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This is a task from the Illustrative Mathematics website that is one ...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

Subject:
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
10/10/2017 Conditional Remix & Share Permitted
CC BY-NC-SA
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The problem presents a context where a quadratic function arises. Careful analysis, ...

The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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The problem statement describes a changing algae population as reported by the ...

The problem statement describes a changing algae population as reported by the Maryland Department of Natural Resources. In part (a), students are expected to build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth (F-LE.2).

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Educational Use
Rating

In this video segment from Cyberchase, Matt tries for a second time ...

In this video segment from Cyberchase, Matt tries for a second time to arrange tables and chairs to accommodate 20 workers.

Subject:
Mathematics
Algebra
Functions
Material Type:
Lecture
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Teachers' Domain
Author:
U.S. Department of Education
WNET
09/23/2008 Rating

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data ...

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Elana Joram and Christina Hartman
11/05/2008 Conditional Remix & Share Permitted
CC BY-NC-SA
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In this real world problem students solve questions based on the relationship ...

In this real world problem students solve questions based on the relationship between production costs and price.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task provides a real world context for interpreting and solving exponential ...

This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task could be put to good use in an instructional sequence ...

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task involves a fairly straightforward decaying exponential. Filling out the table ...

This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task describes two linear functions using two different representations. To draw ...

This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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The purpose of this task is for students to interpret two distance-time ...

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task provides an exploration of a quadratic equation by descriptive, numerical, ...

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

Subject:
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task is for instructional purposes only and builds on ``Building an ...

This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

Subject:
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/20/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This is the first of a series of task aiming at understanding ...

This is the first of a series of task aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/15/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task is intended for instruction and to motivate "Building a general ...

This task is intended for instruction and to motivate "Building a general quadratic function.''

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/26/2013 Rating

This course begins with a review of algebra specifically designed to help ...

This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

Subject:
Calculus
Functions
Material Type:
Assessment
Full Course
Syllabus
Textbook
Provider:
The Saylor Foundation
10/13/2017 Unrestricted Use
CC BY
Rating

This course is an introduction to contemporary calculus and is the first ...

This course is an introduction to contemporary calculus and is the first of a three-part sequence. In this course students explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl

Subject:
Calculus
Functions
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Lesson Plan
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
10/31/2011 Conditional Remix & Share Permitted
CC BY-NC-SA
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The purpose of this task is to give students practice constructing functions ...

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 that context. It can be used as either an assessment or a teaching task.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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The primary purpose of this task is to lead students to a ...

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. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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The task requires the student to use logarithms to solve an exponential ...

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

Subject:
Mathematics
Functions
Archaeology
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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In the task "Carbon 14 Dating'' the amount of Carbon 14 in ...

In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/21/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This problem introduces the method used by scientists to date certain organic ...

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/21/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This exploratory task requires the student to use a property of exponential ...

This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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The goal of this class is to prove that category theory is ...

The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.

Subject:
Functions
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
David I. Spivak
01/01/2013 Conditional Remix & Share Permitted
CC BY-NC-SA
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This simple task assesses whether students can interpret function notation. The four ...

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Rating

This Java applet activity allows students to explore the various situations described ...

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
11/05/2011 Rating

In this lesson from Illuminations, students explore and discover linear relationships. Linear ...

In this lesson from Illuminations, students explore and discover linear relationships. Linear patterns are identified, extended and described verbally, numerically and algebraically through three investigations. Using manipulatives and the linked applet, "Chairs", learners determine the number of chairs needed when the number of tables is known, and vice versa. Instructional plan, questions for the students, assessment options, extensions and teacher reflections are provided.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Samuel E. Zordak
11/05/2011 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task presents a real world situation that can be modeled with ...

This task presents a real world situation that can be modeled with a linear function best suited for an instructional context.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task is intended strictly for instructional purposes with the goal of ...

This task is intended strictly for instructional purposes with the goal of building understandings of linear relationships within a meaningful and, hopefully, somewhat familiar context.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task gives students an opportunity to work with exponential functions in ...

This task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This task is preliminary to F-LE Compounding Interest with a 5% Interest ...

This task is preliminary to F-LE Compounding Interest with a 5% Interest Rate which further develops the relationship between e and compound interest.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task develops reasoning behind the general formula for balances under continuously ...

This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically addresses the standard (F-BF), building functions from a context, a auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
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This word problem requires students to create expressions to calculate gas milage ...

This word problem requires students to create expressions to calculate gas milage for a vehicle.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Educational Use
Rating

In this visualization adapted from the University of Massachusetts Medical School, discover ...

In this visualization adapted from the University of Massachusetts Medical School, discover the role that dengue viral proteins play in a human cell as the virus prepares to replicate.

Subject:
Life Science
Functions
Chemistry
Material Type:
Lecture
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Teachers' Domain
Author:
National Institutes of Health/National Institute of Allergy and Infectious Diseases
UMASS Medical School
WGBH Educational Foundation
04/28/2008 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task asks students to find a linear function that models something ...

This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
12/14/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This problem allows the student to think geometrically about lines and then ...

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This task is designed as a follow-up to the task F-LE Do ...

This task is designed as a follow-up to the task F-LE Do Two Points Always Determine a Linear Function? Linear equations and linear functions are closely related, and there advantages and disadvantages to viewing a given problem through each of these points of view. This task is intended to show the depth of the standard F-LE.2 and its relationship to other important concepts of the middle school and high school curriculum, including ratio, algebra, and geometry.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

This problem complements the problem ``Do two points always determine a linear ...

This problem complements the problem ``Do two points always determine a linear function?''

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

The purpose of this task to help students think about an expression ...

The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable, and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012 Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

An important property of linear functions is that they grow by equal ...

An important property of linear functions is that they grow by equal differences over equal intervals. In this task students prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope. In F.LE Equal Differences over Equal Intervals 2, students prove the property in general (for equal intervals of any length).

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics