teaching number and number sense.ppt

Counting and Number
Sense in Early
Childhood and
Primary Grades
CHAPTER 7
Tina Rye Sloan
To accompany Helping Children Learn Math9e, Reys et al.
©2009 John Wiley & Sons

Focus Questions
• Why is subitizing an important early step in
number sense?
• What characteristics are associated with the
different counting stages?
• How can calculators help children develop
number sense?
Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math,
9th
Edition, © 2009

Understand numbers, ways of
representing numbers, relationships
among numbers, and number systems
• Count with understanding and recognize “how many” in
sets of objects
• Develop understanding of the relative position and
magnitude of whole numbers and of ordinal and cardinal
numbers and their connections.
• Connect number words and numerals to the quantities they
represent, using various physical models and
representations
Excerpts of Expectations from the Number and Operations
Standard Grades Pre-K-2
NCTM(2000). Principles and Standards for School Mathematics.
9th
Edition, © 2009

Number Sense
Number Sense includes:
• An understanding of number concepts and operations
on these numbers.
• The development of useful strategies for handling
numbers and operations.
• The facility to compute accurately and efficiently, to
detect errors, and to recognize results as reasonable.
9th
Edition, © 2009

Number Sense
• The ability and inclination to use this understanding
in flexible ways to make mathematical judgments.
• An expectation that numbers are useful and that work
with numbers is meaningful and makes sense.
9th
Edition, © 2009

Number Sense Stages
• Number sense is not a ﬁnite entity that a student either
has or does not have. Its development is a lifelong
process, and in early childhood and elementary school
number sense development involves several stages:
• Prenumber Concepts
• Early Number Development
• Number Development
9th
Edition, © 2009

Prenumber Concepts are those that do
not rely on numbers but provide a
foundation for later number concepts and
skills.
•Classification
•Patterns
9th
Edition, © 2009
Number Sense Stages

Classification
Size: large, small
(L, S)
Color: blue, red,
green (B, R, G)
Shape: square,
triangle,
pentagon, circle
(S, T, P, C)
9th
Edition, © 2009
Attribute blocks can be used for classification
and reasoning.

Patterns
9th
Edition, © 2009
Each car in a train is like
the car it follows in one
or two ways, or it is
different from the car it
follows in one or two
ways.
Find the alike-and-
difference pattern in
each train, and describe
the missing car:

Extending a Pattern
9th
Edition, © 2009
Ask students to complete number 5

Early Number Development
• Conservation
• Group Recognition
• Comparisons and One-to-one
Correspondence
9th
Edition, © 2009

Conservation of Number
9th
Edition, © 2009
Groups of 5 counters are
arranged in the following
3 patterns

Student A
• T: Are there more red, blue, or yellow counters?
• S: More blue.
• T: How do you know?
• S: I can tell by looking.
• T: How many of each?
• S: One, two, three, four, five... five red. One, two, three, four,
five...five blue. One, two, three, four, five...five yellow.
• T: Five of each?
• S: Yes.
• T: Do you still think there are more blue?
• S: Yes, I can just see there's more blue.
9th
Edition, © 2009

Student B
• T: Are there more red, blue, or yellow counters?
• S: They're the same.
• T: How do you know?
• S: I counted them.
• T: How many of each?
• S: One, two, three, four, five...Five red. Five blue.
Five yellow.
• T: Five of each?
• S: Yes.
9th
Edition, © 2009

Group Recognition
9th
Edition, © 2009
How many birds do you see in each group? Is
one group easier to subitize (recognize) than
another?

Comparisons and One-to-One
Correspondence
9th
Edition, © 2009
Figure 7-5
Models for
making
comparisons by
(a) counting;
(b) physically
comparing
without
counting; and
(c) one-to-one
correspondence

Number Development
• - Connecting groups with number names,
including oral and written cardinal and ordinal
numbers
• - Group recognition
• - Counting forward and backward
• - Skip counting
• - Establishing benchmarks of quantities, such as
5 or 10
• - Place value
9th
Edition, © 2009

Counting: Principles
• One-to-One Rule
• Stable Order Rule
• Order Irrelevance Rule
• Cardinality Rule
9th
Edition, © 2009

Counting: Counting Stages
• Rote Counters may know the proper counting sequence, but
they may not always be able to maintain a correct
correspondence between the objects being counted and the
number names.
• Rational Counters not only uses one-to-one
correspondence but also are able to answer the question
about the number of objects being counted.
9th
Edition, © 2009

Counting: Counting Strategies
• Counting On
• Counting Back
• Skip Counting 3,6,9,12,15….
9th
Edition, © 2009

Counting: Counting Practice
Counting practice should include counting on and counting
back.
A calculator is a valuable instructional tool that helps
improve children’s ability to count, but it is also a
powerful counting tool that they love to explore.
9th
Edition, © 2009

Counting: Developing Number
Benchmarks
The five-frame
(5 x1 array) and the
ten-frame (5 x 2 array)
use these early
benchmarks.
9th
Edition, © 2009

Counting: Making Connections
9th
Edition, © 2009
Figure 7-15 Connections form representations on the ten-frame

Cardinal, Ordinal, and Nominal
Numbers
Cardinal- “How many?”
Ordinal- “Which one?” (i.e.
first, second, third)
Nominal- “Name” (i.e.
phone number or address)
9th
Edition, © 2009

Writing Numerals
9th
Edition, © 2009
Children should begin by tracing the digits
and here is a recommended stroke sequence:

Counting Principles
Student A
• T: Here are some blocks in a row. Start with this one
on the end and count them.
• S: One, two, three, four, five, SIX. There are six
blocks.
• T: What if you start at the other end of the row and
count them?
• S: One, two, three, four, five, SIX. There are six.
9th
Edition, © 2009

Counting Principles (cont’d)
Student B
• T: Here are some red blocks in a row. Start with this
one on the end and count them.
• S: (Touches each of the 5 blocks) One, two, three,
five, six. Six red blocks
• T: Now count these blue blocks.
• S: (Touches each of the 4 blocks) One, two, three,
five. Five blue blocks.
9th
Edition, © 2009

Student C
• T: Here are some blocks in a row. Start with the one
on this end and count them.
• S: One, two, three, four, five, six. There are six.
• T: What if you start at the other end of the row and
count them?
• S: I already counted them! There are six!
9th
Edition, © 2009

Student D
• T: Here are some red blocks (4) in a row. Start with
this one on the end and count them.
• S: (Points to each but says two numbers with each
point) One, two, three, four, five, six, seven, eight.
Eight red blocks.
9th
Edition, © 2009

Construct a Pattern
• The color spinner will be used to select the colors to
be used in constructing the pattern.
• Using the colors chosen, make a pattern that repeats
at least twice in the time allotted.
• When the time is up, compare patterns with others.
Did you come up with a unique pattern idea?
9th
Edition, © 2009

Construct a Pattern
• Try another pattern with new colors or different types
of manipulatives.
• Why should students have an opportunity to
participate in patterning activities?
• Do you have other suggestions for patterning
activities?
9th
Edition, © 2009

teaching number and number sense.ppt

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