Name 
Description 
MAFS.912.ACED.1.1:  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. ★ 

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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.ACED.1.2:  Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales. ★ 

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Name 
Description 
MAFS.912.ACED.1.AP.2a:  Graph equations in two or more variables on coordinate axes with labels and scales. 

MAFS.912.ACED.1.3:  Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or nonviable
options in a modeling context. For example, represent inequalities
describing nutritional and cost constraints on combinations of different
foods. ★ 

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Name 
Description 
MAFS.912.ACED.1.AP.3a:  Identify and interpret the solution of a system of linear equations from a realworld context that has been graphed. 

MAFS.912.ACED.1.4:  Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. For example, rearrange Ohm’s law V =
IR to highlight resistance R. ★ 

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Name 
Description 
MAFS.912.ACED.1.AP.4a:  Solve multivariable formulas or literal equations for a specific variable. 

MAFS.912.AREI.1.1:  Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a
viable argument to justify a solution method.

MAFS.912.AREI.2.3:  Solve linear equations and inequalities in one variable, including
equations with coefficients represented by letters. 

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Name 
Description 
MAFS.912.AREI.2.AP.3a:  Solve linear equations in one variable, including coefficients represented by letters.  MAFS.912.AREI.2.AP.3b:  Solve linear inequalities in one variable, including coefficients represented by letters. 

MAFS.912.AREI.3.5:  Prove that, given a system of two equations in two variables, replacing
one equation by the sum of that equation and a multiple of the other
produces a system with the same solutions. 

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MAFS.912.AREI.3.6:  Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.


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MAFS.912.AREI.4.10:  Understand that the graph of an equation in two variables is the set of
all its solutions plotted in the coordinate plane, often forming a curve
(which could be a line). 

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Name 
Description 
MAFS.912.AREI.4.In.10a:  Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables.  MAFS.912.AREI.4.AP.10a:  Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables. 

MAFS.912.AREI.4.11:  Explain why the xcoordinates of the points where the graphs of
the equations y = f(x) and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x)
are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions. ★ 

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Name 
Description 
MAFS.912.AREI.4.In.11a:  Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically.  MAFS.912.AREI.4.AP.11a:  Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically 

MAFS.912.AREI.4.12:  Graph the solutions to a linear inequality in two variables as a halfplane
(excluding the boundary in the case of a strict inequality), and
graph the solution set to a system of linear inequalities in two variables
as the intersection of the corresponding halfplanes. 

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Name 
Description 
MAFS.912.AREI.4.In.12a:  Graph a linear inequality in two variables using at least two coordinate pairs that are solutions.  MAFS.912.AREI.4.In.12b:  Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality.  MAFS.912.AREI.4.AP.12a:  Graph a linear inequality in two variables using at least two coordinate pairs that are solutions.  MAFS.912.AREI.4.AP.12b:  Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality. 

MAFS.912.ASSE.1.1:  Interpret expressions that represent a quantity in terms of its context. ★
 Interpret parts of an expression, such as terms, factors, and coefficients.
 Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of P and a factor not depending on P.


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Name 
Description 
MAFS.912.ASSE.1.AP.1a:  Identify the different parts of the expression and explain their meaning within the context of a problem.  MAFS.912.ASSE.1.AP.1b:  Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts. 

MAFS.912.ASSE.2.3:  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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Name 
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.FBF.1.1:  Write a function that describes a relationship between two quantities. ★
 Determine an explicit expression, a recursive process, or steps for calculation from a context.
 Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
 Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.


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Description 
MAFS.912.FBF.1.AP.1a:  Select a function that describes a relationship between two quantities (e.g., relationship between inches and centimeters, Celsius Fahrenheit, distance = rate x time, recipe for peanut butter and jelly relationship of peanut butter to jelly f(x)=2x, where x is the quantity of jelly, and f(x) is peanut butter. 

MAFS.912.FBF.2.3:  Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),
f(kx), and f(x + k) for specific values of k (both positive and negative);
find the value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology.
Include recognizing even and odd functions from their graphs and
algebraic expressions for them.


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Name 
Description 
MAFS.912.FBF.2.AP.3a:  Write or select the graph that represents a defined change in the function (e.g., recognize the effect of changing k on the corresponding graph). 

MAFS.912.FIF.1.1:  Understand that a function from one set (called the domain) to
another set (called the range) assigns to each element of the domain
exactly one element of the range. If f is a function and x is an element
of its domain, then f(x) denotes the output of f corresponding to the
input x. The graph of f is the graph of the equation y = f(x). 

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Name 
Description 
MAFS.912.FIF.1.AP.1a:  Demonstrate that to be a function, from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.  MAFS.912.FIF.1.AP.1b:  Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship. 

MAFS.912.FIF.1.2:  Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context. 

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Name 
Description 
MAFS.912.FIF.1.AP.2a:  Match the correct function notation to a function or a model of a function (e.g., x f(x) y). 

MAFS.912.FIF.1.3:  Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, the
Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) +
f(n1) for n ≥ 1.


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Description 
MAFS.912.FIF.1.AP.3a:  Recognize that the domain of a sequence is a subset of the integers. . 

MAFS.912.FIF.2.4:  For a function that models a relationship between two quantities,
interpret key features of graphs and tables in terms of the quantities,
and sketch graphs showing key features given a verbal description
of the relationship. Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative maximums
and minimums; symmetries; end behavior; and periodicity. ★ 

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Name 
Description 
MAFS.912.FIF.2.AP.4a:  Recognize and interpret the key features of a function.  MAFS.912.FIF.2.AP.4b:  Select the graph that matches the description of the relationship between two quantities in the function. 

MAFS.912.FIF.2.5:  Relate the domain of a function to its graph and, where applicable, to
the quantitative relationship it describes. For example, if the function
h(n) gives the number of personhours it takes to assemble engines in a
factory, then the positive integers would be an appropriate domain for the
function. ★ 

Related Access Points

MAFS.912.FIF.2.6:  Calculate and interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval.
Estimate the rate of change from a graph. ★ 

Related Access Points

MAFS.912.FIF.3.7:  Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ Graph linear and quadratic functions and show intercepts, maxima, and minima.
 Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions.
 Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift.


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MAFS.912.FIF.3.9:  Compare properties of two functions each represented in a different
way (algebraically, graphically, numerically in tables, or by verbal
descriptions). For example, given a graph of one quadratic function and
an algebraic expression for another, say which has the larger maximum.

MAFS.912.FLE.1.1:  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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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.FLE.1.2:  Construct linear and exponential functions, including arithmetic and
geometric sequences, given a graph, a description of a relationship, or
two inputoutput pairs (include reading these from a table). ★ 

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MAFS.912.FLE.1.AP.2a:  Select the graph, the description of a relationship or two inputoutput pairs of linear functions. 

MAFS.912.FLE.1.3:  Observe using graphs and tables that a quantity increasing
exponentially eventually exceeds a quantity increasing linearly,
quadratically, or (more generally) as a polynomial function. ★ 

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Name 
Description 
MAFS.912.FLE.1.AP.3a:  Compare graphs of linear, exponential, and quadratic growth graphed on the same coordinate plane. 

MAFS.912.FLE.2.5:  Interpret the parameters in a linear or exponential function in terms of
a context. ★ 

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Description 
MAFS.912.FLE.2.AP.5a:  Describe the meaning of the factors and intercepts on linear and exponential functions. 

MAFS.912.NQ.1.1:  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.NQ.1.2:  Define appropriate quantities for the purpose of descriptive modeling. ★Clarifications:
Algebra 1 Content Notes:
Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions.  

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MAFS.912.NQ.1.AP.2a:  Determine and interpret appropriate quantities when using descriptive modeling. 

MAFS.912.NQ.1.3:  Choose a level of accuracy appropriate to limitations on measurement
when reporting quantities. ★ 

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MAFS.912.NQ.1.AP.3a:  Describe the accuracy of measurement when reporting quantities (you can lessen your limitations by measuring precisely). 

MAFS.912.NRN.1.1:  Explain how the definition of the meaning of rational exponents
follows from extending the properties of integer exponents to
those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define to be the cube root of 5
because we want = to hold, so must equal 5. 

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Name 
Description 
MAFS.912.NRN.1.AP.1a:  Understand that the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand (e.g., 5^{1/2} = √5). Extend the properties of exponents to justify that (5^{1/2})^{2}=5  MAFS.912.NRN.1.AP.1b:  Extend the properties of exponents to justify that (5^{1/2})^{2}=5 

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

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

MAFS.912.SID.1.1:  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.  

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

MAFS.912.SID.1.4:  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:  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:  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:  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:  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:  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:  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:  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:  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:  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.RST.2.4:  Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. 
LAFS.910.RST.3.7:  Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. 
LAFS.910.SL.1.1:  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:  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
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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:  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:  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. 

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Name 
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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:  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:  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 
LAFS.910.WHST.3.9:  Draw evidence from informational texts to support analysis, reflection, and research. 
ELD.K12.ELL.MA.1:  English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 
ELD.K12.ELL.SI.1:  English language learners communicate for social and instructional purposes within the school setting. 