Organization: Pearson
Product Name: enVision Florida Algebra 1 2020
Product Version: 1




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Curriculum Standards:


Describe the rate of change of a function using words. - c69f37dc-f5de-4cc3-88bd-531febed5c09
When solving a multi-step problem, use units to evaluate the appropriateness of the solution. - 3d49f891-55fb-4246-8289-b091c823a246
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. - 1d1f44f9-3b27-4ba9-8a74-8cf374455d45
Create a scatter plot from two quantitative variables. - 9f0d7e5c-cfb0-4062-9f0a-2bf3fd6ff6a8
Factor a quadratic expression to reveal the zeros of the function it defines. - 6e8d693f-acb0-4a9c-a13e-5b0e76b6634c
Solve linear inequalities in one variable, including coefficients represented by letters. - ef330e48-fb51-46de-81d2-def304e3fb07
Use the structure of an expression to identify ways to rewrite it. Example: For example, see 𝘹⁴ – 𝘹𝘺⁴ as (𝘹𝘺𝘹²)² – (𝘹𝘺𝘹𝘺²)², thus recognizing it as a difference of squares that can be factored as (𝘹𝘺𝘹𝘺𝘹² – 𝘹𝘺𝘹𝘺𝘹𝘺²)(𝘹𝘺𝘹𝘺𝘹𝘺𝘹² + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺²). - ab53e453-944a-43b3-9178-8443bbd95b16
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). - 474b6b9a-5fce-4c3f-b2ab-0d9d7978ed3b
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - 74b31224-ff95-4c0d-a7d3-3ed7d443ee48
Write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y - y1 = m(x - x1), Ax + By = C]. - a03d1c29-e08a-4bdf-a0b1-3f46a6812114
Categorize data as linear or not. - f2bf8b64-e2b4-4f15-84b1-b604b337ee60
Know and justify that when adding a rational number and an irrational number the result is irrational. - b85fd2f7-4a52-47a3-9c5b-80d6d2c37594
Solve multi-variable formulas or literal equations for a specific variable. - cc623fad-16c6-4436-97e3-e5b469567ac6
Use the method of completing the square to transform any quadratic equation in 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹 into an equation of the form (𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹 – 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱)² = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲 that has the same solutions. Derive the quadratic formula from this form. - 2d950d92-7ee9-4947-b5c7-82f4494ada91
Create linear, quadratic, rational, and exponential equations and inequalities in one variable and use them in a contextual situation to solve problems. - f516795e-3f58-4dfa-9059-7653a0fc9bb9
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. Example: For example, calculate mortgage payments. - c28aa5db-7078-471e-9b27-0453d9883e22
Use the correct measure of center and spread to describe a distribution that is symmetric or skewed. - 8339f879-aea2-4622-8a27-dba5bf19ab85
Describe the meaning of the factors and intercepts on linear and exponential functions. - 9e77ef68-ba32-4bac-a9c7-198c68aba2f4
Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality. - 4bce082d-cd58-400e-adbc-b93957373622
Rewrite algebraic expressions in different equivalent forms, such as factoring or combining like terms. - 47e437a4-51d0-450c-a4b4-1f94bcdfa2c5
Use statistical vocabulary to describe the difference in shape, spread, outliers and the center (mean). - 214509b7-b53a-45ba-bbb1-8531d3397157
Identify outliers (extreme data points) and their effects on data sets. - 62c81d24-f14a-421b-b0e2-387f2cbc00bf
Understand the solution to a system of two linear equations in two variables corresponds to a point(s) of an intersection of their graphs, because the point(s) of intersection satisfies both equations simultaneously. - 99e125fa-bdd5-45f8-9fa7-50d3d10ca505
Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts. - 33fca141-a135-473f-babc-45b3ca2be4b6
Interpret the meaning of the slope and y-intercept in context. - d25fa299-4e4b-4031-8529-727c470ed36b
Given a graph, describe or select the solution to a system of linear equations. - efe17d35-83a1-4683-85dd-750619b04733
Solve quadratic equations by factoring. - 0b86b8bb-82be-4134-8228-8f6cd1fae56d
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. - 604f911f-7b09-48ad-8ca3-d5dc05924acc
(HONORS ONLY) Verify by composition that one function is the inverse of another. - 4dc6ff62-3014-4961-b45f-3fd1f4eaf653
Match the correct function notation to a function or a model of a function (e.g., x f(x) y). - 4e45d5a0-bf97-455b-89c0-0ca1871dd520
Determine and interpret appropriate quantities when using descriptive modeling. - 53130ce8-3654-420d-8dbf-adf1358322bb
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 9–10 texts and topics. - d88fd899-f951-4e74-a8f5-cccd3347b4ba
(HONORS ONLY) Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: For example, find the points of intersection between the line 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺 = –3𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹 and the circle 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹² + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺² = 3. - 8ff0f22d-117f-49bc-a3b3-c068e87e737c
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - 4db017ec-c7d0-4c7c-acc9-b6a3facb0dbe
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. - b4324bcf-6bee-49d9-aac5-f2767d2d9a92
Compare graphs of linear, exponential, and quadratic growth graphed on the same coordinate plane. - 051d965d-ddb3-42b2-b8c7-e01a5f5774ab
Identify the effect on the graph of replacing 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹) by 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹) + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬, 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹), 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹), and 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹 + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬) for specific values of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬 (both positive and negative); find the value of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬 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. - 6b38a99d-560c-4cab-81a9-84c58508eb20
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?). - c0e261b0-1f80-43c6-acf3-60894551c1d3
Convert from radical representation to using rational exponents and vice versa. - 4fabf9f2-00ce-42ec-a866-7ba87ba58eeb
Recognize and interpret the key features of a function. - fb792cd6-8318-44dd-892b-4580c9c9e438
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). - 9105ae41-4874-4c65-99c3-bc85f3af2897
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. Example: For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. - 3bf3bf8d-8807-4549-a096-8887e7cfc300
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. - 75d55b82-83c7-43ca-ab1f-998a20e958f4
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift. - e5b40fc6-d095-4429-804f-6a10cbac51ee
Recognize that the domain of a sequence is a subset of the integers. - 7c93be7c-7146-445b-a122-21c931f62000
Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. - 9a9afa20-1326-4b2b-adce-30513f018bab
(HONORS ONLY) Solve an equation of the form 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹) = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤 for a simple function 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧 that has an inverse and write an expression for the inverse. Example: For example, 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹) =2 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹³ or 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹) = (𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹+1)/(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹–1) for 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹 ≠ 1. - 49b475dd-0964-4f64-a441-8f66f0eccaaf
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. - 6e8e6d55-1f83-4826-9cd6-d78eef7370c3
Identify the correlation coefficient (r) of a linear fit. - 8ed9e19c-6885-4dc9-9d49-d71753c26142
Choose and interpret both the scale and the origin in graphs and data displays. - a8c544ca-bed3-4567-b1ca-4c35ab23409c
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. - 78332818-27d5-4b06-9369-fd35deb0af11
Understand the concepts of combining like terms and closure. - f51e09ec-e597-4c8f-b313-c5f844c2f02c
Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. - 9a40d419-ee6e-4423-a2c0-36141274aea2
Fit a linear function for a scatter plot that suggests a linear association. - a8e8d561-8efb-48d7-87be-923852ff0e98
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. - 06253520-5db9-40bb-9bb7-bb5ca1a7b2e8
Describe the form, strength, and direction of the relationship. - c9b4e73e-ba1f-4142-9672-74c3a9db992e
Use the function to predict values. - ead8002d-c125-42f5-b33f-12d1897a9ffe
Understand that the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand (e.g., 51/2 = 5). - 42d708a1-7744-4603-a914-c8096b7f787a
(HONORS ONLY) Rewrite simple rational expressions in different forms; write 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹)/𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹) in the form 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹) + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹)/𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹), where 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹), 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹), 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹), and 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹) are polynomials with the degree of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹) less than the degree of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. - 37c1428a-15f3-47ec-88cd-141f70720584
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. - 3940bed0-00a3-49dc-9b74-172f6db23b03
Given a correlation in a real-world scenario, determine if there is causation. - 45b5227d-af07-4309-b857-296c66bc9f06
Compare the properties of two functions. - 30bbec0a-9c1c-4a59-aa12-04cfe0452585
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. - caec55d0-18be-4e92-a8b1-8d8a3677f8b6
Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context. - 1860f45b-3b24-4bcc-8881-02599bcad7b7
Solve equations with one or two variables and explain the process. - fa699064-054d-4e1e-ad59-7aa981d6a0be
Graph linear and quadratic functions and show intercepts, maxima, and minima. - 39c4a7bf-37d3-4b65-9448-981cc401c99a
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 x-intercepts (if a and c are real)). - 8ce50f6e-257b-480d-8f3a-eba602ebae37
Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables. - 8c41e8d5-2ca2-498b-a64c-3b1198a5fc99
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. - 2191a90d-1030-4c19-980d-a90826e2ce9e
Explain the meaning of the constant and coefficients in context. - 392cbd1c-e448-4660-88e7-fd73ecf2c986
English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. - 61EB17D7-11AC-43F1-8B9B-D315C6E267D2
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. - caa1c5ce-9954-4bd4-913c-82f5740ef25c
Select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5). - eb68fb17-55fb-4272-aafa-4fa01a8b570e
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 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧 is a function and 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹 is an element of its domain, then 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹) denotes the output of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧 corresponding to the input 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹. The graph of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧 is the graph of the equation 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺 = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹). - 3b9e7038-0e8e-4ad9-b588-f99932d41bed
Describe the correlation coefficient (r) of a linear fit (e.g., a strong or weak positive, negative, perfect correlation). - 24291925-16ab-47a5-b4bb-51a43c47bd16
Describe the accuracy of measurement when reporting quantities (you can lessen your limitations by measuring precisely). - c42588ae-ba2e-46d7-b498-bcf772394434
Recognize associations and trends in data from a two-way table. - 5898e471-ef6e-41d0-8954-d226f7cb298d
Interpret the parameters in a linear or exponential function in terms of a context. - 3d9245a7-1c9a-4797-80f5-9265839bcc7d
Use descriptive stats like range, median, mode, mean and outliers/gaps to describe the data set. - 78d22ad3-e3d5-47c3-9ec9-761859359447
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). - d0ac8473-5f07-4ed0-bf7c-0cb34217022f
Find the sum of two equations. - 45f34c21-383c-40cc-83b2-578bb74fcb4a
Solve linear equations in one variable, including coefficients represented by letters. - 1628e058-42da-4b30-b702-efa63b38c46d
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. - ef092516-4307-497b-8ffb-f57bfe6d5100
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. - 789fc7d6-8cae-495f-9e63-c14fb1c4dfd6
Describe the rate of change of a function using numbers. - 6e922cdc-2a08-4610-ab72-0475e8101248
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. - 0dea4bea-7abf-4711-8598-d7d8a3c941f9
Determine an explicit expression, a recursive process, or steps for calculation from a context. - 1ae9b1ba-954d-42ee-8b3d-ce806d59fe78
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: For example, rearrange Ohm’s law 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝 = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙 to highlight resistance 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙. - 18186a04-0947-4402-bdac-f6aba4c9e901
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. - cb1cbbc6-8b32-4339-bc18-7439326ebb04
English language learners communicate for social and instructional purposes within the school setting. - D7BEB0F4-C962-45CD-A245-6DF8AED7773D
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). - 57b1356c-e08b-4304-9fe9-42ae9435d20b
Compose functions. Example: For example, if 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺) is the temperature in the atmosphere as a function of height, and 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵) is the height of a weather balloon as a function of time, then 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵)) is the temperature at the location of the weather balloon as a function of time. - 8d2c080b-7ebb-45cb-ab26-f80ed10c6ef0
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. - 58884854-41ae-4a67-9f44-0d60b8d2a193
Identify and interpret the solution of a system of linear equations from a real-world context that has been graphed. - 4232009b-ab8f-4dd1-adbf-9db9ac36bfa1
Solve quadratic equations by completing the square. - 41a632ea-55aa-4a5b-af6b-9f11462e3656
Select the appropriate graphical representation of a linear model based on real-world events. - 8506b643-9233-47d9-8173-d7ef570dfe76
Understand and apply the remainder theorem. - a1eed755-9a59-4255-a2fc-6e1afde0926c
Interpret parts of an expression, such as terms, factors, and coefficients. - 8f350077-a0f8-40fa-99b2-7f4e0d02815a
Select the graph that matches the description of the relationship between two quantities in the function. - adf6937f-b4ef-4a29-a2ac-3810a177bedf
Use the zeros of a function to sketch a graph of the function. - 26361f76-a5e1-4d81-9c84-6caa5646c152
(HONORS ONLY) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. - cfa65496-45b0-4a5f-8a62-ddfbfc42a87a
Know and justify that when adding or multiplying two rational numbers the result is a rational number. - 867c7459-cf1b-415a-bdfb-90a277274442
Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship. - 288d82e8-8fc0-4b0c-971d-a806453485d3
Compute (using technology) and interpret the correlation coefficient of a linear fit. - f30051bf-3298-4ca0-90c8-d33d533a9bfc
Represent data with plots on the real number line (dot plots, histograms, and box plots). - 5c4a6eb4-8864-4748-a2b3-9f905af11859
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: For example, if the function 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯) gives the number of person-hours it takes to assemble 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯 engines in a factory, then the positive integers would be an appropriate domain for the function. - 3cba67ec-19a0-405c-8b9c-e48dbaf918ca
(HONORS ONLY) Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - 43c9f03d-deaa-4f60-8bb7-c09c5c1068b2
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. - 405d5c75-38c0-47cd-b95e-2be742152109
Describe a distribution using center and spread. - 3e2ef8f1-4549-4dba-9ebc-35b0c02636dd
(HONORS ONLY) Produce an invertible function from a non-invertible function by restricting the domain. - d0d39548-4500-42f2-beea-e91b256d6b2e
Distinguish between correlation and causation. - 92629a54-c742-4be8-a09d-9b87bdf65717
(HONORS ONLY) Know and apply the Remainder Theorem: For a polynomial 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹) and a number 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢, the remainder on division by 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹 – 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢 is 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢), so 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢) = 0 if and only if (𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹 – 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢) is a factor of 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹). - dd06b50d-5364-4b96-9f62-93fda1f14cfb
(HONORS ONLY) 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. - 96d80795-c716-44aa-b1fa-28ba14d290c0
Identify the different parts of the expression and explain their meaning within the context of a problem. - 86f66ac4-52de-4b01-b0bd-64b9d1722add
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. - d759abab-27e2-481c-9921-907efa5d74be
Create a multiple of a linear equation showing that they are equivalent (e.g., x + y = 6 is equivalent to 2x + 2y = 12). - 458eb193-8bc0-4657-85c3-a4b617316015
Pair the rate of change with its graph. - d03ec69d-986b-4199-a078-d1be7c49195a
Explain why the 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹-coordinates of the points where the graphs of the equations 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺 = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹) and 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺 = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹) intersect are the solutions of the equation 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹) = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹) and/or 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - 8747c55b-cbc9-4ef6-b38a-95fde44f15c3
Write arguments focused on discipline-specific content. a. 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. b. 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 discipline-appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. c. 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. d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented. - 202825df-c3a2-43e4-948c-3429f9f3d77d
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. - e779da50-d12e-4314-966c-08e1656d94a3
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. - 1cc1fb51-16ed-4934-ae76-87698c73367c
Understand that a is a root of a polynomial function if and only if x-a is a factor of the function. - 85aaf90d-097a-455b-b3a2-3b29f9244158
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). - a764f529-16f8-4fa9-b5cd-3d0831349fe3
Find the zeros of a polynomial when the polynomial is factored (e.g., If given the polynomial equation y = x ² + 5x + 6, factor the polynomial as y = (x + 3)(x + 2). Then find the zeros of y by setting each factor equal to zero and solving. x = -2 and x = -3 are the two zeroes of y.). - 379be92a-3dac-425d-9359-4bae30c7fb12
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. - e3897065-ef41-4286-880b-2070c9ddb24d
Complete a graph given the data, using dot plots, histograms or box plots. - 7aea444c-ac6c-40ab-a194-a522f8860d3b
Use algebraic methods and technology to fit a linear function to the data. - 3410d4f7-acc8-45a6-a409-f5326c40c9f7
Locate the key features of linear and quadratic equations. - f8a502e6-916b-4a60-88a8-ecd687e98d4c
Know and justify that when multiplying of a nonzero rational number and an irrational number the result is irrational. - 254c1422-e9c5-47d6-9351-f5255ab6a33f
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. - 470f61e3-5bd1-47e2-a139-740035813e91
Graph equations in two or more variables on coordinate axes with labels and scales. - 7a4aa91b-c778-429d-ad50-346529b9816d
Informally assess the fit of a function by plotting and analyzing residuals. - 95dcb5d7-a3e3-4577-9e6e-b14ffdda13ce
Write expressions in equivalent forms by factoring to find the zeros of a quadratic function and explain the meaning of the zeros. - 80c302a6-c77d-4877-bf8f-c5687a46ed2b
Extend the properties of exponents to justify that (51/2)2=5. - 849c1265-fe8c-4957-8650-12abeb37ae2a
Solve simple rational and radical equations in one variable. - 64c5bca0-1420-43f3-9286-813ec5ed052c
Interpret units in the context of the problem. - 41961540-0e42-46a5-b66e-696c83e8edcb
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. - 0895ac3a-a4af-48a4-adee-700e9bf4b6b7
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. - 3ff81b1a-0429-4077-b975-7bf3ef39b19b
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Example: For example, the Fibonacci sequence is defined recursively by 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧(0) = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧(1) = 1, 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯+1) = 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯) + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧(𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯-1) for 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯 greater than or equal to 1. - 46d77c7e-5843-4183-950c-b7ba0a8c2f3f
Understand the definition of a polynomial. - f68b0506-3ae4-49f7-9b23-509dc19980ab
Simplify expressions including combining like terms, using the distributive property, and other operations with polynomials. - 19cfcf55-311e-46ae-8119-82b61dc71bb3
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. - 7d111c6b-17f8-47af-a1ba-eeb71253561d
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). - 2fdbdd0a-4139-4e9c-bd71-d65d15db100d
Graph a linear inequality in two variables using at least two coordinate pairs that are solutions. - 33375461-533b-4b5d-8c60-32316702a80c
Use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely. - b5a6d825-102b-4c95-a199-29073ebdc75b
Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. 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, well-reasoned exchange of ideas. b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. c. 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. d. 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. - 39b2240a-0c67-426e-99bb-c1a880e6c4b8
Describe the properties of a function (e.g., rate of change, maximum, minimum, etc.). - 80018ccd-3b6c-4e32-b983-2694670b2ae2
(HONORS ONLY) Prove polynomial identities and use them to describe numerical relationships. Example: For example, the polynomial identity (𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹² + 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺²)² = (𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹² – 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺²)² + (2𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺)² can be used to generate Pythagorean triples. - f414f786-5e26-45a2-a1c4-330764ca685d
Solve quadratic equations by using the quadratic formula. - a686f336-08fc-4917-becf-487d5d9d05bb
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - 08878758-8098-43fd-9f51-ced6566042b4
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. - 92e6f323-be53-4506-86e4-350312f8a433
Combine standard function types using arithmetic operations. Example: 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. - 2b53cd9d-2997-422d-90f1-057cd438db7a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. - d3c157cf-a905-43b1-8b4b-d8bbe584c3d6
Given the graph of a function, determine the domain. - 5f266b29-4721-43d7-a700-11f6fa0e0918
(HONORS ONLY) Read values of an inverse function from a graph or a table, given that the function has an inverse. - 58d366b5-0df6-4494-adba-d67270412506
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. - 85786a83-8e8e-4f2c-9ee5-c473a733533a
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - 8cd34c46-8d1f-4227-bedb-e17c417a5e44
Compare two or more different data sets using the center and spread of each. - d6b8ada1-720b-4f48-bce2-fa9153be0a30
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. - ea4e177b-0dc6-4d90-bad7-6398ddb60b27
Solve quadratic equations by inspection (e.g., for 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘢 ± 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘢𝘣𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘢𝘣𝘪 for real numbers 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘢𝘣𝘪𝘢 and 𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘝𝘭𝘙𝘙𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘧𝘧𝘯𝘧𝘯𝘧𝘯𝘯𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘢𝘣𝘪𝘢𝘣. - 5b718173-1711-4db7-912f-2629db1814fb
Graph the solutions to a linear inequality in two variables as a half-plane (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 half-planes. - 9abd3084-f1f5-4743-88a5-bb311178c5b7
Rewrite expressions involving radicals and rational exponents using the properties of exponents. - b8a7e69e-d432-491e-a178-6d0c6369ece1
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - 6dd64416-2b83-4d29-af53-77be3b9c8693
Add, subtract, and multiply polynomials and understand how closure applies under these operations. - 424bb2fc-e2b5-4eb6-b76b-0235482eeb7c
Select the graph, the description of a relationship or two input-output pairs of linear functions. - 5c368626-fb88-4217-8c0e-8aab4cbf832d




List of all Files Validated:


imsmanifest.xml
I_0023e954-e59b-3de4-8946-b31e32371852_1_R/BasicLTI.xml
I_00737141-430d-3f4d-86c2-9b77675f0845_1_R/BasicLTI.xml
I_00a621bc-aa50-308e-bdc4-07a0089a32a7_R/BasicLTI.xml
I_00b9ddcd-430d-3cf5-96fe-fdbc60800880_1_R/BasicLTI.xml
I_00b9ddcd-430d-3cf5-96fe-fdbc60800880_3_R/BasicLTI.xml
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