Download Common Core state Standards

Overview
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Objectives

General Content
Overview

Mathematical
Practices Overview
◦ Focus and Coherence
◦ Purpose
◦ Similarities
◦ Structure
◦ Shifts
◦ 8 Practices
◦ Structure/Organization
◦ Standards
Alignment
◦ Activity
◦ Activity
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Avoid the
problem
of “mile
wide and
an inch
deep”
Recognize that
“fewer
standards” are
no substitute
for focused
standards
Aim for
clarity and
specificity
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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



Topics and performances are logical
over time
Based on learning progressions
research on how students learn
Reflect hierarchical nature of the
content
Evolve from particulars to deeper
structures
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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
Define what students should understand and
be able to do in their study of mathematics
◦ Is the ability to justify appropriate to student’s
math maturity
◦ Understanding and procedural skill are equally
important and can be assessed using tasks of
sufficient richness

Are internationally benchmarked
◦ Reflect rigor, focus and coherence of standards in
top-performing countries
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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
Do:
◦ Set grade-level standards K-8
◦ Identify standards for Algebra 1
◦ Provide conceptual cluster standards in
high school
◦ Provide clear signposts along the way
toward the goal of college and career
readiness for all students
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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
Do not:
◦ Define intervention methods or
materials
◦ Define the full range of supports for
English learners, students with special
needs and students who are well above
or below grade level expectations
◦ Dictate curriculum or teaching methods
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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

Mathematical Content (different at
each grade level)
Mathematical Practice (recurring
throughout the grades)
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Mathematical Content
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Mathematical Content Comparison
Common Core State Standards
for CA DOMAINS
California Standards •
Grades K-7 STRANDS
K-5
•Counting and Cardinality (K only)
•Operations and Algebraic Thinking
•Number and Operations in Base 10
•Number and Operations-Fractions
•Measurement and Data
•
Number Sense
•
Algebra and Functions
•
Measurement and
Geometry
•
6-8
•Ratio and Proportional Relationships
(grade 6-7)
•The Number System
•Expressions and Equations
•Functions (Grade 8)
•Geometry
•Statistics and probability
Statistics, Data Analysis
and Probability
•
Mathematical Reasoning
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Grade
Fifth
Sixth
Seventh
California Standard
Understand the concept of
multiplication and division of
fractions.
Common Core
Apply and extend previous understandings of
multiplication to multiply a fraction or whole
number by a fraction.
Apply and extend previous understandings of
division to divide unit fractions by whole
numbers and whole numbers by unit
fractions. (A unit fraction is one with a
numerator of 1 and the denominator is a
positive integer)
Interpret and use ratios in different
Understand the concept of a ratio and use
contexts (e.g., batting averages, miles ratio language to describe a ratio relationship
per hour) to show the relative sizes of between two quantities.
two quantities, using appropriate
notations ( a/b, a to b, a:b ).
Use variables and appropriate
operations to write an expression, an
equation, an inequality, or a system
of equations or inequalities that
represents a verbal description (e.g.,
three is less than a number, half as
large as area A).
Use variables to represent quantities in realworld and mathematical problems and
construct simple equations and inequalities to
solve problems about the quantities.
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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K
1
2
3
4
5
6
Counting & Cardinality
x
Operations & Algebraic
Thinking
x
x
x
x
x
X
Number & Base Ten
x
x
x
x
X
x
x
x
X
Numbers & OperationsFractions
7
8
Ratios & Proportional
Relationships
x
x
The Number system
x
x
x
Expressions & Equation
x
x
X
x
Functions
Geometry
x
x
x
x
x
x
Measurement & Data
x
x
x
x
x
X
Statistics & Probability
x
x
X
x
x
x
© 2013 Actions Learning Systems, Inc.
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© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Grade Shifts: Examples
Concept
1997 Standards
CCCS
Compose simple shapes to
form larger shapes (e.g., 2
triangles to form a
rectangle)
Grade
2
K
Introduction to Probability
Grade
3
Grade
7
Introduction of fractions as
numbers
Grade
2
Grade
3
Add and subtract simple
fractions
Grade
3
Grade
4
Introduction of integers
Grade
4
Grade
6
Developed by SCFIRD
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Example of Common Core Math in a 6th
Grade Classroom

Teaching Probability of Independent and
Dependent Events
https://www.teachingchannel.org/videos/tea
ching-dependent-and-independentevents?fd=1
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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
Overview page
◦ Lists domains, clusters and mathematical practices

Domains
◦ Larger groups of related standards. Standards from different
domains may be closely related.

Standards-by grade level
◦ Defines what students should understand and be able to do

Clusters
◦ Groups of related standards. Standards from different
clusters may be closely related
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Grade 6 Overview
Ratios and Proportional Relationships
Mathematical Practices
1. Make sense of problems and
• Understand ratio concepts and use ratio reasoning to solve
persevere in solving them.
problems.
2. Reason abstractly and
The Number System
quantitatively.
• Apply and extend previous understandings of
3. Construct viable arguments
Multiplication and division to divide fractions by fractions.
and critique the reasoning of
• Compute fluently with multi-digit numbers and find common
others.
factors and multiples.
4. Model with mathematics.
5. Use appropriate tools
• Apply and extend previous understandings of numbers to
strategically.
The system of rational numbers.
6. Attend to precision.
Expressions and Equations
7. Look for and make use of
• Apply and extend previous understandings of arithmetic to
structure.
algebraic expressions.
8. Look for and express
• Reason about and solve one-variable equations and
regularity in repeated reasoning.
inequalities.
• Represent and analyze quantitative relationships between dependent and independent
variables.
Geometry
• Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
• Develop understanding of statistical variability.
• Summarize and describe distributions.
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Reading the Standards
Standards-by grade level: Defines what students should understand and be able to do
Clusters: Groups of related standards. Standards from different clusters may be closely
related
Domains: Larger groups of related standards. Standards from different domains may
be closely related.
Domain
Ratios and Proportional Relationships
6.RP
Understand ratio concepts and use ratio reasoning to solve problems.
Standard 1. Understand the concept of a ratio and use ratio language to describe a ratio
relationship between two quantities. For example, “The ratio of wings to beaks
in the bird house at the zoo was 2:1, because for every 2 wings there was 1
beak.” “For every vote candidate A received, candidate C received nearly
three votes.”
2. Understand the concept of a unit rate a/b associated with a ratio a:b with b
≠ 0, and use rate language in the context of a ratio relationship. For example,
“This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4
cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is
a rate of $5 per hamburger.”1
C
L
U
S
T
E
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Mathematical Content Activity





Label the Domain, Standards, and Clusters
for Grade 6 Common Core Mathematics.
Circle, underline or highlight key academic
vocabulary within the standards.
Go to U Drive, Curriculum, Common Core
State Standards, Common Core Unpacked
Math, k-12_math_crosswalk pgs. 97-128.
Choose a standard and compare similarities
and differences.
Be prepared to discuss.
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Mathematical Practice
20

Standards for Mathematical Practice
◦ Describe habits of mind of a
mathematically expert student
◦ Relate to mathematical proficiency as
defined by the California Framework
◦ Consistent throughout grade levels
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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“WHERE”
THE
MATHEMATICS
WORK
Problem
Solving
Computational
& Procedural
Skills
DOING
MATH
Conceptual
Understanding
“HOW”
THE
MATHEMATICS
WORK
“WHY”
THE
MATHEMATICS
WORK
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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“ …describe ways in which developing
student practitioners of the discipline
of mathematics increasingly ought to
engage with the subject matter as
they grow in mathematical maturity
and expertise throughout the
elementary, middle and high schools
years.”
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Structuring the Standards for Mathematical
Practice
1. Make sense of
problems and
persevere in solving
them.
6. Attend to
precision
2. Reason abstractly
and quantitatively
3. Construct viable
arguments and
critique the reasoning
of other
Reasoning and
explaining
4. Model with
mathematics
5. Use appropriate
tools strategies
Modeling and using
tools
7. Look for and make
use of structure
8. Look for and
express regularity
in repeated
reasoning
Seeing structure and
generalizing
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1. Make sense of problems and persevere
in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique
the reasoning
4. Model with mathematics
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Standards for Mathematical Practice
Mathematically proficient students:
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for an express regularity in repeated
reasoning
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Inside Mathematics Video

Example of MP 3, 6, 7, and 8 in an
intermediate classroom
http://www.insidemathematics.org/index.php/exemplary-lessonsintegrating-practice-standards
© 2011 California County Superintendents Educational Services Association • Mathematics General Overview
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Mathematical Practices Aligned to
Common Core Standards

Activity
◦ Label the Mathematical Practices that align with
specific standards.
◦ Choose a standard and its Mathematical
Practice(s)
◦ Go to U Drive, Curriculum, Common Core State
Standards, Common Core Unpacked Math, Find
your grade level
◦ Brain storm how you can integrate the
Mathematical Practice with the Common Core
Standard you chose.
◦ Be prepared to share.
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SBAC Math Test
http://www.smarterbalanced.org/practice-test/
SCROLL DOWN AND CLICK ON PRACTICE TEST
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