10/24/2008
Place Value
Grades 1-5
Central Maine Inclusive Schools
October 9, 2008
Jim Cook
jcook@msad54.org
What we’ll do:
• Understand what place value is
• Review what students should know about
place value
• Find out what research says about students’
understanding of place value
• Discuss important aspects of place value
instruction
• Try some activities related to helping students
learn place value concepts
What is place value?
• A system that relates the position of the digits
in a number to the value of each digit and the
number.
• We use a base 10 number system
– Ten digits are used
– Each digit to the left has a value that is ten times
the value of the digit to the right
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What should students know about
place value?
• There’s a relationship between the place of a
digit and its value
– Early on, the relationship that’s important is the
groups of tens and ones to the meaning of the
number (just two places, two values)
• For example 36 things means that there are 3 groups of
ten and 6 extras
• If there are 4 groups of ten and 2 extras, there are 42
things
What should students know about
place value?
• There is a meaning to the placement of a digit
in a number
– Students should be able to explain that in 36, the
3 means 3 tens and the 6 means 6 individual units
– It is not enough to have students learn the place
names and ask, “in 36, what digit is in the tens
place?”
What should students know about
place value?
• Later on, students should understand that a
hundred is a group of 10 tens, that a thousand
is a group of ten hundreds, etc.
• Still later, students should know that the
relationship is the same for parts of wholes,
that is, that there are 10 tenths in a whole, 10
hundredths in a tenth, etc.
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What should students know about
place value?
• Students should be able to apply their
understanding of place values to computation
– Children should make use of tens and ones when
adding and subtracting
• Regrouping and carrying are based on place value
understanding
– Multiplication and division depend on place value
understanding
• 3 x 36 means three 30’s and three 6’s (which makes
nine tens plus 18--which is a ten and an eight—so
there’s ten 10’s and 8, which is 108)
What does research say?
• Many children do not understand place value
– When presented with 25 sticks, and asked about the
digit 5 and how it relates to the objects and the digit
2 and its relationship to the objects
• One third of fifth graders and one half of fourth graders in a
study did not know that the 2 represents twenty sticks.
• Second and third graders performed more poorly on the task
Research Ideas for the Classroom, Early Childhood
Mathematics, Robert J. Jensen ed., NCTM, 1993, p. 54.
What does research say?
• Children in grade 1 “achieved near mastery on a
wide variety of place-value tasks after a longer
than usual instructional time—fifteen lessons.”
• Research Ideas for the Classroom, Early Childhood
Mathematics, Robert J. Jensen ed., NCTM, 1993, p. 54.
• The instruction focused around three aspects of
place-value instruction
• Base representation
• Oral name
• numeral
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What does research say?
• Language and wording create difficulties for
our students
– Our “twelve” in some Oriental cultures is “ten
two” and our “forty seven” is “four ten seven.”
– “ty” is used to mean “ten” but “twen-,” “thir-,”
and “fif-” don’t sound like “two,” “three” and
“five.”
– Teen numbers are reversed. “Seventeen” is often
written “71.”
Place Value Instruction
• Begin with a focus on tens and ones.
– Students should begin to know that ten can be one
thing (a group of ten) as well as ten individual things
• Make the connection between aspects of place
value understanding.
– Base representation
– Oral name
– Numeral
• Highlight the repeating pattern of 0-9 in numbers
Place Value Instruction
• Count objects in more than one way (counting by
ones is secure, but counting in groups is more
efficient).
– Count by 2’s, 5’s, 10’s
– Children should realize that the count remains the
same
• Count objects that are already grouped into tens
and ones
– Base 10 blocks
– Ten-frame cards
– Flash math using base 10 blocks
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More place Value Instruction
• Use a hundred chart to highlight the sequence
of numbers, patterns, and the structure of
tens and ones.
• Play “The Game of Tens and Ones” to highlight
adding and subtracting tens and ones.
Using Tens and Ones in Addition
• Students can apply place value knowledge of
tens and ones to learn math facts
– Make a ten strategy
– See Place Value/Make a Ten game
• Students can use tens and ones in addition
– Observe how students use their understanding of
tens and ones to add
– Observe how the teacher uses representation to
model the students’ thinking
More place Value Instruction
• For numbers in the hundreds, use a placevalue chart to model numbers and relate
reading/writing numbers to a representation
• Use base ten blocks and place value charts to
build numbers in more than one way
– Supports regrouping
– Chips representing hundreds, tens, and ones may
not show the physical 10-1 relationship that base10 blocks do
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Thousands and beyond
• Students in grade 3 should understand
thousands (up to 9,999 per 2007 MLR)
• Students in grade 4: up to 100,000
• Students in grade 5: up to 10 million
Using Place Value in Multiplication
• Observe how the teacher handles 2 x 30
– How does she respond to the child who says, “just
add a zero”
– What place value concepts does the teacher want
to support?
• Play Target 300
Place Value in Decimals
• Focus on relationships between word form,
standard number form, and representation for
developing concepts of tenths, hundredths,
and thousandths
• Relate decimal relationships to whole number
relationships (ten tenths to make a whole; ten
hundredths to make a tenth, etc.)
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