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Learning about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute

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Learning about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute

Grade Levels

6th Grade, 7th Grade, 8th Grade

Course, Subject

Algebra I, Algebra II
Related Academic Standards
CC.2.2.HS.C.1 CC.2.2.HS.C.1
Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.2.HS.C.2 CC.2.2.HS.C.2
Graph and analyze functions and use their properties to make connections between the different representations.
CC.2.2.HS.C.3 CC.2.2.HS.C.3
Write functions or sequences that model relationships between two quantities.
CC.2.2.HS.C.4 CC.2.2.HS.C.4
Interpret the effects transformations have on functions and find the inverses of functions.
CC.2.2.HS.C.5 CC.2.2.HS.C.5
Construct and compare linear, quadratic and exponential models to solve problems.
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  • Big Ideas
    Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
    Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Numerical measures describe the center and spread of numerical data.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.
    Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
    The likelihood of an event occurring can be described numerically and used to make predictions.
    The set of real numbers has infinite subsets including the sets of whole numbers, integers, rational, and irrational numbers.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
    Two variable quantities are proportional if their values are in a constant ratio. The relationship between proportional quantities can be represented as a linear function.
  • Concepts
    Analysis of one and two variable (univariate and bivariate) data
    Data displays: Histograms, circle graphs, stem and leaf plots, line graphs
    Functions and multiple representations
    Graphing on a coordinate plane
    Linear equations and inequalities
    Linear functions
    Linear relationships: Equation and inequalities in one and two variables
    Linear system of equations and inequalities
    Prediction and Inference
    Proportionality: Similar figures and objects, scale factors, unit rate
    Rate of change
    Representations
    Sampling as a method of estimation and prediction
    Theoretical probability
  • Competencies
    Answer questions regarding a data set using measures of center and spread and interpreting the graphical representation (including box-and-whisker plots) of the data set.
    Apply a variety of strategies for proportional reasoning and use them to solve real world problems, including problems dealing with similarity and rates of change.
    Recognize problem situations in which two or more variables have a linear relationship to each other. Understand the connections between linear equations and the patterns in the tables and graphs of those equations: rate of change, slope, and y-intercept.
    Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
    Use algebraic properties and processes in mathematical situations and apply them to solve real world problems.
    Use linear functions, linear equations, and linear inequalities to represent, analyze, and solve a variety of problems.
    Use the appropriate graphical data representation and extend understanding of the influence of scale in data interpretation.
    Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.

Description

Your task is to analyze and interpret the two graphs and then to determine how the two graphs are related. First, drag the slider on the second graph (Total Cost).

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Learning about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute

Content Provider

NCTM

 

The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.

 

The National Council of Teachers of Mathematics is the global leader and foremost authority in mathematics education, ensuring that all students have access to the highest quality mathematics teaching and learning. We envision a world where everyone is enthused about mathematics, sees the value and beauty of mathematics, and is empowered by the opportunities mathematics affords.

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