Common Core and
the Number Line
December 9, 2011
Number Line & CCSS
• The number line first appears in the
Measurement & Data domain of the Common
Core Standards in second grade:
– Students are expected to represent numbers as
lengths on the number line.
– They are also expected to represent sums &
differences on a number line.
– They utilize counting numbers within 100.
http://caccssm.cmpso.org/fractions
Grade 2
• Show me:
15
39
56
80
97
Grade 2
15
15
2
13
13
15 + 13 =
28
15 - 13 =
2
=
28
Grade 3
• Number & Operations
– Develop understanding of fractions as numbers.
2. Understand a fraction as a number on the number
line; represent fractions on a number line diagram.
Grade 3
• Spend a few minutes finding the values of the
points on the handout.
• Discuss your answers with a person or two
sitting near you.
• Together, organize the problems in the order
they should be given to students.
1.
2.
3.
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http://caccssm.cmpso.org/
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4th grade
• Measurement and Data:
– Solve problems involving measurement &
conversion of measurements from a larger unit to
a smaller unit.
2. Use the four operations to solve word problems …
including problems that require expressing
measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities
using diagrams such as number line diagrams that
feature a measurement scale.
1 cm = 0.39 inches
1 inch = 2.54 cm
One Day
24 Hours is One Day
One Hour is 60 minutes
1 Minute is 60 Seconds
5th Grade
• Geometry
– Graph points on the coordinate plane to solve realworld and mathematical problems.
1. Use a pair of perpendicular number lines, called axes, to
define a coordinate system, with the intersection of the
lines (the origin) arranged to coincide with the 0 on each
line and a given point in the plane located by using an
ordered pair of numbers, called its coordinates.
Understand that the first number indicates how far to
travel from the origin in the direction of one axis, and the
second number indicates how far to travel in the direction
of the second axis, with the convention that the names of
the two axes and the coordinates correspond (e.g., x-axis
and x-coordinate, y-axis and y-coordinate).
y-axis
From the origin (0,0) to point P.
I go two units to the right and
(x-coordinate, y-coordinate)
three units up.
P(2, 3)
x-axis
origin
6th grade
• Number Systems
– Apply and extend previous understandings of
numbers to the system of rational numbers.
7. Understand ordering and absolute value of rational
numbers.
c.
Understand the absolute value of a rational number as its
distance from 0 on the number line; interpret absolute
value as magnitude for a positive or negative quantity in a
real-world situation. For example, for an account balance of
–30 dollars, write |–30| = 30 to describe the size of the
debt in dollars.
| -6 | = 6 because -6
is 6 units from 0.
a, if a ≥ 0
|a|=
-a, if a < 0
| 4 | = 4 because 4
is 4 units from 0.
1. | 4 | = 4
2. | -6 | = 6
3. - | 8 | = -8
4. - | -2 | = -2
7th & 8th Grade
• The Number System
– Know that there are numbers that that are not
rational, and approximate them by rational
numbers.
5. Use rational approximations of irrational numbers to
compare the size of irrational numbers, locate them
approximately on a number line diagram, and
estimate the value of expressions (e.g., π2). For
example, by truncating the decimal expansion of 2,
show that 2 is between 1 and 2, then between 1.4
and 1.5, and explain how to continue on toget better
approximations.

2 5
3

Locate the following irrational numbers on the number line
above.
2
2
1.5

3

1.8
1 3  4
1. 3
2.25  3  3.24
1 3 4
2. 
1 3  2
2
2
1.7

3

1.8
3. 2 5
1.12  3  1.9 2
2.89  3  3.24
1.21  3  3.61
High School
• Statistics and Probability
– Interpreting Categorical and Quantitative Data
• Summarize, represent, and interpret data on a single
count or measurement variable
1.
Represent data with plots on the real number line (dot plots,
histogram, and box plots.
Data Set: The ages of students in the high school Glee
Club are as follows:
14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18
Number of Students
Age of Glee Club Members
The Number Line
• The number line serves as a visual/physical model to
represent the counting numbers & constitutes an
effective tool to develop estimation techniques, as well
as a helping instrument when solving word problems.
• The number line constitutes a unifying & coherent
representation for the different sets of numbers (N, Z,
Q, R) which the other models cannot do.
• The number line is an appropriate model to make
sense of each set of numbers as an expansion of other
& to build the operations in a coherent mathematical
way.
http://caccssm.cmpso.org/
The Number Line
• The number line enables to present the fractions
as numbers & to explore the notion of equivalent
fractions in a meaningful way.
• The number line, in some way, looks like a ruler,
fostering the use of the metric system & the
decimal numbers.
• The number line fosters the discovery of the
density property of rational numbers.
• The number line provides an opportunity to
consider numbers that are not fractions &
consider the existence of irrational numbers.
http://caccssm.cmpso.org/
Next Steps
• Which model for number operations do you
now most often use?
• Are you ready to begin extending your use of
the number line?
– Do you have a number line up on the wall in your
classroom?
• What do you still need to feel comfortable
with the number line as a useful
representation of number operations?