children Mathematics, 7,

Base-Ten Number System: Place Value Learning about whole number computation must be closely linked to learning about the base-ten number system The heart of this work is relating the written numeral to the quantity and to how that quantity is composed and can be decomposed. Teacher Note, Computational Fluency and Place Value, Investigations Grade K-5. TERC, 2007

Is naming place value enough? Use snap cubes to show 37. Count by ones? Count by groups and singles? Groups by 10’s and singles? Can you make a different arrangement and still have 37 cubes?

Thinking Deeper About 37 Find 37 on a hundreds chart. Work with a partner to find other important ideas about the number 37. Why are these ideas important for children to think about as they begin to work with larger numbers?

Applying What We Know About Base-Ten To Addition Algorithms Numbers can be decomposed into parts. 100’s, 10’s and 1’s »37= »37 = Numbers have a place within the structure of the base-ten system. Within a decade »37 is between 30 and 40 Within a 100 »37 is 3 away from 40 »37 is 63 away from 100

Two Strategies Work with your table partner to figure out what each strategy would look like = ? 1. Add each place from left to right 2.Add on the other number in parts

Use a nice number and compensate First step: = = = 73

Change to an easier equivalent problem = (48 +2) + (25 - 2) = = = 73

Now Try Two on Your Own In what ways did the strategies surface your understanding of place value? of number sense? of the number system?

What are the MPS Learning Target Expectations? Grade 1- Use and explain strategies to solve addition and subtraction basic fact problems (e.g., doubles plus one, make a ten) and word problems (e.g., direct modeling). Grade 2 - Use and explain strategies to compare and rename numbers and to solve addition and subtraction basic facts and word problems while applying place-value concepts and using money Grade 3 - Communicate and use fluent and flexible strategies to represent and compare numbers, estimate, and solve real-world addition and subtraction problems including money. Grade 4 - Use strategies fluently to make estimates, solve, and pose real- world problems (e.g., single and multi-step) for all operations, to compare and rename numbers, and to find factors and multiples. Grade 5 - Pose real-world problems, and use strategies, including number theory concepts and place value, to compare numbers, make estimates, and solve single and multi-step word problems.