A Parent’s Guide to the Common Core Georgia Performance Standards:
A Closer Look at
Mathematical Practice
The Common Core Georgia Performance Standards (CCGPS) are a
natural fit with Gwinnett’s rigorous, world-class AKS curriculum and
its long-standing focus on problem-solving. The CCGPS emphasize
problem-solving as well as a conceptual understanding of mathematical processes. As a result, the learning experience in math classrooms in
Gwinnett include plenty of application opportunities, a teaching strategy
that Gwinnett County teachers have been using all along. One way in
which GCPS teachers are ensuring that students have the 21st century
skills to be successful is to emphasize the development of eight mathematical practices or “behaviors” that promote math success.
Read on to learn more about these practices, some math terminology,
and the content standards at your student’s school level.
Make Sense of Problems and Persevere in Solving Them— When given
a problem, students think about a problem and make a plan to solve it using available
strategies. They predict results, and monitor and evaluate their progress, changing course
or trying new tactics if needed. They test out theories, and check their answers using a
different method. Students ask themselves the question “Does this make sense?” Younger
students might rely on concrete objects or pictures to help “visualize” and solve a problem.
Questions to Develop Mathematical Thinking—
How would you describe the problem in your own words?
Talk me through your steps so far.
What are some other strategies you might try?
How might you use a previous problem to help you begin?
Reason Abstractly and Quantitatively— Students use numbers and words to
help make sense of problems. With quantitative relationships, they decontextualize (use and
manipulate symbols represented in the problem) and contextualize (make meaning of symbols
in a problem). They understand the meaning of quantities and are flexible in using operation
and properties. They attend to the meaning of quantities, not just how to compute them.
Questions to Develop Mathematical Thinking—
What do the numbers used in the problem represent?
How is _______________ related to _______________?
What does ________________ mean to you? (symbol, quantity, diagram)
What properties might you use to find a solution?
Construct Viable Arguments and Critique the Reasoning of Others—
Students can explain their thinking and respond to the mathematical thinking of others.
They understand and use definitions when justifying results. They communicate and defend their
reasoning, using objects, drawings, diagrams, actions, examples and non-examples, and
verbal and written communication. They recognize both correct and flawed logic. They can
decide if arguments make sense, and ask useful questions to clarify or improve arguments.
Questions to Develop Mathematical Thinking—
What evidence would support your solution?
How did you decide to try this strategy?
Will it still work if…?
How did you test whether your approach worked?
Words Matter:
Terminology in
Mathematics
Procedural Fluency is a student’s skill in completing math procedures flexibly, accurately, efficiently, and appropriately. Think of it as “muscle
memory” for the brain.
Conceptual Understanding reflects a student’s
functional understanding of mathematical
concepts, operations, and relations. An example
might be that a student understands that the
equation “2x5” can be expressed visually like
this— • • • • • + • • • • •
Coherence is the progression of content across
grade levels and courses, which allows students
to build new understanding and make connections extending from their previous learning.
Because math skills build upon one another, it’s
important that a student have a firm foundation
in counting before progressing to addition and
subtraction, in addition and subtraction before
moving to multiplication and division, and so on.
Application and Modeling describes the ability
to apply mathematics and analyze resulting data
in real-world scenarios. Students are able to use
strategies from the classroom in everyday life,
work, and decision-making. For example, a high
school student might use geometry skills to solve
a design problem, while a middle schooler might
set up a flowchart to plan a school event.
Domains are the overarching ideas that connect topics across grade levels. Examples are
Counting; Numbers and Operations; Algebra;
Geometry; and Functions. (See the box on the
other side for domains by level.)
Model with Mathematics— Students use familiar math strategies to solve problems that come
up in everyday life. They may apply assumptions and approximations to simplify complicated tasks. They
use tools (diagrams, two-way tables, graphs, flowcharts, and formulas) to tackle everyday problems. They
interpret results to see if they make sense. Younger students may use pictures, symbols, objects, or words to
express the problem and find a solution.
Questions to Develop Mathematical Thinking—
What are some ways to represent the quantities?
What formula might apply in this situation?
How would it help to create a diagram, graph, table…?
What equation or expression matches the diagram, number line, chart, table…?
Use Appropriate Tools Strategically— Students use certain tools, including technology,
Standards: About
Domains and Clusters
These performance standards outline
the specific skills and knowledge that
students need to be successful at each
grade level, building grade to grade,
organized into domains:
Elementary School Content Domains
Students build a strong foundation in numbers and operations:
Counting and Cardinality (K)
to explore and deepen their math understanding. They have a math “toolbox” of both tools (such as
ruler, calculator, manipulatives, protractor, etc.) and strategies. They are familiar with the tools that are
appropriate for their grade/course. They consider available math tools and know how and when to use each
tool. They detect possible errors by using estimation.
Operations and Algebraic Thinking (K–5)
Questions to Develop Mathematical Thinking—
What mathematical tools could you use to visualize and represent the situation?
What information do you have?
What information do you need?
In this situation, would it be helpful to use a __________________?
Geometry(K–5)
Numbers and Operations in Base Ten (K–5)
Numbers and Operations – Fractions (3–5)
Measurement and Data (K–5)
Middle School Content Domains
Students explore more complex operations
and applications:
Ratios and Proportional Relationships
Attend to Precision— Students are precise when solving problems and clear when sharing
The Number System
mathematical ideas. They use correct math vocabulary, symbols that have meaning, accurate labels,
consistent and appropriate units of measure, and accurate and efficient calculations.
Expressions and Equations
Questions to Develop Mathematical Thinking—
What mathematical terms apply in this situation?
How did you know your solution was reasonable?
What symbols or mathematical notations are important in this problem?
How are you showing the meaning of the quantities?
Geometry
? < •/••
Look for and Make Use of Structure— Students see and understand how numbers and shapes
are organized and put together as parts and wholes. They look closely to find patterns or structure, and step
back for an overview of the whole. They see how complicated things are composed of single objects or
several smaller objects. They apply general math rules to specific situations.
Questions to Develop Mathematical Thinking—
What observations can you make about…?
What parts of the problem can you eliminate or simplify?
What are other problems similar to this one?
How can you use previous knowledge to solve this problem?
Functions
Statistics and Probability
High School Content Clusters
Students build knowledge, skills, application, and communication through the
study of advanced mathematical content
in preparation for college and career:
Number and Quantity
Algebra
Geometry
Functions
Probability and Statistics
Modeling
Look for and Express Regularity in Repeated Reasoning— Students notice when
calculations are repeated. For instance, 5 x 2 = 10 is the same as adding 2 five times, counting five rows of
two blocks, or making five hops of 2 on a number line. They look for both generalizations and shortcuts in
solving a problem. They see number patterns across applications. They understand the broader application of
patterns and see the structure in similar situations.
Questions to Develop Mathematical Thinking—
How does this strategy work in other situations?
Is this always true? Sometime true? Never true?
What predictions or generalizations can this pattern support?
What would happen if…?
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