Transcript Common Core State Standards for Mathematics

Standards for Mathematical Practice
• Make sense of problems and persevere in
solving them.
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First explain meaning of problem to themselves
Analyze, conjecture, plan
Consider analogous problems
Try simpler forms of the original problem
Can explain correspondence between graphs,
charts/tables, verbal descriptions, equations
– Check their answers
– Understand approaches of others; see correspondences
between the various approaches
Standards for Mathematical Practice
• Reason abstractly and quantitatively.
– Make sense of quantities and their relationships in problem situations
– Have ability to both decontextualize (abstract a given situation and
represent it symbolically) and to contextualize (consider the actual
meaning of the various parts of the situation)
– Ability to create a coherent representation of the problem – consider
units involve, meaning of quantities as well as how to compute them
– Know and flexibly use different properties of operations and objects
Standards for Mathematical Practice
• Construct viable arguments and critique the
reasoning of others.
– Understand and use state assumptions, definitions, previously
established results in constructing arguments
– Make conjectures and build logical progression of statements to
explore the truth of those conjectures
– Analyze situations by breaking them into cases
– Recognize and use counter examples
– Justify conclusions
– Reason inductively about data
– Compare effectiveness of two plausible arguments
– Read/analyze/question the arguments of others
Standards for Mathematical Practice
• Model with mathematics.
– Apply known mathematics to solve real world problems
– Can comfortably make assumptions and approximations to simplify
complicated situations
– Realize such assumptions/approximations may require later
adjustment
– Identify important quantities and map their relationships using a
variety of tools: diagrams, two-way tables, graphs, flowcharts,
formulas
– Can analyze relationships mathematically to draw conclusions
– Routinely interpret the results in the context of the situation
– Reflect on whether the results make sense
Standards for Mathematical Practice
• Use appropriate tools strategically.
– Consider available tools when solving mathematical problems:
pencil/paper, concrete models, ruler, protractor, calculator, spreadsheet, computer algebra system, dynamic geometry software, etc.
– Sufficiently familiar with tools to recognize the insight that can be
gained from their use and their limitations
– Strategically use estimation to detect possible errors
– Identify relevant external mathematical resources (websites, etc.) and
use them effectively
– Able to use technological tools to explore and deepen understanding
of concepts
Standards for Mathematical Practice
• Attend to precision.
– Communicate precisely to others
– Use clear definitions in discussion with others and in their own
reasoning
– State meaning of symbols they choose (including equal sign)
consistently and appropriately
– Specify units of measures and label axes to clarify correspondence
with quantities in a problem
– Calculate accurately and efficiently
– Express numerical answers with appropriate degree of precision
– Provide carefully formulated explanations
– By high school – examine claims and explicitly use definitions.
Standards for Mathematical Practice
• Look for and make use of structure.
– Examine carefully to discern pattern or structure
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Early: 3 + 7 more is same as 7 + 3 more
Early: Sort shapes by number of sides
Later: 7 x 8 equals 7 x 5 + 7 x 3
Later: x2 (squared) + 9x + 14 – can see the 9 as 2 + 7 and the 14 as 2 x 7
– Recognize significance of an existing line in a geometric figure and can
use the strategy of drawing an auxiliary line for solving problems
– Can step back for overview and shift perspective
– View complicated items as single objects or as being composed of
several objects
Standards for Mathematical Practice
• Look for and express regularity in repeated
reasoning
– Notice if calculations are repeated
– Look for both general methods and shortcuts
• Example: recognize repeating decimal when dividing 25 by 11
• Example: abstract equation (y-2)/(x-1)=3 by paying attention to the calculation of
slope when repeatedly checking whether points are on the line through (1,2) with
slope 3
– Maintain oversight of the process, while attending to details
– Continually evaluate reasonableness of their intermediate results