# 170 Results

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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
Author:
Illustrative Mathematics
08/06/2015
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Rating

Students play a generalized version of connect four, gaining the chance to place a piece on the board by solving an algebraic equation. Parameters: Level of difficulty of equations to solve and type of problem. Algebra Four is one of the Interactivate assessment games.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Assessment
Diagram/Illustration
Game
Interactive
Lesson Plan
Simulation
Student Guide
Provider:
NSDL Staff
Shodor
SMARTR
Provider Set:
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
10/30/2014
Rating

Test your algebra skills by answering questions. This quiz asks you to solve algebraic linear and quadratic equations of one variable. Choose difficulty level, question types, and time limit. Algebra Quiz is one of the Interactivate assessment quizzes.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Assessment
Interactive
Lecture Notes
Lesson Plan
Simulation
Student Guide
Provider:
AMSER: Applied Math and Science Education Repository
NSDL Staff
Shodor
SMARTR
Provider Set:
AMSER: Applied Math and Science Education Repository
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
10/30/2014
Rating

Atmosphere Applet: This program lets you study how the properties of the atmosphere change with altitude. You can study the atmosphere of either the Earth or Mars. The equations used in this program are taken from the ICAO standard day model for the Earth and from some curve fits of the Martian atmosphere gathered by the Global Surveyor spacecraft. Using the airplane graphic you can select an altitude, or you can type an altitude into the input box.

The program instantly outputs a selected property and displays the local temperature and pressure on gauges You can output the temperature, pressure, density, local speed of sound, Mach number for specified velocity, or the ratio of aircraft lift to the lift on Earth at sea level. Input and output can be given in either English or metric units.

Subject:
Engineering
Algebra
Calculus
Functions
Trigonometry
Chemistry
Geoscience
Physics
Space Science
Material Type:
Full Course
Interactive
Provider:
NASA
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
NASA Glenn Research Center
Author:
NASA Glenn Research Center
Tom Benson
08/09/2008
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Rating

Create your own affine cipher for encoding and decoding messages. Input your own constant and multiplier, then input a message to encode.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Lesson Plan
Simulation
Student Guide
Provider:
NSDL Staff
Shodor
SMARTR
Provider Set:
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
10/30/2014
Rating

Encode and decode messages to determine the form for an affine cipher. Input a message to encode, then input your guesses for the constant and multiplier. Caesar Cipher II is one of the Interactivate assessment explorers.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Assessment
Lecture Notes
Lesson Plan
Simulation
Student Guide
Provider:
NSDL Staff
Shodor
SMARTR
Provider Set:
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
10/30/2014
Rating

Decode encrypted messages to determine the form for an affine cipher, and practice your reasoning and arithmetic skills. Input your guesses for the multiplier and constant. Caesar Cipher III is one of the Interactivate assessment explorers.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Assessment
Lecture Notes
Lesson Plan
Simulation
Student Guide
Provider:
NSDL Staff
Shodor
SMARTR
Provider Set:
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
10/30/2014
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Educational Use
Rating

In this interactive activity adapted from the Exploratorium, explore the step-by-step process by which an animal cell divides to make more cells.

Subject:
Life Science
Functions
Material Type:
Activity/Lab
Interactive
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media: Multimedia Resources for the Classroom and Professional Development
Teachers' Domain
Author:
National Science Foundation
WGBH Educational Foundation
08/09/2007
Educational Use
Rating

Explore the parts of a virtual animal cell in this interactive activity adapted from the Exploratorium. Learn about various cell structures and the roles they play in cell division, cellular respiration, and protein synthesis.

Subject:
Life Science
Functions
Material Type:
Activity/Lab
Interactive
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media: Multimedia Resources for the Classroom and Professional Development
Teachers' Domain
Author:
National Science Foundation
WGBH Educational Foundation
08/09/2007
Unrestricted Use
CC BY
Rating

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 6-minute video presents Michelle Bottomley, a teacher at Tetherdown Primary School, north London, sharing a lesson idea that has her students use their knowledge of the properties of number in order to solve problems. Michelle engages her pupils to work systematically to look for patterns when working out how many squares are in different sized chessboards, and then to predict how many squares are in a 25 x 25 squared board.

Subject:
Education
Mathematics
Algebra
Functions
Material Type:
Lesson Plan
Provider:
Maryland Public Television
Provider Set:
Mathlanding: Elementary Mathematics Pathway
Author:
Teaching TV
11/05/2010
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Unrestricted Use
CC BY
Rating

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
Rating

Manipulate different types of conic section equations on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph. Choose from vertical or horizontal parabola, circle, ellipse, and vertical or horizontal hyperbola.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Diagram/Illustration
Interactive
Lesson Plan
Simulation
Student Guide
Provider:
NSDL Staff
Shodor
SMARTR
Provider Set:
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
10/30/2014
Unrestricted Use
CC BY
Rating

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context.

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

Watch the dance of development as a zebrafish egg divides and differentiates on its way to becoming an embryo in this interactive activity adapted from the Exploratorium.

Subject:
Life Science
Functions
Material Type:
Activity/Lab
Interactive
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media: Multimedia Resources for the Classroom and Professional Development
Teachers' Domain
Author:
National Science Foundation
WGBH Educational Foundation
08/09/2007
Rating

Enter a set of data points, then derive a function to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.

Subject:
Computing and Information
Education
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Diagram/Illustration
Interactive
Lecture Notes
Lesson Plan
Simulation
Student Guide
Teaching/Learning Strategy
Provider:
Florida Center for Research in Science, Technology, Engineering, and Mathematics
NSDL Staff
Shodor
SMARTR
Provider Set:
iCPALMS: A Standards-based K-12 Resources and Tools Pathway
NSDL Math Common Core
CSERD: Computational Science Education Reference Desk
SMARTR: Virtual Learning Experiences for Youth
Author:
Shodor