Name 
Description 
MAFS.912.ACED.1.1 (Archived Standard):  Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. ★ 

Related Access Points
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Description 
MAFS.912.ACED.1.AP.1a:  Create linear, quadratic, rational, and exponential equations and inequalities in one variable and use them in a contextual situation to solve problems. 

MAFS.912.ASSE.2.3 (Archived Standard):  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
 Factor a quadratic expression to reveal the zeros of the function it defines.
 Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
 Use the properties of exponents to transform expressions for exponential functions. For example the expression can be rewritten as ≈ to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.


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Description 
MAFS.912.ASSE.2.AP.3b:  Given a quadratic function, explain the meaning of the zeros of the function (e.g., if f(x) = (x  c) (x  a) then f(a) = 0 and f(c) = 0).  MAFS.912.ASSE.2.AP.3c:  Given a quadratic expression, explain the meaning of the zeros graphically (e.g., for an expression (x  a) (x  c), a and c correspond to the xintercepts (if a and c are real).  MAFS.912.ASSE.2.AP.3d:  Write expressions in equivalent forms by completing the square to convey the vertex form, to find the maximum or minimum value of a quadratic function, and to explain the meaning of the vertex.  MAFS.912.ASSE.2.AP.3e:  Use properties of exponents (such as power of a power, product of powers, power of a product, and rational exponents, etc.) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay.  MAFS.912.ASSE.2.AP.4a:  Use the formula for the sum of finite geometric series to solve problems.


MAFS.912.FLE.1.1 (Archived Standard):  Distinguish between situations that can be modeled with linear functions and with exponential functions. ★
 Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
 Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
 Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.


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Description 
MAFS.912.FLE.1.AP.1a:  Select the appropriate graphical representation of a linear model based on realworld events.  MAFS.912.FLE.1.AP.1b:  In a linear situation using graphs or numbers, predict the change in rate based on a given change in one variable (e.g., If I have been adding sugar at a rate of 1T per cup of water, what happens to my rate if I switch to 2T of sugar for every cup of water?). 

MAFS.912.GC.1.1 (Archived Standard):  Prove that all circles are similar. 

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Description 
MAFS.912.GC.1.AP.1a:  Compare the ratio of diameter to circumference for several circles to establish all circles are similar. 

MAFS.912.GC.1.2 (Archived Standard):  Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles;
the radius of a circle is perpendicular to the tangent where the radius
intersects the circle. 

Related Access Points

MAFS.912.GCO.1.1 (Archived Standard):  Know precise definitions of angle, circle, perpendicular line, parallel
line, and line segment, based on the undefined notions of point, line,
distance along a line, and distance around a circular arc. 

Related Access Points
Name 
Description 
MAFS.912.GCO.1.AP.1a:  Identify precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 

MAFS.912.GCO.1.2 (Archived Standard):  Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that
take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those
that do not (e.g., translation versus horizontal stretch). 

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Name 
Description 
MAFS.912.GCO.1.AP.2a:  Represent transformations in the plane using, e.g., transparencies and geometry software.  MAFS.912.GCO.1.AP.2b:  Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). 

MAFS.912.GCO.1.3 (Archived Standard):  Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself. 

Related Access Points
Name 
Description 
MAFS.912.GCO.1.AP.3a:  Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that maps each figure onto itself. 

MAFS.912.GCO.1.4 (Archived Standard):  Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line segments. 

Related Access Points
Name 
Description 
MAFS.912.GCO.1.AP.4a:  Using previous comparisons and descriptions of transformations, develop and understand the meaning of rotations, reflections, and translations based on angles, circles, perpendicular lines, parallel lines, and line segments. 

MAFS.912.GCO.1.5 (Archived Standard):  Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or
geometry software. Specify a sequence of transformations that will
carry a given figure onto another. 

Related Access Points
Name 
Description 
MAFS.912.GCO.1.AP.5b:  Create sequences of transformations that map a geometric figure on to itself and another geometric figure. 

MAFS.912.GCO.2.6 (Archived Standard):  Use geometric descriptions of rigid motions to transform figures and
to predict the effect of a given rigid motion on a given figure; given
two figures, use the definition of congruence in terms of rigid motions
to decide if they are congruent. 

Related Access Points
Name 
Description 
MAFS.912.GCO.2.AP.6a:  Use descriptions of rigid motion and transformed geometric figures to predict the effects rigid motion has on figures in the coordinate plane.  MAFS.912.GCO.2.AP.6b:  Knowing that rigid transformations preserve size and shape or distance and angle, use this fact to connect the idea of congruency and develop the definition of congruent. 

MAFS.912.GCO.2.7 (Archived Standard):  Use the definition of congruence in terms of rigid motions to show
that two triangles are congruent if and only if corresponding pairs of
sides and corresponding pairs of angles are congruent. 

Related Access Points

MAFS.912.GCO.2.8 (Archived Standard):  Explain how the criteria for triangle congruence (ASA, SAS, SSS, and HypotenuseLeg) follow from the definition of congruence in terms of rigid motions. 

Related Access Points
Name 
Description 
MAFS.912.GCO.2.AP.8a:  Use the definition of congruence, based on rigid motion, to develop and explain the triangle congruence criteria; ASA, SSS, and SAS. 

MAFS.912.GGMD.1.1 (Archived Standard):  Give an informal argument for the formulas for the circumference of
a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use
dissection arguments, Cavalieri’s principle, and informal limit arguments. 

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Name 
Description 
MAFS.912.GGMD.1.AP.1a:  Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection. 

MAFS.912.GGMD.1.3 (Archived Standard):  Use volume formulas for cylinders, pyramids, cones, and spheres to
solve problems. ★ 

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Name 
Description 
MAFS.912.GGMD.1.AP.3a:  Use appropriate formulas to calculate volume for cylinders, pyramids, and cones. 

MAFS.912.GGMD.2.4 (Archived Standard):  Identify the shapes of twodimensional crosssections of threedimensional
objects, and identify threedimensional objects generated
by rotations of twodimensional objects. 

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Description 
MAFS.912.GGMD.2.AP.4a:  Identify shapes created by cross sections of twodimensional and threedimensional figures. 

MAFS.912.GGPE.2.4 (Archived Standard):  Use coordinates to prove simple geometric theorems algebraically. For
example, prove or disprove that a figure defined by four given points in the
coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies
on the circle centered at the origin and containing the point (0, 2).
Clarifications: Geometry  Fluency Recommendations
Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.  

Related Access Points

MAFS.912.GGPE.2.6 (Archived Standard):  Find the point on a directed line segment between two given points
that partitions the segment in a given ratio. 

Related Access Points
Name 
Description 
MAFS.912.GGPE.2.AP.6a:  Given two points, find the point on the line segment between the two points that divides the segment into a given ratio. 

MAFS.912.GGPE.2.7 (Archived Standard):  Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.
★Clarifications: Geometry  Fluency Recommendations
Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.  

Related Access Points
Name 
Description 
MAFS.912.GGPE.2.AP.7a:  Use the distance formula to calculate perimeter and area of polygons plotted on a coordinate plane. 

MAFS.912.GMG.1.1 (Archived Standard):  Use geometric shapes, their measures, and their properties to describe
objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★ 

Related Access Points
Name 
Description 
MAFS.912.GMG.1.AP.1a:  Describe the relationship between the attributes of a figure and the changes in the area or volume when one attribute is changed. 

MAFS.912.GMG.1.2 (Archived Standard):  Apply concepts of density based on area and volume in modeling
situations (e.g., persons per square mile, BTUs per cubic foot). ★ 

Related Access Points
Name 
Description 
MAFS.912.GMG.1.AP.2a:  Recognize the relationship between density and area; density and volume using realworld models. 

MAFS.912.GMG.1.3 (Archived Standard):  Apply geometric methods to solve design problems (e.g., designing
an object or structure to satisfy physical constraints or minimize cost;
working with typographic grid systems based on ratios). ★ 

Related Access Points
Name 
Description 
MAFS.912.GMG.1.AP.3a:  Apply the formula of geometric figures to solve design problems (e.g., designing an object or structure to satisfy physical restraints or minimize cost). 

MAFS.912.GSRT.1.1 (Archived Standard):  Verify experimentally the properties of dilations given by a center and a scale factor:
 A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
 The dilation of a line segment is longer or shorter in the ratio given by the scale factor.


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Name 
Description 
MAFS.912.GSRT.1.AP.1b:  Given a center and a scale factor, verify experimentally that when performing dilations of a line segment, the preimage, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor. 

MAFS.912.GSRT.1.2 (Archived Standard):  Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the proportionality of all
corresponding pairs of sides. 

Related Access Points
Name 
Description 
MAFS.912.GSRT.1.AP.2a:  Determine if two figures are similar.  MAFS.912.GSRT.1.AP.2b:  Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides. 

MAFS.912.GSRT.1.3 (Archived Standard):  Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar. 

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Name 
Description 
MAFS.912.GSRT.1.AP.3a:  Apply the angleangle (AA) criteria for triangle similarity on two triangles. 

MAFS.912.GSRT.2.5 (Archived Standard):  Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
Clarifications: Geometry  Fluency Recommendations
Fluency with the triangle congruence and similarity criteria will help students throughout their investigations of triangles, quadrilaterals, circles, parallelism, and trigonometric ratios. These criteria are necessary tools in many geometric modeling tasks.  

Related Access Points
Name 
Description 
MAFS.912.GSRT.2.AP.5a:  Apply the criteria for triangle congruence and/or similarity (anglesideangle [ASA], sideangleside [SAS], sidesideside [SSS], angleangle [AA] to determine if geometric shapes that divide into triangles are or are not congruent and/or can be similar. 

MAFS.912.NQ.1.1 (Archived Standard):  Use units as a way to understand problems and to guide the solution
of multistep problems; choose and interpret units consistently in
formulas; choose and interpret the scale and the origin in graphs and
data displays. ★ 

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Name 
Description 
MAFS.912.NQ.1.AP.1a:  Interpret units in the context of the problem.  MAFS.912.NQ.1.AP.1b:  When solving a multistep problem, use units to evaluate the appropriateness of the solution.  MAFS.912.NQ.1.AP.1c:  Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context.  MAFS.912.NQ.1.AP.1d:  Choose and interpret both the scale and the origin in graphs and data displays. 

MAFS.912.NRN.1.2 (Archived Standard):  Rewrite expressions involving radicals and rational exponents using
the properties of exponents. 

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Name 
Description 
MAFS.912.NRN.1.AP.2a:  Convert from radical representation to using rational exponents and vice versa. 

MAFS.912.SID.1.1 (Archived Standard):  Represent data with plots on the real number line (dot plots,
histograms, and box plots). ★Clarifications: In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.  

Related Access Points
Name 
Description 
MAFS.912.SID.1.AP.1a:  Complete a graph given the data, using dot plots, histograms or box plots. 

MAFS.912.SID.1.4 (Archived Standard):  Use the mean and standard deviation of a data set to fit it to a normal
distribution and to estimate population percentages. Recognize that
there are data sets for which such a procedure is not appropriate.
Use calculators, spreadsheets, and tables to estimate areas under the
normal curve. ★ 
MAFS.K12.MP.1.1 (Archived Standard):  Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 
MAFS.K12.MP.2.1 (Archived Standard):  Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 
MAFS.K12.MP.3.1 (Archived Standard):  Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 
MAFS.K12.MP.4.1 (Archived Standard):  Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, twoway tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. 
MAFS.K12.MP.5.1 (Archived Standard):  Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. 
MAFS.K12.MP.6.1 (Archived Standard):  Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 
MAFS.K12.MP.7.1 (Archived Standard):  Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 
MAFS.K12.MP.8.1 (Archived Standard):  Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. 
LAFS.910.RST.1.3 (Archived Standard):  Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. 
LAFS.910.SL.1.1 (Archived Standard):  Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively.
 Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, wellreasoned exchange of ideas.
 Work with peers to set rules for collegial discussions and decisionmaking (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.
 Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.
 Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.


Related Access Points
Name 
Description 
LAFS.910.SL.1.AP.1a:  Clarify, verify or challenge ideas and conclusions within a discussion on a given topic or text.  LAFS.910.SL.1.AP.1b:  Summarize points of agreement and disagreement within a discussion on a given topic or text.  LAFS.910.SL.1.AP.1c:  Use evidence and reasoning presented in discussion on topic or text to make new connections with own view or understanding.  LAFS.910.SL.1.AP.1d:  Work with peers to set rules for collegial discussions and decision making.  LAFS.910.SL.1.AP.1e:  Actively seek the ideas or opinions of others in a discussion on a given topic or text.  LAFS.910.SL.1.AP.1f:  Engage appropriately in discussion with others who have a diverse or divergent perspective. 

LAFS.910.SL.1.2 (Archived Standard):  Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. 

Related Access Points
Name 
Description 
LAFS.910.SL.1.AP.2a:  Analyze credibility of sources and accuracy of information presented in social media regarding a given topic or text. 

LAFS.910.SL.1.3 (Archived Standard):  Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. 

Related Access Points

LAFS.910.SL.2.4 (Archived Standard):  Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. 

Related Access Points
Name 
Description 
LAFS.910.SL.2.AP.4a:  Orally report on a topic, with a logical sequence of ideas, appropriate facts and relevant, descriptive details that support the main ideas. 

LAFS.910.WHST.1.1 (Archived Standard):  Write arguments focused on disciplinespecific content.  Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence.
 Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a disciplineappropriate form and in a manner that anticipates the audience’s knowledge level and concerns.
 Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.
 Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.
 Provide a concluding statement or section that follows from or supports the argument presented.

LAFS.910.WHST.2.4 (Archived Standard):  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 
LAFS.910.WHST.3.9 (Archived Standard):  Draw evidence from informational texts to support analysis, reflection, and research. 