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Common Core: Shifts,
Practices, Rigor
Cathy Battles
Consultant
UMKC-Regional Professional Development Center
[email protected]
Starter Problem
Using each of the digits 1 through 9 only once, find two 3digit numbers whose sum uses the remaining three digits
Some Answers
681
368
352
+127
+467
+273
495
819
954
324
+567
891
Partner Time
 Turn to your partner and tell them what you know about
the common core and what you or your district has
done.
About the Common Core Standards
 Clarity: The standards are focused, coherent, and clear.
Clearer standards help students (and parents and
teachers) understand what is expected of them.
•Collaboration: The standards create a foundation to work
collaboratively across states and districts, pooling
resources and expertise, to create curricular tools,
professional development, common assessments and
other materials.
Source: Adapted From Student Achievement Partners
Education Week: COMMON STANDARDS www.edweek.org/go/standardsreport
4/25/12
Common Core Standards Shifts
 Significantly narrow the scope of content and deepen how
time and energy is spent in the classroom
 Focus deeply on what is emphasized in the standards, so
students gain strong foundations
 Equity: Expectations are consistent for all – and not
dependent on a student’s zip code. Level the playing field
for students across the country…
CCSS Domain Progression
K
1
2
3
4
5
6
7
8
HS
Counting &
Cardinality
Number and Operations in Base Ten
Number and Operations –
Fractions
Ratios and Proportional
Relationships
Number &
Quantity
The Number System
Expressions and Equations
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics &
Probability
1.
Make sense of problems
and persevere in solving them.
Counting
and
Cardinality
Kindergarten
Grades K-5
7.
Look for and make
use of structure.
Grades 3-5
Numbers
and
Operations
in Base Ten
Operations
and Algebraic
Thinking
Grades K-5
Grades K-5
3.
Construct viable arguments and
critique the reasoning of others.
Geometry
Fractions
Measurement and Data
Grades K-5
5.
Use appropriate tools
strategically.
http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg
Kathy Anderson
1.
Make sense of problems
and persevere in solving them.
Ratios and
Proportional
Relationships
Grades 6-7
Geometry
7.
Look for and make
use of structure.
Grade 8
Grades 6-8
Expressions
and
Equations
Statistics and
Probability
Grades 6-8
Grades 6-8
3.
Construct viable arguments and
critique the reasoning of others.
Functions
The Number System
Grades 6-8
5.
Use appropriate tools
strategically.
http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg
Kathy Anderson
1.
Make sense of problems
and persevere in solving them.
Modeling
Algebra
7.
Look for and make
use of structure.
Functions
3.
Statistics
and
Probability
Construct viable arguments and
critique the reasoning of others.
Geometry
Number and
Quantity
5.
Use appropriate tools
strategically.
http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg
Kathy Anderson
Mathematical Practices are
Not:
 A checklist
 Disconnected from content standards
 Grade specific
 New
 Restricted to math
 Taught in isolation
 Sequential
 A Friday problem solving activity
CORE ACADEMIC
STANDARDS(CAS)
Missouri’s Core Academic Standards are the same as the
Common Core Standards for Math and ELA but also
include Social Studies and Science
RIGOR
A balance of :
A.Conceptual Understanding
B.Fluency
C.Application
National Mathematics Advisory Panel
Of all pre-college curricula, the highest level of
mathematics in secondary school has the
strongest continuing influence on bachelor’s
degree completion. Finishing a course beyond
Algebra 2 more than doubles the odds that a
student who enters post-secondary education
will complete a bachelor’s degree.
Adams, C. (2006). Answers in the toolbox: academic intensity, attendance
patterns, and bachelor’s degree attainment. (Office of Educational Research
and Improvement Publication.) http://www.ed.gov/pubs/Toolbox/Title.htm.
National Mathematics Advisory Panel
Recommendations
1. A focused, coherent progression of
mathematics learning, with an emphasis on
proficiency with key topics, should become the
norm in elementary and middle school
mathematics curricula; the most important
topics underlying success in school algebra.
National Mathematics Advisory Panel
Recommendations
2. A major goal of K – 8 mathematics education
should be proficiency with fractions (including
decimals, percent, and negative fractions), for
such proficiency is foundational for algebra and
seems to be severely underdeveloped. In
addition, the Panel identified Critical
Foundations of Algebra (p 17).
Fractions
Turn to your neighbor and share one thing that you know
about the Common Core and changes with fractions
“It is possible to have
good number sense for
whole numbers, but not
for fractions.”
Sowder, J. and Schappelle, Eds. 1989
18
Fraction Sense?
Problem: 7/8 – 1/8 = ?
Interviewer:
Melanie these two
circles represent
pies that were each
cut into eight pieces
for a party. This pie
on the left had
seven pieces eaten
from it. How much
pie is left there?
Melanie: Oneeighth, writes 1/8
Interviewer: The pie
on the right had
three pieces eaten
from it. How much is
left of that pie?
Melanie: Fiveeighths, writes 5/8
Interviewer: That’s not the same
as you told me before. Is that OK?
Melanie: Yes, this is the
answer you get when you add.
• Interviewer: If you
put those two
together, how much
of a pie is left?
• Melanie: Sixeighths, writes 6/8.
Interviewer: Could
you write a number
sentence to show
what you just did?
Melanie: Writes 1/8
+ 5/8 = 6/16.
American students’ weak understanding
of fractions
2004 NAEP - 50% of 8th-graders could
not order three fractions from least to
greatest (NCTM, 2007)
American students’ weak understanding
of fractions
2004 NAEP, Fewer than 30% of 17year-olds correctly translated 0.029 as
29/1000 (Kloosterman, 2010)
American students’ weak understanding
of fractions
One-on-one controlled experiment
tests - when asked which of two
decimals, 0.274 and 0.83 is greater,
most 5th- and 6th-graders choose
0.274 (Rittle-Johnson, Siegler, and
Alibali, 2001)
American students’ weak understanding
of fractions
Knowledge of fractions differs even
more between students in the U.S. and
students in East Asia than does
knowledge of whole numbers (Mullis,
et al., 1997)
Fractions
Facets of the lack of student conceptual
understanding:
• Not viewing fractions as numbers at all, but
rather as meaningless symbols that need to be
manipulated in arbitrary ways to produce
answers that satisfy a teacher
• Focusing on numerators and denominators as
separate numbers rather than thinking of the
fraction as a single number.
• Confusing properties of fractions with those of
whole numbers
rd
3
Grade Number and
Operations Fractions(3.NF)
 Develop understanding of fractions as numbers.
 Understand a fraction 1/b as the quantity formed by 1 part
when a whole is partitioned into b equal parts; understand
a fraction a/b as the quantity formed by a parts of size
1/b.
3rd Grade Fractions (Cont)
Understand a fraction as a number on the number line;
represent fractions on a number line diagram.
 Represent a fraction 1/b on a number line diagram by
defining the interval from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each part has size 1/b
and that the endpoint of the part based at 0 locates the
number 1/b on the number line.
 Represent a fraction a/b on a number line diagram by
marking off a lengths 1/b from 0. Recognize that the
resulting interval has size a/b and that its endpoint locates
the number a/b on the number line.
Build fraction understanding from whole
number understanding.
28
Build fraction understanding from whole
number understanding.
29
Build fraction understanding from whole
number understanding.
Fraction equivalence on the number line.
number line.
30