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

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
18
63
48
99
72
23
25
56
17
19
39
49
45
98
34
68
37
36
69
29
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, 154 - 158.
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= 30 + 7
» 37 = 20 + 17
• 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.
48 + 25 = ?
1. Add each place from left to right
2. Add on the other number in parts
Use a nice number and
compensate
48 + 25
First step:
48 + 2 = 50
50 + 25 = 75
75 - 2 = 73
Change to an easier
equivalent problem
48 + 25
48 + 25 = (48 +2) + (25 - 2)
48 + 2 = 50
25 - 2 = 23
50 + 23 = 73
Now Try Two on Your Own
581 + 397
445 + 273
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 realworld 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.