CMI2012 CCSS for Mathematics

Designing
Common
Core
State
Standards

Systemic
Mathema4cs
Curriculum

Presented
By
Janet
Hale



www.CurriculumMapping101.com

Backchannel: todaysmeet.com/ccssm

Architects Contractors
design. build.
LEARN TEACH

Aspen Grove Mentality

Systemic Design - Interdependent
1 Grove…1 Root System

Designing Systemic K-12
CCSS Math Collaborative Maps

How long will it take
for the K-12 Task
Force to complete
Stage 1?

Part 1 Design / Part 2 Design
Vertical Alignment Horizontal Alignment
Design units that represent Design units of study that
K-12 learning continuum integrate learning within and/
(e.g., Geometry, Measurement/Data) or among strands
by single/mixed domains in one grade level
across grade levels (e.g., intradisciplinary,
program-based,
interdisciplinary)

Part 1 – Phase I

•  Unit Names

•  Enduring Understandings/
Essential Questions

•  Standards for Mathematical Practice

•  Vocabulary

Designing
UNIT NAMES

Quickly locating
learning
by reading electronic
(Pre-‐K)
K
through
12

“binder” spine.

Arizona
http://www.azed.gov/standards-practices/
mathematics-standards/

Ohio
http://education.ohio.gov/GD/Templates/Pages/ODE/
ODEDetail.aspxPage=3&TopicRelationID=1704&Con
tent=123507 (Transitional Tools)



High School
Course
Design

Determine
Desired
Pathway

Math CCSS
Appendix A



Math CCSS Courses – Suggested Starting Points K-8
Math (K-8)
GEOMETRY (K-2, 6-8)
GEOMETRY/MEASURMENT (3-5)
DATA: MEASUREMENT/DATA (K-5)
DATA: STATISTICS/PROBABILITY (6-8)
NUMBER/QUANTITATIVE: COUNTING/CARDINALITY (K)
NUMBER/ALGEBRAIC: NUMBER BASE 10/OPERATIONS (K-5)
NUMBER: NUMBER SYSTEM/EXPRESSIONS/EQUATIONS (6-8)
QUANTITATIVE: RATIOS/PROPORTIONAL RELATIONSHIPS (6-8)
Coordinate Algebra (9) (Integrated Pathway)
EXPRESSIONS/EQUATIONS
LINEAR FUNCTIONS
EXPOTENTIAL FUNCTIONS
DATA ANALYSIS
COORDINATE PLANE
INEQUALITIES
Analytic Geometry (10) Advanced Algebra (11)
(Above examples based on work in Muscogee CSD, Columbus, GA)

K-12 CCSS Aligned/Designed
Enduring Understandings/
Essential Questions

Create CCSS-based EUs/EQs prior to Part 1
or…
Create CCSS-based EUs/EQs prior to Part 2

Enduring Understandings/
Essential Questions
It usually takes a task force two full days
(including initial training: “What are EUs/EQs/SQs?”)
to create K-12 CCSS-based Math EUs/EQs.

Part 1 – Phase I
•  Unit Names

•  Understandings/
Essential Questions

•  Standards for Mathematical Practice

•  Vocabulary



Domains, Cluster, Standard Statements
(CCSS,
p.
5)

Page
7-‐8,
CCSSM

1.  Make sense of problems and persevere in solving them.
2.  Reason abstractly and quantitatively.
3.  Construct viable arguments and critique the reasoning of
others.
4.  Model with mathematics.
5.  Use appropriate tools strategically.
6.  Attend to precision.
7.  Look for and make use of structure.
8.  Look for and express regularity
in repeated reasoning.

Standards for Mathematical Practice are the same K-12…

http://www.azed.gov/standards-practices/mathematics-standards/



Standards for Mathematical Practice
Choices…
1.  Embed SMP expectations as part of skill
statements by asking for justifying reasoning and
provide examples (e.g., ____) for teachers to gain
insight into higher level of expectation (students
“owning” the learning) 3. Construct viable arguments
and critique the reasoning of
others.

2.  Create SMP-based skill statements
that represent the essence
of the eight practices to be
included as a part of Part 2’s
units of study.

Grade
1

GEOMETRY

Content

E.
Geometrical
Rela.onships:
Composi.on

-‐-‐2-‐Dimensional
(Quarter
Circle,
Half
Circle,
Quarter
Circle,
Circle,

Square,
Rectangle,
Triangle,
Trapezoid,
Hexagon)

-‐-‐3-‐Dimensional
(Cube)

Skill

E.
Compose
manipula.vely,
orally,
and
in
wri.ng
1
two-‐dimensional

shape/figure
using
appropriate
2-‐dimensional
shapes
(i.e.,
see
Possible

Composi/ons
reference)
and
jus.fy
reasoning
(e.g.,
Ami
has
a
cardstock

square
in
front
of
her.
She
has
various
cardstock
shapes
nearby.
Mr.
Mar/n
asks

her
to
show
him
3
ways
she
can
compose
a
square
with
the
various
shapes.
Ami

makes
1
square
first
using
4
smaller
squares;
next
using
2
rectangles;
and
then

using
4
triangles.
The
teachers
asks
her
to
explain
in
wri/ng
what
she
did
and
why.

Ami
shared,
“I
first
composed
1
large
square
using
4
small
squares…See
1,
2,
3,
4

equal
shares.
Then
I
took
them
off
and
used
2
equal
shares;
2
rectangles.
And
last,

I
took
off
the
rectangles
and
used
4
equal
shares,
but
this
/me
they
were
triangles

instead
of
squares,
but
the
s/ll
fit
just
right
on
the
large
square.”)

Design
Note
…
Use
of
parentheses
in
skill
statements

Reduce
complex
frac.on
(frac.on
over
frac.on)
by
mul.plying

by
common
denominator
(e.g.,
see
complex
frac/on
example)

Describe
orally
and
in
wri.ng
par..oned
shares
using

6
terms
(halves,
half
of,
thirds,
third
of,
quarters,
quarter
of)

(e.g.,
Carmen
par//ons
a
circle
into
2
equal
shares.
She
writes:
The
circle

has
2
equal
shares
or
2
halves.)

(e.g.,
_____________
)
=

(i.e.,
______________)
=

(______________)

=

Algebra
“Connec4ons”
….
Use
of
“Baby
a”

Content

S.
Addi.on/Subtrac.on:
Differen.a.on
Between

1-‐Step/2-‐Step

Word
Problems

Skills

Sa.
Differen.ate
orally
and
in
wri.ng
between
1-‐step
word
problem

having
1-‐event
equa.on
(1
sum/1
difference)
versus
2-‐step
problem

where
sum/difference
of
1st-‐event
equa.on
must
be
used
in
2nd-‐
event
equa.on
to
find
final
sum/difference
and
jus.fy
reasoning

(e.g.,
Mr.
Bryan
reads
2
displayed
word
problems
to
his
class,
"The
first
problem
says:

George
collects
coins.
He
has
32
coins.
His
uncle
brought
him
14
coins
from
Japan
to
add
to

the
his
collec/on.
How
many
coins
does
George
have
now?
The
second
problem
says:
A

cafeteria
has
a
basket
of
25
oranges.
The
basket
has
5
oranges
leY
in
it
at
the
end
of
lunch.

The
next
morning
a
cafeteria
worker
adds
10
more
oranges
to
the
basket.
How
many

oranges
will
be
available
for
lunch
today?"
Mr.
Bryan
asks,
"Which
problem
is
a
1-‐step

problem
and
which
problem
is
a
2-‐step
problem?"
Jeb
raises
his
hand.
Mr.
Bryan
asks
him
to

come
to
the
board.
Jeb
comes
up
and
shares
his
reasoning,
"The
problem
about
the
coins
is

a
1-‐step
problem
because
all
you
have
to
do
is
add
the
2
sets
of
coins
together
so
it
is
1

event.”
He
writes
on
the
board:
32
+
14

=
46.
"The
second
problem
is
a
2-‐step
problem

because
it
has
2
events.
For
the
1st
event
you
have
to
subtract
to
find
the
difference.
Then

you
have
to
add
10
to
the
difference
in
the
2nd
event."
He
writes:
25
–
20
=
5,
5
+
10
=
15).



Vocabulary

Choices…
Embed vocabulary terms
and definitions within Content field?
Skills field? Resources as an attachment?
Format…
Agree on visual format so vocabulary will
be consistent for curriculum design not
only for Math, but other disciplines as well.
The more continuity among disciplines,
the more accurate and useful the reporting
features are within a mapping system.

Grade
6

QUANTITATIVE:
RATIOS/PROPORTIONAL
RELATIONSHIPS

A.
Communicate
concepts/explana.ons
orally

and
in
wri.ng
using
3
terms:

Part 1 – Phase I

•  Unit Names

•  Enduring Understandings/
Essential Questions

•  Standards for
Mathematical Practice

•  Vocabulary

Part 1 – Phase II
•  Breaking Apart (Translating, Unpacking)
Standards
(Design Influences – Key Shifts, Depth of Knowledge)

•  Systemic Content / Skills Development
(Process: Format … Collaborative Agreement on Tight and Loose)

•  PreK-12 Vertical Reviews
(Internal Alignment – Content/Skills
& External Alignment to CCSS)

•  Horizontal Units of Study
(Bridging Part 1 and Part 2 Design Work)

Implicit Influences
•  Breaking Apart (Translating, Unpacking)
Standards

Teachers will, as architects-designers, spend extensive
time studying the explicit and implicit intent of the codes,
but need to first consider design influences.

•  Math CCSS - 3 Key Shifts

•  Depth of Knowledge
(PARCC, SMARTER Balance)

CCSS Mathematics – 3 Key Shifts
(www.achievethecore.org)

1.  FOCUS
Focus Strongly Where the Standards Focus
(narrow the scope of content to allow in-depth learning; no “but we have so much to cover”;
need “inch wide, mile deep” mindset to ensure time necessary for students to explore, test,
and reach personal conceptual understanding)

2. COHERENCE
Think across grade levels (systemic design)
(each new standard is not a “new event” … each new standard is an extension of previous
distinct or linked learning)
Link learning among domains within one grade level (leverage)
(conceptual relationships across and among standards to aid in conceptual understanding
and reasoning)

3. RIGOR
Equitable, balanced curriculum
(learning/teaching):
–Conceptual Understanding
–Procedural Skills and Fluencies
–Application of Math Process using
real-world/authentic problems/tasks
(within/across disciplines)

1.  FOCUS

2.  COHERENCE

Presenta.on
Slide
from
CCSS
for
Mathema/cs:
Key
ShiYs
-‐Sandra
Alber.,
Student
Achievement
Partners

3.
RIGOR
Grade
7

(Content
lis/ng
in
an
Essen/al
Map
unit)

--Conceptual Understanding Algebraic
Representa.ons:

--Procedural Skills and Fluencies
--Application of Math Process

Equa.on
Fluency
Involving
4
Opera.ons

Mul.-‐Step
Word
Problems
(Posi.ve/Nega.ve

Ra.onal
Numbers,
Inequali.es,
Complex

www.achievethecore.org

Frac.ons)

CCSS
Fluency
≠
Rote
Memoriza4on

CCSS
Fluency

=

Speed
and
Accuracy

using
self-‐selected
strategies

High
School
Fluencies:
Algebra,
Func4ons,

Geometry,
Sta4s4cs
&
Probability,
and
Modeling

Cognitive Complexity
New
BLOOM’S

DOK

New
Bloo
m’s
Evaluate Predict Hypothesize
Generate Speculate Forecast Output Creating/
Imagine If/then Create E/C Evaluating
Judge Apply Speculate
Compare Distinguish Analyze
Contrast Explain Synthesize Process Analyzing/
Classify Discriminate Reason A/A Applying
Infer Sequence Interpret
Duplicate Identify Paraphrase
Count List Recite Input Understanding/
Define Memorize Locate R/U Remembering
Describe Name Reproduce

New
BLOOM’S

R/U A/A E/C
Input Process Output

DOK

Norman
Webb’s

Depths
of
Knowledge

DOK
Model
(1997)
created
to
analyze
the
cogni.ve
expecta.on

demanded
by
standards,
curricular
ac.vi.es,
and
assessment
tasks.

redesign.rcu.msstate.edu

Several
things
are
involved,

including
the
content,
the
ac4vity

and/or
thinking
processes,
and
the

complexity
of
both
the
content
and

ac4vity/thinking
processes.

-‐-‐Debbie
Baughman,

The
Standards
Company

DOK

Four
Levels

Level
1
Recall/Reproduc4on

Recall
facts,
informa.on,
procedures,

basic
concept
founda.ons

(minor
comprehension
involved
at
this
level,

no
depth,
no
complexity)

Level
2
Skill/Concept

Apply/process
facts,
informa.on,
procedures,

conceptual
understanding
involving
at
least
two

steps
that
require
reasoning

(a
need
to
interpret
material
and
make
simple
decisions
about
how
to

approach
a
problem,
but
does
not
yet
have
a
deep
complexity)

DOK

Four
Levels

Level
3
Strategic
Thinking

Requires
deeper
reasoning,
developing
a

plan
or
sequence
of
steps
to
complete
a
task;

more
than
one
possible
solu.on/answer

(deal
with
abstrac/ons
and
open-‐ended
conclusions
and
able
to

support
one’s
reasoning;
wrestle
with
complex
concepts,
tasks,
material)

Level
4
Extended
Thinking

Process
mul.ple
condi.ons
and
solu.ons
for
the

problem;
extend
thinking
by
comple.ng
much
deeper

and
complex
tasks

(according
to
Webb,
higher-‐level
thinking
is
absolutely
central;

interac/on
with
concepts,
tasks,
material
is
in-‐depth
and
purposeful)

CAUTION!

Bloom’s
Verbs
cannot
be
applied
with
the
same
mindset

for
what
students
must
cogni9vely
do
when
applying

Webb’s
Depth
Of
Knowledge
(DOK)
to
student
learning,

teaching,
and
assessment
items/tasks.

The
“cau4on”
inﬂuences
wri4ng
skills…

Measurable
Verb
+
Descriptor

DOK
1
–
Describe
shape-‐pabern
term/number-‐pabern
rule

using
real-‐world
examples
(e.g.,
Pretend
you
are
walking
outside.

Draw
and
explain
a
natural
or
man-‐made
pafern’s
term.)

DOK
2
–
Describe
number/shape
paberns
that
follow

determined
term/rule
and
jus.fy
reasoning
(e.g.,
Look
at
the

bowling
pins
pafern.
What
will
the
next
two
rows
look
like
in
this

pafern?
Explain
the
increase
using
textual,
visual,
and
number

representa/ons.
Without
drawing,
what
would
be
the
number
of
pins
in

the
15th
row?
Explain
your
reasoning.
)

New
BLOOM’S

R/U A/A E/C
Input Process Output

1 2 3 4
Recall/ Skill/ Strategic Extended
Reproduction Concept Thinking Thinking

DOK
PARCC Smarter Balanced
www.smarterbalanced.org/wordpress/wp-content/uploads/2012/03/
www.parcconline.org/parcc-content-frameworks DRAFTMathItemSpecsShowcase2.pdf

www.illustrativemathematics.org

Part
2
–
Phase
II

K-‐8
Process
For

“Pla4ng”
Quartered
Learning
Expecta4ons

Step
1:
Code
hard-‐copy
of
each
Part
1
“full-‐year”
UNIT’s
Content/
Skill
statements
to
aligned
standards.

Step
2
(Quartered
Units):
Cut
out

Content/Skills
Sets
and
create

graphic
organizers
that
represent
full

year
of
“quartered”
UNIT
learning.

Part
2
–
Phase
II

K-‐8
Process
For

“Pla4ng”
the
Learning
Expecta4ons

Step
3:
Create
quartered
UNITS
in
mapping
system
(ensure
newly

created
UNITS
include
aligned
standards
for
each
quarter’s
learning).

Step
4:
Ensure
abachments
are

included
properly
in
each
quartered

UNIT
(preferably
as
.pdf
ﬁles).

Part
2
–
Phase
II

Process
For

“Pla4ng”
Sequen4al
Learning
Expecta4ons

Step
1:
Code
hard-‐copy
of
each
UNIT’s
Content/Skill
statements
to

aligned
standards.

Step
2
(Sequen.al
Units):
Cut
out
Content/Skills
Sets
and
create

graphic
organizers
that
represent
full
year
of
learning.

Step
3:
Create
sequen.al

UNITS
in
mapping
system

(ensure
newly
created
UNITS

include
aligned
standards
for

each
UNIT’s
learning).

Step
4:
Ensure
abachments
are

included
properly
in
each
UNIT

(preferably
as
.pdf
ﬁles).

Wearing
the
right
design
gear,
dive
on
in!

(Even
though
it
may
feel
a
liple
unnerving
at
ﬁrst…)

Janet
Hale

www.CurriculumMapping101.com

teachtucson@aol.com

520-‐241-‐8797

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