Common Core State
Standards for
Mathematics:
Shifts and Implications for
Mathematics Instruction
Morning Session
Focus, Coherence, and Rigor;
Realizing the Common Core in
Elementary Mathematics


Understand how the Common Core influences
our Instruction
Identify the 3 major shifts in math education
Out to lunch…
“I’m not good
at math, you figure
it out.”
Last week, I was
at a restaurant
with a group of
friends. The bill
came and this is
what was said…
Next time we go…
“I’m not good
reading, can
you read this
to me?”
Same Reaction?
Illiteracy
Innumeracy
Why is it socially
acceptable to be
innumerate?
Innumeracy
21% of Americans possess
numeracy skills at the lowest
level . . . [which] means that
people cannot . . . work out
the change from $2 when
buying goods worth $1.58.
(Murray, 2000. p. 2)
www.lausd.net/District_8/math/secmath/0607/math_anx_nc
sm.ppt
Procedures = Understanding
Explain to your partner how you would
use the traditional algorithm to solve
this
17
-6
Procedures = Understanding
Now explain to your partner how you
would use the traditional algorithm
to solve this
10
-6
Procedures = Understanding
17
-6

10
-6
How did changing the numbers
influence the “difficulty” of the task?
Procedures = Understanding
10
-6

Do they
understand?
Xtranormal video- I will email the
link as soon as it is released. If it’s
not released in time, you can simply
say “What do I do first? I can’t take
6 away from 0, so I have to cross off
the 1 and …”.  Teachers always
get a chuckle out of this.
Procedures & Algorithms
At your table, fill your large paper with
examples of algorithms/procedures
you learned as a student.
Examples:
Foil method in algebra
Butterfly to compare fractions
Standard Algorithm for multiplication or division
Algorithms

Choose one procedure or algorithm
that you learned as a student.


E.g., Finding common denominator,
FOIL, Butterfly to compare fractions,
multiplication or division algorithm,
dividing fractions
Do a sample problem using it…

Then explain it to your neighbor –
explain the process and why it works
Algorithms

What algorithms did you explain?

How does understanding the math
relate to following the steps of the
algorithm?
Break

When you come back, please sit in
grade level groups.
Welcome Back
According to the
Common Core,
What is MOST
IMPORTANT at
your grade level?
 Answer by placing
one sticker on the
chart.

The Three Shifts in Mathematics
Authors of the Common
Core Math Standards
have emphasized 3
shifts from old state
standards
(like the NCSCOS)



Focus
Coherence
Rigor
Shift One: Focus
strongly where the Standards focus
Significantly narrow the scope of
content and deepen how time and
energy is spent in the math classroom
 Focus deeply only on what is
emphasized in the standards, so that
students gain strong foundations

Why Focus?

The U.S. curriculum before the
Common Core was known as ‘a mile
wide and an inch deep.’


What did this look like in the NCSCOS?
Focus is necessary in order to achieve
the rigor set forth in the standards
Mathematics topics intended at each grade
By at least 2/3 of US States
By at least 2/3 of A+ Countries
The Shape
of
Math
Instruction
1
Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of
Content Emphasis
Focus
Designed to help
teachers focus on
what is most important
at each grade level.
Content Emphases by Cluster




Not all of the content in a given grade is emphasized equally
in the standards.
Some clusters require greater emphasis based on the depth
of the ideas, the time that they take to master, and/or their
importance to future mathematics or the demands of college
and career readiness.
An intense focus on the most critical material at each grade
allows depth in learning, which is carried out through the
Standards for Mathematical Practice.
Focus does not mean neglecting certain standards.
Neglecting material will leave gaps in student skill and
understanding and may leave students unprepared for the
challenges of a later grade.
Sample Content Emphases
Focus – your grade level

With your grade level team
Focus

Look at the Content Emphasis

In YOUR copy of the Common Core –
highlight areas of focus at your grade
level.
With your grade level
team, discuss…
K-2 Teachers


3-5 Teachers
Look at the supporting
 Identify major changes
standards at your
within your grade level.
grade level.
 How has the focus
Generate specific
changed from the 2003
examples of how each
NCSCOS?
supporting standard
relates to major
Focus
standards
Focus

Would you
change where
you placed your
sticker?
Focus
Break!~
Coherence Within Grade

Use the handout of your Grade Level
Clusters

Analyze how these clusters are classified
How do these clusters overlap or
address similar “larger concepts”?
 How do Supporting Clusters align with
Major Clusters.

Coherence
Pick a unit from Investigations that
incorporates multiple clusters
 What are the pre-requisite skills
you hope students have before this
unit starts?
 As students are doing the work in
the unit, what is the Major Cluster?


What other clusters are also
incorporated?
Coherence

Move and group with teachers from
multiple grade levels

Exchange ideas and discuss what
your grade level came up with
Coherence Wrap-up



When teaching the Common Core, teachers should:
Carefully connect the learning within and across
grades so that students can build new
understanding onto foundations built in previous
years.
Begin to count on solid conceptual understanding of
core content and build on it. Each standard is not a
new set of events, but an extension of previous
learning.
Shift Three: Rigor

The CCSSM require a balance of:




Solid conceptual understanding
Procedural skill and fluency
Application of skills in problem solving situations
This requires balanced intensity in time,
activities, and resources in pursuit of all three
Rigor
Place Value…
Why do we need rigor when we work
with place value concepts?
Hundreds, Tens, and Ones
In groups with teachers from different
grade levels, analyze the two
Hundreds, Tens, and Ones activities.
How does each provide…
Solid conceptual understanding
 Procedural skill and fluency
 Application of skills in problem solving
situations

Hundreds, Tens and Ones

Do these promote Conceptual
Understanding?

Why or why not?
Hundreds, Tens and Ones

Do these promote Procedural Skill
and Fluency?

Why or why not?
Hundreds, Tens and Ones

Do these promote skill application in
problem solving situations?

Why or why not?
DPI 3-5 Released Item
Mrs. Gregory assigned a project that
required each of her 20 students to
use 36 toothpicks. How many
toothpicks did the students use?
A)72
B)620
C)720 D)7,200
Common Core
Rigor
Compare the two previous multiplication
items, and discuss how each does/does not
provide the opportunity for students to
demonstrate…
 Solid conceptual understanding
 Procedural skill and fluency
 Application of skills in problem solving
situations
Three Mathematical Shifts

Which shift will have the greatest
impact on student learning?

Decide with your team and be
prepared to share!
Realizing the Promise of the
Common Core
It will take hard
work on our part
to move a society
from this…
10
-6
To This!
Afternoon Session

Ensuring the Standards for
Mathematical Practice at the
student level.
Illustrating the
Mathematical Practices
Afternoon Session

Ensuring the Standards for
Mathematical Practice at the
student level.
A pen for Aramis and Elise (Great Danes) is shown
below. Amy wants to add a safe place for her
Chihuahua to run around the great Danes (and not
get stepped on!). If she adds a fence that is 2½
feet from the current perimeter, how much fencing
will she need for the Chihuahua’s run?
The Chihuahua run
must be built 2½ feet
from the edge of the
Great Dane pen!
7¼
3
5
2
Solutions
Standards for
Mathematical Practice

4 and 5

In pictures and words, show how you
used either mathematical practice 4
or 5 as you solved this task

(you might have to pull these out and
re-read )
An Experience with Students

The following slides are from DPI.
The Task
What would that look like…

With our students?
Step 1: Introduce/Review Standards for
Mathematical Practice # 4 and #5
Date:
Briefly describe how you will introduce/review Standards for Mathematical Practice #
4 and #5
Step 2: Apply Standards for Mathematical Practice # 4 and #5 to a math lesson.
Select a lesson that provides students the Briefly describe lesson chosen:
opportunity to choose appropriate tools
strategically and model with mathematics.
Toward the end of the lesson, ask students to illustrate how they used mathematical
practice #4 OR #5 in their work today.
Step 3: Bring illustrations to math planning.
As a team, choose 2 illustrations (one that shows a solid understanding and one that
shows minimal understanding). Send illustrations in to Amy and Marilyn (use
envelope provided).