IN MATHEMATICS
OVERCOMING SPEED BUMPS IN THE TRANSITION
to the Common Core State Standards in
MATHEMATICS
Robert J. Riehs
robert.riehs@doe.state.nj.us
February 2012
Jaredand Corin
“Speed bump” should be interpreted
as a synonym for “challenge.”
These speed bumps should be thought
of less as obstacles than as
challenges, which necessitate caution
and careful planning.
Speed Bumps
Practices/Content
Jaredand Corin
The challenge of merging the
Mathematical Content Standards
with the
Standards for Mathematical Practice
Speed Bumps
Details
"The devil is in the details."
Details
Subtleties
Particulars
Nuances
Whether you modify the old curriculum one step
at a time, or you throw it all out and start afresh,
there are potential speed bumps
Details
Subtleties
Particulars
Nuances
3.MD.4 Generate measurement data by measuring lengths using
rulers marked with halves and fourths of an inch. Show the data
by making a line plot, where the horizontal scale is marked off in
appropriate units—whole numbers, halves, or quarters.
(At grade 4, a related standard this includes eighths of an inch.)
Details
Subtleties
Particulars
Nuances
3.MD.4 Generate measurement data by measuring lengths using
rulers marked with halves and fourths of an inch. Show the data
by making a line plot, where the horizontal scale is marked off in
appropriate units—whole numbers, halves, or quarters.
(At grade 4, a related standard this includes eighths of an inch.)
The line plot below shows the test scores of 26 students:
3.MD.4 Generate measurement data by measuring lengths using
rulers marked with halves and fourths of an inch. Show the data
by making a line plot, where the horizontal scale is marked off in
appropriate units—whole numbers, halves, or quarters.
(At grade 4, a related standard this includes eighths of an inch.)
--Arizona Department of Education
One of the Common Core High School Clusters:
Solve systems of equations
Details
Subtleties
Particulars
Nuances
One of the Common Core High School Clusters:
Solve systems of equations
A.REI.7 Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically. For example, find the
points of intersection between the line y = –3x and
the circle x2 + y2 = 3.
Whether you modify the old curriculum one step
at a time, or you throw it all out and start afresh,
there are potential speed bumps
Details
Subtleties
Particulars
Nuances
Things we shouldn’t forget…
Grades 2, 3, and 4
The importance of actually measuring
NEW Grade 2


CCSS 2.MD.1 Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
[2.MD.9 limits this expectation to the nearest whole unit.]
CCSS 2.MD.6 Represent whole numbers as lengths from 0 on a number line
diagram with equally spaced points corresponding to the numbers 0, 1, 2, ...,
and represent whole-number sums and differences within 100 on a number line
diagram.
NEW Grade 3

CCSS 3.MD.4 Generate measurement data by measuring lengths using rulers
marked with halves and fourths of an inch. Show the data by making a line plot,
where the horizontal scale is marked off in appropriate units—whole numbers,
halves, or quarters.
[In grade 4 (CCSS 4.MD.4), the expectation is extended
to include eighths.]
Things we shouldn’t forget…
Grade 5
Adding & subtracting decimals includes
decimals and whole numbers
NEW Grade 5
 CCSS 5.NBT.7
Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Example:
Paula’s tractor holds 3 liters of gasoline. Tom’s tractor holds
2.4 liters. How much more does one tractor hold than the
other?
2.4
─3
3
─ 2.4
3.0
─ 2.4
[Not money - Not Multiple Choice]
Things we shouldn’t forget…
Grade 6
Various types of questions can be linked
to the same standard
NEW Grade 6
 CCSS 6.NS.7 Understand ordering and absolute
value of rational numbers. (there are bullets)
Example:
Find a number that is between 1/3 and 0.36.
Example (contextualized):
Mark and Tom played little league baseball last summer. Mark was at bat 33
times and had 11 hits. Tom had a batting average of .360. Find another
possible batting average that is better than Mark’s but not as good as
Tom’s.
Example (student-developed context):
Find a number that is between 1/3 and 0.36, and describe a situation in
which you might actually need to answer such a question.
Things we shouldn’t forget…
Grade 7
There are percents greater than 100
NEW Grade 7
 CCSS 7.RP.3
Use proportional relationships to solve multistep
ratio and percent problems. Examples: simple interest, tax,
markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error.
Example:
Dottie’s Teacher told her that when he started teaching in 1970
he could purchase a gallon of regular gasoline for his car for
approximately 30¢. Now, in 2004, a gallon of gasoline costs
approximately $1.80. What is the percent increase in price?
Misunderstanding:
1.50/.30 = 5%
1.80/.30 = 6%
.30/1.50 = .2 = 20%
Understanding:
1.50/.30 = 5 = 500%
Things we shouldn’t forget…
Grade 7
There is more to mathematics than
substituting into formulas
NEW Grade 7
 CCSS 7.G.2 Draw (freehand, with ruler and protractor, and with
technology) geometric shapes with given conditions. Focus on
constructing triangles from three measures of angles or sides,
noticing when the conditions determine a unique triangle, more than
one triangle, or no triangle.
Example:
The hypotenuse of a right triangle has a length of 34 centimeters.
Which of the following could be the perimeter of the triangle?
a. 20 cm
b. 50 cm
34cm
c 80 cm
d. 110 cm
Things we shouldn’t forget…
High School/Grade 7
There is more to mathematics than
substituting into formulas
NEW Grade 7

CCSS 7.G.4 Apply geometric methods to solve design problems
(e.g., designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on
ratios).★
Example:
Jennie has a souvenir baseball, which she wants to store in a
cubical box. She knows that a baseball is 2 3/4" (7 cm) in diameter.
What would be the smallest possible dimensions for a cubical box
that Jennie could use to store her baseball?
Misunderstanding:
(4/3) πr3 ≈ 179.6 cm3
Edge of box ≈ 5.65 cm
(4/3) πr3 ≈ 10.89 in.3
Edge of box ≈ 2.22 in.
Understanding:
Edge of box = 7 cm
Edge of box = 2 3/4"
15%
Speed Bumps
15%
Some have the misconception that the mathematics in
the Common Core is all the mathematics there is to learn.
Avoid this speed bump! Take advantage of the district’s
prerogative to add additional content.
Others are tempted to try to include all
or nearly all that they have taught in
previous years.
Avoid this speed bump also! Don’t lose
focus
Mathematics | Grade 3
In Grade 3, instructional time should focus on four
critical areas:
(1) developing understanding of multiplication and
division and strategies for multiplication and division
within 100;
(2) developing understanding of fractions, especially unit
fractions (fractions with numerator 1);
(3) developing understanding of the structure of
rectangular arrays and of area; and
(4) describing and analyzing two-dimensional shapes.
Mathematics | Grade 4
In Grade 4, instructional time should focus on three critical
areas:
(1) developing understanding and fluency with multi-digit
multiplication, and developing understanding of dividing to
find quotients involving multi-digit dividends;
(2) developing an understanding of fraction equivalence,
addition and subtraction of fractions with like denominators,
and multiplication of fractions by whole numbers;
(3) understanding that geometric figures can be analyzed and
classified based on their properties, such as having parallel
sides, perpendicular sides, particular angle measures, and
symmetry.
Some have the misconception that the mathematics in
the Common Core is all the mathematics there is to learn.
Avoid this speed bump! Take advantage of the
district’s prerogative to add additional content.
Others are tempted to try to include all
or nearly all that they have taught in
previous years.
Avoid this speed bump also! Don’t lose
focus
Potential Challenges in Transitioning
to the Common Core in Mathematics
Common Core State Standards (CCSS)
adopted June 16, 2010
1.NBT.3. Compare two two-digit numbers based on meanings of
the tens and ones digits, recording the results of comparisons with
the symbols >, =, and <.
2.OA.3. Determine whether a group of objects (up to 20) has an
odd or even number of members, e.g., by pairing objects or
counting them by 2s; write an equation to express an even number
as a sum of two equal addends.
Grade/
Course
Gr. 2
CCSS move symbols ( = , < , > ) from
grade 3 (NJ cccs 4.3.3.D.2) to grade 1.
CCSS move “determining whether a
whole number is odd or even” from grade
3 (NJ cccs 4.1.3.A.3) to grade 2.
Gr. 3
2.NBT.4. Compare two three-digit numbers based on meanings of
the hundreds, tens, and ones digits, using >, =, and < symbols to
record the results of comparisons.
3.OA.7. Fluently multiply and divide within 100, using strategies
such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of
operations.
By the end of Grade 3, know from memory all products of two onedigit numbers.
Change
CCSS move symbols ( = , < , > ) from
grade 3 (NJ cccs 4.3.3.D.2) to grade 2
(actually grade 1, in 1.NBT.3).
Gr. 4
CCSS move memorizing the multiplication
table from grade 4 to grade 3
Transition
Speed Bumps
Transition
Measuring Angles
An Example of a Challenge in the Transition
Grade 4
Grade 5
Cohort 2010-11
1
Old State Standards
2011-12
Old State Standards
(Includes Measuring
angles in grade 5)
Cohort 2011-12
2
Old State Standards
2012-13
CCSS
Cohort 2012-13
3
CCSS
Measuring angles (?)
4.MD.5. Recognize angles as
geometric shapes that are
formed wherever two rays share
a common endpoint, and
understand concepts of angle
measurement.
4.MD.6. Measure angles in
whole-number degrees using a
protractor. Sketch angles of
specified measure.
2013-14
CCSS
Measuring angles
was learned in
grade 4.
Overcoming speed bumps during the
transition to the Common Core State
Standards in Mathematics
Prioritize interweaving the practices with content.
Pay attention to details in the CCSS.
Focus on critical content areas.
Build in adjustments during the transition.
Questions?
Prioritize interweaving the practices with content.
Pay attention to details in the CCSS.
Focus on critical content areas.
Build in adjustments during the transition.