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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
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Also assesses:
- Assessment Limits :
Functions represented algebraically are limited to linear, quadratic, or
exponential.Functions may be represented using tables, graphs or verbally.
Functions represented using these representations are not limited to
linear, quadratic or exponential.Functions may have closed domains.
Functions may be discontinuous.
Items may not require the student to use or know interval notation.
Key features include x-intercepts, y-intercepts; intervals where the
function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; and end behavior. - Calculator :
Neutral
- Clarification :
Students will determine and relate the key features of a function
within a real-world context by examining the function’s table.Students will determine and relate the key features of a function
within a real-world context by examining the function’s graph.Students will use a given verbal description of the relationship
between two quantities to label key features of a graph of a function
that model the relationship.Students will differentiate between different types of functions using
a variety of descriptors (e.g., graphically, verbally, numerically, and
algebraically).Students will compare and contrast properties of two functions using
a variety of function representations (e.g., algebraic, graphic, numeric
in tables, or verbal descriptions). - Stimulus Attributes :
For F-IF.2.4, items should be set in a real-world context.For F-IF.3.9, items may be set in a real-world or mathematical
context.Items may use verbal descriptions of functions.
Items must use function notation.
- Response Attributes :
For F-IF.2.4, items may require the student to apply the basic
modeling cycle.Items may require the student to write intervals using inequalities.
Items may require the student to choose an appropriate level of
accuracy.Items may require the student to choose and interpret the scale in a
graph.Items may require the student to choose and interpret units.
MAFS.912.F-IF.3.9
- Test Item #: Sample Item 1
- Question:
Kim is driving from Miami to Key West. The graph shows her distance from Key West.
During what interval is Kim driving the fastest? Drag numbers to the boxes to complete the inequality.
- Difficulty: N/A
- Type: GRID: Graphic Response Item Display
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Experts
Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
Tutorial
Unit/Lesson Sequence
Virtual Manipulatives
STEM Lessons - Model Eliciting Activity
"To The Limit" MEA has students identify several factors that can affect a population’s growth. Students will examine photos to list limiting factors and discuss their impact on populations. As a group they will develop a solution to minimize the impact of pollution on fish population.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to evaluate three verbal descriptions and to state why each does or does not match a given graph.
Students are asked to interpret key features of a graph (symmetry) in the context of a problem situation.
Students are given a table of functional values and asked to describe and interpret key features of the graph in the context of the problem.
Students are asked to interpret key features of a graph (intercepts and intervals over which the graph is increasing) in the context of a problem situation.
Original Student Tutorials Mathematics - Grades 9-12
Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.
Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.
Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.
Learn how to interpret key features of linear functions and translate between representations of linear functions through exploring jobs for teenagers in this interactive tutorial.
Learn about different formats of quadratic equations and their graphs with experiments involving launching and shooting of balls in this interactive tutorial.
This is part 2 of a two-part series: Click HERE to open part 1.
Join us as we watch ball games and explore how the height of a ball bounce over time is represented by quadratic functions, which provides opportunities to interpret key features of the function in this interactive tutorial.
This is part 1 of a two-part series: Click HERE to open part 2.
Student Resources
Original Student Tutorials
Learn about different formats of quadratic equations and their graphs with experiments involving launching and shooting of balls in this interactive tutorial.
This is part 2 of a two-part series: Click HERE to open part 1.
Type: Original Student Tutorial
Join us as we watch ball games and explore how the height of a ball bounce over time is represented by quadratic functions, which provides opportunities to interpret key features of the function in this interactive tutorial.
This is part 1 of a two-part series: Click HERE to open part 2.
Type: Original Student Tutorial
Learn about exponential decay as you calculate the value of used cars by examining equations, graphs, and tables in this interactive tutorial.
Type: Original Student Tutorial
Learn how to interpret key features of linear functions and translate between representations of linear functions through exploring jobs for teenagers in this interactive tutorial.
Type: Original Student Tutorial
Learn about exponential growth in the context of interest earned as money is put in a savings account by examining equations, graphs, and tables in this interactive tutorial.
Type: Original Student Tutorial
Learn about exponential functions and how they are different from linear functions by examining real world situations, their graphs and their tables in this interactive tutorial.
Type: Original Student Tutorial
Perspectives Video: Expert
<p>Jump to it and learn more about how quadratic equations are used in robot navigation problem solving!</p>
Type: Perspectives Video: Expert
Problem-Solving Tasks
In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.
Type: Problem-Solving Task
This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, t = 0 is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.
Type: Problem-Solving Task
This task could be used for assessment or for practice. It allows students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, students are asked to determine which function has the greatest maximum and the greatest non-negative root.
Type: Problem-Solving Task
This task asks students to find the average, write an equation, find the domain, and create a graph of the cost of producing DVDs.
Type: Problem-Solving Task
In this task students are given graphs of quantities related to weather. The purpose of the task is to show that graphs are more than a collection of coordinate points; they can tell a story about the variables that are involved, and together they can paint a very complete picture of a situation, in this case the weather. Features in one graph, like maximum and minimum points, correspond to features in another graph. For example, on a rainy day, the solar radiation is very low, and the cumulative rainfall graph is increasing with a large slope.
Type: Problem-Solving Task
This problem introduces a logistic growth model in the concrete settings of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models.
Type: Problem-Solving Task
This task is for instructional purposes only and students should already be familiar with some specific examples of logistic growth functions. The goal of this task is to have students appreciate how different constants influence the shape of a graph.
Type: Problem-Solving Task
This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.
Type: Problem-Solving Task
Students explore and manipulate expressions based on the following statement:
A function f defined for -a < x="">< a="" is="" even="" if="" f(-x)="f(x)" and="" is="" odd="" if="" f(-x)="-f(x)" when="" -a="">< x="">< a.="" in="" this="" task="" we="" assume="" f="" is="" defined="" on="" such="" an="" interval,="" which="" might="" be="" the="" full="" real="" line="" (i.e.,="" a="">
Type: Problem-Solving Task
The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function.
Type: Problem-Solving Task
The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task.
Type: Problem-Solving Task
Virtual Manipulatives
In this activity, students adjust slider bars which adjust the coefficients and constants of a linear function and examine how their changes affect the graph. The equation of the line can be in slope-intercept form or standard form. This activity allows students to explore linear equations, slopes, and y-intercepts and their visual representation on a graph. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.
Type: Virtual Manipulative
Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
Parent Resources
Problem-Solving Tasks
In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.
Type: Problem-Solving Task
This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, t = 0 is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.
Type: Problem-Solving Task
This task could be used for assessment or for practice. It allows students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, students are asked to determine which function has the greatest maximum and the greatest non-negative root.
Type: Problem-Solving Task
This task asks students to find the average, write an equation, find the domain, and create a graph of the cost of producing DVDs.
Type: Problem-Solving Task
In this task students are given graphs of quantities related to weather. The purpose of the task is to show that graphs are more than a collection of coordinate points; they can tell a story about the variables that are involved, and together they can paint a very complete picture of a situation, in this case the weather. Features in one graph, like maximum and minimum points, correspond to features in another graph. For example, on a rainy day, the solar radiation is very low, and the cumulative rainfall graph is increasing with a large slope.
Type: Problem-Solving Task
This problem introduces a logistic growth model in the concrete settings of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models.
Type: Problem-Solving Task
This task is for instructional purposes only and students should already be familiar with some specific examples of logistic growth functions. The goal of this task is to have students appreciate how different constants influence the shape of a graph.
Type: Problem-Solving Task
This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match. The first and third graphs look very similar at first glance, but the function values are very different since the scales on the vertical axes are very different. The task could also be used to generate a group discussion on interpreting functions given by graphs.
Type: Problem-Solving Task
Students explore and manipulate expressions based on the following statement:
A function f defined for -a < x="">< a="" is="" even="" if="" f(-x)="f(x)" and="" is="" odd="" if="" f(-x)="-f(x)" when="" -a="">< x="">< a.="" in="" this="" task="" we="" assume="" f="" is="" defined="" on="" such="" an="" interval,="" which="" might="" be="" the="" full="" real="" line="" (i.e.,="" a="">
Type: Problem-Solving Task
The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function.
Type: Problem-Solving Task
The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task.
Type: Problem-Solving Task
Virtual Manipulative
Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.
Type: Virtual Manipulative
