|MAFS.912.A-APR.1.1 (Archived Standard):|| Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction,
and multiplication; add, subtract, and multiply polynomials.|
|MAFS.912.A-CED.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. ★|
|MAFS.912.A-CED.1.2 (Archived Standard):||Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ★|
|MAFS.912.A-CED.1.4 (Archived Standard):||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. ★|
|MAFS.912.A-REI.2.4 (Archived Standard):|| Solve quadratic equations in one variable.
|MAFS.912.A-REI.3.7 (Archived Standard):||Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3.|
|MAFS.912.A-SSE.1.1 (Archived Standard):|| Interpret expressions that represent a quantity in terms of its context. ★
|MAFS.912.A-SSE.1.2 (Archived Standard):|| Use the structure of an expression to identify ways to rewrite it. For
example, see x4- y4 as (x²)² – (y²)², thus recognizing it as a difference of
squares that can be factored as (x² – y²)(x² + y²).|
|MAFS.912.F-BF.2.3 (Archived Standard):|| 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.|
|MAFS.912.F-IF.2.4 (Archived Standard):||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. ★|
|MAFS.912.F-IF.2.5 (Archived Standard):||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 person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function. ★|
|MAFS.912.F-IF.2.6 (Archived Standard):||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. ★|
|MAFS.912.F-IF.3.7 (Archived Standard):|| Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★|
|MAFS.912.F-IF.3.9 (Archived Standard):|| 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.F-LE.1.3 (Archived Standard):||Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. ★|
|MAFS.912.G-SRT.1.1 (Archived Standard):|| Verify experimentally the properties of dilations given by a center and a scale factor:
|MAFS.912.N-CN.1.1 (Archived Standard):||Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.|
|MAFS.912.N-CN.1.2 (Archived Standard):||Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.|
|MAFS.912.N-CN.1.3 (Archived Standard):||Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.|
|MAFS.912.N-CN.3.7 (Archived Standard):||Solve quadratic equations with real coefficients that have complex solutions.|
|MAFS.912.N-RN.1.1 (Archived Standard):||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.|
|MAFS.912.N-RN.1.2 (Archived Standard):||Rewrite expressions involving radicals and rational exponents using the properties of exponents.|
|MAFS.912.N-RN.2.3 (Archived Standard):||Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.|
|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, two-way 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.1112.RST.1.3 (Archived Standard):||Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.|
|LAFS.1112.RST.2.4 (Archived Standard):||Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics.|
|LAFS.1112.RST.3.7 (Archived Standard):||Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.|
|LAFS.1112.WHST.1.1 (Archived Standard):|| Write arguments focused on discipline-specific content. |
|LAFS.1112.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.1112.WHST.3.9 (Archived Standard):||Draw evidence from informational texts to support analysis, reflection, and research.|
General Course Information and Notes
|Course Number: 1206330||
Course Path: Section: Grades PreK to 12 Education Courses > Grade Group: Grades 9 to 12 and Adult Education Courses > Subject: Mathematics > SubSubject: Geometry >
|Abbreviated Title: ANLY GEO HON|
|Course Level: 3|
|Course Status: Terminated|
|Grade Level(s): 9,10,11,12|