Description
- Overview:
- This is course material published for a secondary Math 1 course. Authors of this work are: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius and updated from the original work in 2013 in partnership with the Utah State Office of Education.
- Subject:
- Mathematics
- Level:
- High School
- Material Type:
- Activity/Lab, Homework/Assignment, Lesson, Module
- Author:
- Gina Loveless
- Provider:
- Mathematics Vision Project
- Date Added:
- 09/02/2020
- License:
- Creative Commons Attribution
- Language:
- English, Spanish
- Media Format:
- Downloadable docs
Standards
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Learning Domain: Algebra: Creating Equations
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 and exponential functions.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Creating Equations
Standard: Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Creating Equations
Standard: 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Creating Equations
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.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: 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.
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Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: 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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Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: 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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Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: 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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Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: Explain why the x-coordinates 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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Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: 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.
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Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Interpret expressions that represent a quantity in terms of its context.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Interpret parts of an expression, such as terms, factors, and coefficients.*
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Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.*
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Learning Domain: Functions: Building Functions
Standard: Write a function that describes a relationship between two quantities.*
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Learning Domain: Functions: Building Functions
Standard: Determine an explicit expression, a recursive process, or steps for calculation from a context.
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Learning Domain: Functions: Building Functions
Standard: 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.
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Learning Domain: Functions: Building Functions
Standard: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
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Learning Domain: Functions: Building Functions
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.
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Learning Domain: Functions: Interpreting Functions
Standard: 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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Learning Domain: Functions: Interpreting Functions
Standard: 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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Learning Domain: Functions: Interpreting Functions
Standard: 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(n-1) for n ≥ 1 (n is greater than or equal to 1).
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
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.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
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 n engines in a factory, then the positive integers would be an appropriate domain for the function.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
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.*
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Learning Domain: Functions: Interpreting Functions
Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima.*
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Learning Domain: Functions: Interpreting Functions
Standard: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.*
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Learning Domain: Functions: Interpreting Functions
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.
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Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Distinguish between situations that can be modeled with linear functions and with exponential functions.*
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Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.*
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Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*
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Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*
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Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Construct and compare linear, quadratic, and exponential models and solve problems. 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).*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
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.*
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Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Interpret the parameters in a linear or exponential function in terms of a context.*
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Learning Domain: Geometry: Congruence
Standard: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Geometry: Congruence
Standard: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Degree of Alignment: Not Rated (0 users)
Learning Domain: Geometry: Congruence
Standard: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
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Learning Domain: Geometry: Congruence
Standard: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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Learning Domain: Geometry: Congruence
Standard: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Degree of Alignment: Not Rated (0 users)
Learning Domain: Geometry: Congruence
Standard: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
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Learning Domain: Geometry: Congruence
Standard: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
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Learning Domain: Geometry: Congruence
Standard: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
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Learning Domain: Geometry: Congruence
Standard: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
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Learning Domain: Geometry: Congruence
Standard: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
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Learning Domain: Geometry: Expressing Geometric Properties with Equations
Standard: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
Degree of Alignment: Not Rated (0 users)
Learning Domain: Geometry: Expressing Geometric Properties with Equations
Standard: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Degree of Alignment: Not Rated (0 users)
Learning Domain: Geometry: Expressing Geometric Properties with Equations
Standard: Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Number and Quantity: Quantities
Standard: Use units as a way to understand problems and to guide the solution of multi-step 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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Learning Domain: Number and Quantity: Quantities
Standard: Define appropriate quantities for the purpose of descriptive modeling.*
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Learning Domain: Number and Quantity: Quantities
Standard: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Represent data with plots on the real number line (dot plots, histograms, and box plots).*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: 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.*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).*
Degree of Alignment: Not Rated (0 users)
Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: 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.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: 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.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Informally assess the fit of a function by plotting and analyzing residuals.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Fit a linear function for a scatter plot that suggests a linear association.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Compute (using technology) and interpret the correlation coefficient of a linear fit.*
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Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data
Standard: Distinguish between correlation and causation.*
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Tags (13)
- Congruence
- Connecting Algebra & Geometry
- Equations
- Exponential Functions
- Functions
- Inequalities
- Linear Functions
- Mathematics Vision Project
- Math Sequences
- Modeling Data
- Proof
- Symmetry
- Systems
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