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Taajah Witherspoon
Mountain Brook Schools
Learning Conference
July 21, 2013
 Use
an index card to
Define a number line
 Write
teach
the grade level that you
Yea! Number
Lines are a tool

none indicated the
benefit had a formality
based upon the
repetition of a unit
interval and the
partition of the interval.
perceptual features
dominated the definitions
Instead
Only 1, described as ………
“A line that contains all rational and
irrational numbers. It is an infinite
line.”
“The use of number lines
increases students’ ability
to use numbers flexibly,
estimate, and visualize
numbers and therefore
increase number sense.”
Wright, 2001
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Number sequencing
Greater than and less than
Estimation and Rounding
Measuring length
Elapsed Time
Strategy for various operation
(+, -, x, ÷)

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Integers
Etc.
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Counters i.e. separate unifix cubes
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Unifix cubes length model (tens)
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Beaded necklace (counting)
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Structured number line (model strategies)
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Dual sided number line
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Empty number line
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Double number line
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Fraction / percentage bar
Kindergarten to First Grade
 Take up space
 Unifix cubes
 Beads (concrete number line)
 1-20
 Discrete items
Grade
Number K-1
Paths
Number 2-8
Line
Model
Physical Count
/ Finite
Each
cube can
be
counted
Model / Length Count
Infinite
length
units
Position is
on the
number of
cubes/
space is the
number
Specific
point
Number line - Measurement model
rather than a counting model

Structured Number line 1-10 then 1-20
 Missing number(s)
 Double-sided number line
◦ Where is number 13 on the line?

End of 2nd Grade

Open number line
O.G.A.P.
 Counting
by tens (N+10)
 Jumping across or bridging tens
 Place Value strategy
More Sophisticated Strategies
 Sequential
strategies
 Compensation strategy
(Bobis, 2007)
Powerful model for reasoning
Recording and Sharing students’ thinking
strategies
Students should only record relevant
numbers
Transitional
Early –
Transitional
Early
BSU Subtraction Progression
Traditional
Algorithm
Partial
Difference
Adding Up
Compensation
13
-7
“0 – 8 = 2”
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Model for distance
Links geometric and arithmetic
Equivalency
Ordering
Hundreds Chart or
Arithmetic Block
Visualization
Number Line
Cognitive involvement
(partitioning or labeling)

Over half - overgeneralized (Wong, 2008)
Pick any 2 of the following problems.
Model with the Number Line
On January 1 in Minnesota the low temperature was -4
degrees F and the high temperature was 6 degrees F.
How much did the temperature increase?
Use number line to solve 17 + ______ = 52
The distance between 50 and me is 27. What number(s)
can I be?
Solve (–n x –n) with the number line.
Can you name a number smaller than nothing?
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K – unifix cubes as counters
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1st – connected unifix cubes linear model
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1st / 2nd – Bead necklace
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2nd – model strategies on structured number line
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3rd – open number line
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3rd – 5th model rational numbers on number line
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6th – model ratios
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7th – model +, -, x, ÷ integers
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8th – locate irrational numbers on number line
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Represent whole numbers as lengths from 0
on a number line diagram …0, 1, 2, …, and
represent whole-number sums and
differences within 100 on a number line
diagram.
Make a Line Plot with whole numbers
Use multiplication and division within 100 to
solve word problems…
Three equal jumps
forward from 0 on the
number line to 12 or
three equal jumps
backwards from 12 to 0.

Understand a fraction as a number
In which order would you present
the following number lines?
http://caccssm.cmpso.org/
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Compare two fractions with different
numerators and different denominators…
Explain why a fraction is equivalent
Make a line plot to display a data set of
measurements in fractions of a unit (1/2,
1/4, 1/8). Find the sum and difference.
5th Grade & CCSS (Number Line)
– Coordinate Plane, (+) and (-) fractions
Round 14.235 to the nearest tenth
Make a line plot to
display a data set of
measurements in
fractions of a unit (1/2,
1/4, 1/8).
Use ratio and rate reasoning to
solve real-world …. problems,
e.g., by reasoning about …
double number line diagrams…
(If 6 is 30% what is that value?)
Understand ordering and absolute
value of rational numbers.
Represent account balance
of -6 , write |–6| = 6 to
describe the size of the
debt in dollars.
http://caccssm.cmpso.org/
7th - Apply and extend …..understandings ….to add and
subtract rational numbers; on …number line diagram.
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You have $4 and you need to pay a friend $3. What will you have
after paying your friend?
4 + (-3) = 1 or (-3) + 4 = 1
8th- Use rational approximations …..to compare the size
of irrational numbers, locate them approximately on a
number line diagram….(e.g., π2).

Compare √2 and √3 by estimating their values, plotting them on a
number line….
How will the number
line impact your
instruction?