Transcript Fiveton: The Wise Kingdom of Renaming and Place Value

FIVETON:
THE WISE KINGDOM OF
RENAMING AND PLACE VALUE
Brief Description: The NCTM “Focal Points”
emphasize place value, addition, and subtraction in
second grade. Learn how to use chip trading and a
story about the hidden kingdom of Fiveton to get
students truly invested in building understanding of
these vital concepts.
Mark Roddy – Seattle University
Master in Teaching Program
NCTM 2008 Annual Meeting & Exposition
April 10, 2008
Salt Lake City, Utah
Chip Trading
A white is worth one.
It takes five whites to get a red.
It takes five reds to get a blue.
It takes five blues to get a green
etc.
Fuys, D. & R. Tischler (1979). Teaching Mathematics in the Elementary School
.
NCTM Focal Points
1. Developing understandings of addition and subtraction
and strategies for basic addition facts and related
subtraction facts
2. Developing an understanding of whole number
relationships, including grouping in tens and ones
3. Composing and decomposing geometric shapes
1. Developing an understanding of the base-ten numeration
system and place value concepts
2. Developing quick recall of addition facts and related
subtraction facts and fluency with multi-digit addition and
subtraction
3. Developing understanding of linear measurement &
facility in measuring lengths
NCTM (2006). “Focal Points for Pre-Kindergarten Through Grade 8 Mathematics: A Quest for Coherence,”
NCTM Focal Points
1. Developing understandings of addition and subtraction
and strategies for basic addition facts and related
subtraction facts
2. Developing an understanding of whole number
relationships, including grouping in tens and ones
3. Composing and decomposing geometric shapes
1. Developing an understanding of the base-ten numeration
system and place value concepts
2. Developing quick recall of addition facts and related
subtraction facts and fluency with multi-digit addition and
subtraction
3. Developing understanding of linear measurement &
facility in measuring lengths
NCTM (2006). “Focal Points for Pre-Kindergarten Through Grade 8 Mathematics: A Quest for Coherence,”
NCTM Focal Points
“Children develop, discuss, and use efficient,
accurate and generalizable methods to add
and subtract multi-digit whole numbers....
They develop fluency with efficient
procedures including standard algorithms for
adding and subtracting whole numbers,
understand why the procedures work (on the
basis of place value and properties of
operations) and use them to solve problems.”
NCTM (2006). “Focal Points for Pre-Kindergarten Through Grade 8 Mathematics: A Quest for Coherence,”
Developing
Understanding
Marilyn Burns on
“Problem situations should be the starting place
for developing understanding of each of the
four basic operations of arithmetic – addition,
subtraction, multiplication, and division –
thereby establishing the need and context for
computation skills. Children need to see that
learning to compute serves a purpose – for
solving problems.” (p. 14)
Marilyn Burns (2007). About Teaching Mathematics: A K-8 Resource. (3rd Edition)
Developing
Understanding
National Research Council on
“Research indicates that students’ experiences
using physical models to represent hundreds,
tens and ones can be effective if the materials
help them think about how to combine
quantities and, eventually how these processes
connect with written procedures. The models,
however, are not automatically meaningful for
students; the meaning must be constructed as
they work with the materials.” (p. 198)
National Research Council (2001). “Adding It Up: Helping Children Learn Mathematics.”
J. Kilpatrick, J. Swafford, and B. Findell, (Eds.)
Developing
Understanding
Marilyn Burns on
“For learning to occur, three conditions are necessary: maturity, physical
experience, and social interaction.”
Maturity “The older children are the more likely their mental structure will act in
coordinated ways.”
Physical Experience “The more experiences children have with physical objects
in the environment, the more likely related understanding will develop….
Testing an idea with physical materials provides valuable feedback for
understanding relationships.”
Social Interaction “The more opportunities children have to interact with peers,
parents and teachers, the more they hear other viewpoints that help them gain
perspective on their own ideas. Social interactions stimulate children to think
through their own ideas and to approach objectivity.” (p. 31)
Marilyn Burns (2007). About Teaching Mathematics: A K-8 Resource. (3rd Edition)
Fiveton Learning Targets
1. Students understand place value.
2. Students are able to use renaming and the
standard algorithms for addition and
subtraction for 2 and 3-digit numbers.
3. Students enjoy math in this context and feel
confident in their grasp of Targets 1 and 2
Fiveton
http://www.artist.omsk.ru/
The Dragon
FIVETON:
THE WISE KINGDOM OF
RENAMING AND PLACE VALUE
Mark Roddy – Seattle University
Master in Teaching Program
NCTM 2008 Annual Meeting & Exposition
April 10, 2008
Salt Lake City, Utah