Explore innovative Apps to invigorate AP math and physics instruction. Teachers will align instructional Apps and digital resources with the goals of AP Calculus, and integrate National Council of Teachers of Math’s – Core Math Tools

Core Math Tools is a downloadable suite of interactive software tools for algebra and functions, geometry and trigonometry, and statistics and probability. The tools are appropriate for use with any high school mathematics curriculum and compatible with the Common Core State Standards for Mathematics in terms of content and mathematical practices. Java required.

Custom Apps
Focused explorations of specific topics

Advanced Apps
Focused explorations of advanced topics

Sample Lessons
Problem-based lessons that employ Core Math Tools

Data Sets
Wealth of data sets organized by data type

How-To Pages
Help, hints and steps to do basic tasks

Use by Teachers and Students

Core Math Tools can be saved on a computer or USB drive, making it possible to use without Internet access. Files can be saved and reloaded by students and teachers. Its portability allows easy access for students, teachers and parents outside the classroom. Core Math Tools will automatically check for updates when launched and Internet access is available. Core Math Tools Conference Sessions
2013 Teaching and Learning with Technology Symposium at the AMTE Conference

Core Math Tools and Its Affordances for Teacher Educators and for Prospective Teachers -- Download thesession PowerpointPresenters: Christian Hirsch, Pat Hopfensperger, Gary Martin, and Rose ZbiekIn this symposium, the presenters provide an overview of the features of NCTM's Core Math Tools, together with three perspectives on its use with prospective secondary school mathematics teachers.

Mathematical Modeling: The Core of the Common Core State Standards Thursday, November 29, 2012: 9:30-10:30 AM -- Download a PDF of the session Powerpoint Lead Speaker: Christian Hirsch As a CCSSM content standard and a standard for mathematical practice, mathematical modeling affords a rich opportunity around which to develop and unify the mathematical content of the high school conceptual categories and related mathematical practices. We will examine several illustrative modeling tasks in terms of teaching and learning.

Core Math Tools: Supporting Inquiry, Conceptual Understanding, and Problem Solving Thursday, October 11, 2012, 2:00-3:00 PM - Lead Speaker: Christian HirschIn this interactive session, we will illustrate features of NCTM's new open source software tools as we make sense of, and solve, problems in context.

High School Student Reasoning with Support of Core Math Tools Thursday, October 11, 2012: 2:30-4:00 PMLead Speaker: Henry S. KepnerParticipants will engage in exemplary lessons designed to explore and reason mathematically with the support of mathematical software tools. We will focus on student reasoning, conjecturing, and justification opportunities using NCTM’s new Core Math Tools, downloadable to any computer. Bring a laptop, load, and reason mathematically.

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Your feedback is important! Comments or concerns regarding the content of this page may be sent to nctm@nctm.org. Thank you.

General Purpose Tools

General purpose tools are used to gain access to a wide range of problem-solving situations and mathematical content. These tools require strategies and skills highly applicable or transferable to other technology tools being used simultaneously or in the future. Algebra & Functions

Gen_Alg_CAS

The //Computer Algebra System (CAS)// tool manipulates symbolic expressions, equations and inequalities; solves in exact and decimal forms; produces graphs and tables; expands and factors polynomials; explores parameters used in functions; slices implicitly-defined surfaces; and computes with matrices.

Gen_Alg_Spreadsheet

The //Spreadsheet// tool displays and computes data stored in cells of a table; relates rows and columns by formulas; explores problems and models numerically including linear programming and “what-if” scenarios; and produces graphs for models not easily represented by algebraic models.

Geometry & Trigonometry

Gen_Geo_Synthetic

The Interactive Geometry tool is a interactive geometry platform that constructs, measures, manipulates, transforms (translations, reflections, rotations, dilations) and animates geometric figures including lines, circles, angles, perpendiculars, bisectors, tangents and vectors; offers synthetic and //coordinate// representations of geometric objects and transformations supporting the discovery of geometric relationships and structures; supports analytic geometry using matrices; and contains a simple command-oriented programming language that supports the construction of algorithms.

Statistics & Probability

Gen_Stat_DataAnalysis

The //Data Analysis// tool produces graphs and analysis of univariate and bivariate (categorical and quantitative) data including fitting algebraic models by-hand or “best-fit”; calculates descriptive statistics; performs chi-square tests for two-way tables; and contains pre-loaded data sets that have been carefully selected to highlight centrals ideas of statistics.

Gen_Stat_Simulation

The //Simulation// tool models probabilistic situations involving discrete and continuous outcomes; constructs simple and complex events with and without replacement; displays tabular and graphical results; and produces samples of varying size from distributions with an underlying probability model.

Function Iteration: Illustrate the graphical iteration process for functions. The function and initial value can be adjusted dynamically, and a time series plot showing the number of iterations versus the evaluated function values can be displayed.

Custom_Alg_Linear

Linear Programming: Analyze an optimization situation graphically by using constraint inequalities and an objective function to find the minimum/maximum. Both two-dimensional (2-D) and three-dimensional (3-D) linear programming problems can be examined. The linear programming situation can be graphically analyzed one constraint inequality at a time, resulting in the determination of the feasible region. See the Solver in the spreadsheets for numeric solutions and more variables.

Geometry

Custom_Geo_TriCong

//Triangle Congruence//: Explore whether three specified side or angle measures are sufficient information to determine the existence of a unique triangle (or the congruence of two triangles). Rigid transformations are used to verify the congruence of two triangles. Alternatively, measures of two triangles can be displayed to check for congruence, or created triangles can be manipulated and compared by clicking and dragging.

Custom_Geo_TilingTri

Tilings with Triangles or Quadrilaterals: Explore tiling the plane with congruent triangles or quadrilaterals using rotations of 180° about the midpoints of sides.

Custom_Geo_TilingReg

Tilings with Regular Polygons: Explore tiling the plane with one or more regular polygons to create regular and semi-regular tessellations.

Custom_Geo_Design

//Design by Robot//: Create both simple and complex designs by entering program commands for the robot to draw and move.

Custom_Geo_SSA

Explore SSA: Experiment with various side and angle measures to explore the side-side-angle condition for triangles. Determine which measurements or intervals of measurements determine no triangle, exactly one triangle, or two noncongruent triangles.

Custom_Geo_Similar

Explore Similar Triangles: Explore whether two specified side or angle measures are sufficient information to create similar triangles. A sequence of size (dilation) and rigid transformations are used to verify the similarity of two triangles. Alternatively, measures of two triangles can be displayed to check for similarity or compared directly using the mouse.

Custom_Geo_ArcsAngles

Explore Arcs and Angles: Explore the relationship between the measures of inscribed angles and their intercepted arcs. Features include the dragging the points on the circle to change the arc length or angle measure and display measures of angles and arcs.

Custom_Geo_Radians

Explore Radians: Experiment with measuring angles in radians and with how radian measures are related to degrees and revolutions. Features include guessing a target value displayed in radians, degrees, or revolutions in another unit of measure.

Custom_Geo_Slicing

Slicing or Unfolding Polyhedra: Visualize common polyhedra and manipulate 3-D modeling options such as cutting and unfolding. Features include rotating the shape in 3-D space and displaying the vertices, edges, and faces of a solid and its topological dual. Transform options include truncate, punch, and stellate.

Custom_Geo_Silcing2

Slicing Cones, Cylinders, and Spheres: Dynamically manipulate a plane slicing a single or double cone, cylinder, or sphere and view the corresponding conic section. Features include manipulation of the position of the plane of intersection and the cone itself, identification of the cross-section, and the option to display the wire frame.

Custom_Geo_Revolution

Surface of Revolution: Draw and manipulate a line or a connected series of line segments in two-dimensional space to simultaneously generate a surface of revolution in three-dimensional space. Features include choosing the axis of rotation, setting the angle of rotation, and showing the wire frame and quadrilateral faces of the surface of revolution.

Statistics

Custom_Stat_Balance

Estimate Center: Estimate the mean of a distribution by dynamically finding the balance point of the histogram. Preloaded or user-entered data sets can be analyzed.

Custom_Stat_Spread

Estimate Center and Spread: Estimate the mean of a distribution as in the Estimate Center app, and estimate the spread of a distribution by estimating a proportion (such as two-thirds) of the data within a distance of the mean. Preloaded or user-entered data sets can be analyzed.

Custom_Stat_Model

Modeling: Estimate a curve of “best-fit” on a scatterplot and compare to the regression equation. Features include a movable “best fit” curve and display of the estimate function equation with the regression equation. Available models are linear, exponential, power, logarithmic, quadratic, cubic, quartic, polynomial, and sinusoidal. Alternatively, users can enter an algebraic function model.

Custom_Stat_Distribution

Randomization Distribution: Create an approximate sampling distribution of possible differences in means, medians, or standard deviations of two treatments by re-randomizing and, then, identify extreme events. Features include adjusting histogram settings and displaying the count or relative frequency of resampling results in each bar of the histogram.

Custom_Stat_Random

Distribution of a Sample: Explore the shape, mean, and standard deviation of distributions of sample means, medians, or standard deviations for various sample sizes. Results are displayed in a histogram as counts or relative frequencies. Summary statistics are available.

Custom_Stat_Binomial

Binomial Distributions:Vary the number of trials and the probability of a success on each trial to see how the shape, center, and spread of binomial distributions are affected. Conduct experiments and compare theoretical models of distributions to simulation results. Features include moveable sliders for p and n, comparison of simulation results with theoretical binomial or normal distributions, and simultaneous display of multiple distributions.

Advanced Apps

Adv_VertexEdge

//Vertex-Edge Graphs//: Create andanalyze a vertex-edge graph—a collection of vertices and edges. Add color, weight, and direction to a graph; run tests and algorithms to find spanning trees, circuits, critical paths or colorings; and investigate the adjacency matrix or other matrices for a vertex-edge graph.

Adv_Control

//Control Charts//: Examine the run chart for a chosen data set and enter the desired mean and standard deviation. Then test for out-of-control behavior using one or more of eight tests commonly used in industry.

Adv_RankedChoice

Ranked Choice Voting: Determine voting outcomes based on various ranked choice voting methods. Voting methods include plurality, majority, runoff, pairwise-comparison, points-for-preference, and instant runoff.

Adv_WeightedVoting

Weighted Voting: Investigate a voting situation with the Banzhaf power index; measure the weight of a voter and determine if the voter is critical or not.

Adv_CodesCrypt

Codes and Cryptography: Encode and decrypt messages using ciphers and cryptography. Features include the Rot13, Caesar, affine, matrix (Hill) ciphers, and the RSA public-key cryptosystem.

Adv_Contour

Contour Diagrams: Represent elevation or other data with contour lines. Simultaneously view 3-D and relief lines. Contour diagrams can be modeled from pre-set or user-generated rectangular array of data or spreadsheet. See also 3-D graphing in CAS.

## APIP: Math Apps for AP & Pre-AP Teachers -- 3/12/13

## Agenda:

## Fluidity Software - Presentented by

Dr. Donald Carney, CEO, Co-Founder## NCTM Core Math Tools - Presented by Robert Agoglia, M.Ed. Instructional Specialist NYCDOE

## Advanced Placement Exam Preparation 2013 - Presented by Denise Lewis, APIP Instructional Specialist NYCDOE

Explore innovative Apps to invigorate AP math and physics instruction. Teachers willalign instructional Apps and digital resources with the goals of AP Calculus, and integrate National Council of Teachers of Math’s – Core Math Tools## Fluidity Software, Inc. provides the next-generation math teaching tools for math teachers.

## Core Math Tools Home

CAS, Spreadsheet, Geometry, Data Analysis, and Simulation

Focused explorations of specific topics

Focused explorations of advanced topics

Problem-based lessons that employ

Core Math ToolsWealth of data sets organized by data type

Help, hints and steps to do basic tasks

## Use by Teachers and Students

Core Math Tools can be saved on a computer or USB drive, making it possible to use without Internet access. Files can be saved and reloaded by students and teachers. Its portability allows easy access for students, teachers and parents outside the classroom. Core Math Tools will automatically check for updates when launched and Internet access is available.Core Math Tools Conference Sessions2013 Teaching and Learning with Technology Symposium at the AMTE Conference

2012 NCTM Regional Conference in ChicagoCore Math Tools and Its Affordances for Teacher Educators and for Prospective Teachers-- Download thesession PowerpointPresenters: Christian Hirsch, Pat Hopfensperger, Gary Martin, and Rose ZbiekIn this symposium, the presenters provide an overview of the features of NCTM's Core Math Tools, together with three perspectives on its use with prospective secondary school mathematics teachers.

2012 NCTM Regional Conference in DallasMathematical Modeling: The Core of the Common Core State StandardsThursday, November 29, 2012: 9:30-10:30 AM -- Download a PDF of the session Powerpoint Lead Speaker: Christian Hirsch As a CCSSM content standard and a standard for mathematical practice, mathematical modeling affords a rich opportunity around which to develop and unify the mathematical content of the high school conceptual categories and related mathematical practices. We will examine several illustrative modeling tasks in terms of teaching and learning.Core Math Tools: Supporting Inquiry, Conceptual Understanding, and Problem SolvingThursday, October 11, 2012, 2:00-3:00 PM - Lead Speaker: Christian HirschIn this interactive session, we will illustrate features of NCTM's new open source software tools as we make sense of, and solve, problems in context.High School Student Reasoning with Support of Core Math ToolsThursday, October 11, 2012: 2:30-4:00 PMLead Speaker: Henry S. KepnerParticipants will engage in exemplary lessons designed to explore and reason mathematically with the support of mathematical software tools. We will focus on student reasoning, conjecturing, and justification opportunities using NCTM’s new Core Math Tools, downloadable to any computer. Bring a laptop, load, and reason mathematically.## Page Feedback

Your feedback is important! Comments or concerns regarding the content of this page may be sent to nctm@nctm.org. Thank you.## General Purpose Tools

General purpose tools are used to gain access to a wide range of problem-solving situations and mathematical content. These tools require strategies and skills highly applicable or transferable to other technology tools being used simultaneously or in the future.Algebra & FunctionsGeometry & TrigonometryInteractive Geometrytool is a interactive geometry platform that constructs, measures, manipulates, transforms (translations, reflections, rotations, dilations) and animates geometric figures including lines, circles, angles, perpendiculars, bisectors, tangents and vectors; offerssyntheticand //coordinate// representations of geometric objects and transformations supporting the discovery of geometric relationships and structures; supports analytic geometry using matrices; and contains a simple command-oriented programming language that supports the construction of algorithms.Statistics & Probability## Custom Apps

AlgebraFunction Iteration:Illustrate the graphical iteration process for functions. The function and initial value can be adjusted dynamically, and a time series plot showing the number of iterations versus the evaluated function values can be displayed.Linear Programming:Analyze an optimization situation graphically by using constraint inequalities and an objective function to find the minimum/maximum. Both two-dimensional (2-D) and three-dimensional (3-D) linear programming problems can be examined. The linear programming situation can be graphically analyzed one constraint inequality at a time, resulting in the determination of the feasible region. See theSolverin the spreadsheets for numeric solutions and more variables.Geometry:Explore whether three specified side or angle measures are sufficient information to determine the existence of a unique triangle (or the congruence of two triangles). Rigid transformations are used to verify the congruence of two triangles. Alternatively, measures of two triangles can be displayed to check for congruence, or created triangles can be manipulated and compared by clicking and dragging.Tilings with Triangles or Quadrilaterals:Explore tiling the plane with congruent triangles or quadrilaterals using rotations of 180° about the midpoints of sides.Tilings with Regular Polygons:Explore tiling the plane with one or more regular polygons to create regular and semi-regular tessellations.:Create both simple and complex designs by entering program commands for the robot to draw and move.Explore SSA:Experiment with various side and angle measures to explore the side-side-angle condition for triangles. Determine which measurements or intervals of measurements determine no triangle, exactly one triangle, or two noncongruent triangles.Explore Similar Triangles:Explore whether two specified side or angle measures are sufficient information to create similar triangles. A sequence of size (dilation) and rigid transformations are used to verify the similarity of two triangles. Alternatively, measures of two triangles can be displayed to check for similarity or compared directly using the mouse.Explore Arcs and Angles: Explore the relationship between the measures of inscribed angles and their intercepted arcs.Features include the dragging the points on the circle to change the arc length or angle measure and display measures of angles and arcs.Explore Radians:Experiment with measuring angles in radians and with how radian measures are related to degrees and revolutions. Features include guessing a target value displayed in radians, degrees, or revolutions in another unit of measure.Slicing or Unfolding Polyhedra:Visualize common polyhedra and manipulate 3-D modeling options such as cutting and unfolding. Features include rotating the shape in 3-D space and displaying the vertices, edges, and faces of a solid and its topological dual. Transform options include truncate, punch, and stellate.Slicing Cones, Cylinders, and Spheres:Dynamically manipulate a plane slicing a single or double cone, cylinder, or sphere and view the corresponding conic section. Features include manipulation of the position of the plane of intersection and the cone itself, identification of the cross-section, and the option to display the wire frame.Surface of Revolution:Draw and manipulate a line or a connected series of line segments in two-dimensional space to simultaneously generate a surface of revolution in three-dimensional space. Features include choosing the axis of rotation, setting the angle of rotation, and showing the wire frame and quadrilateral faces of the surface of revolution.StatisticsEstimate Center:Estimate the mean of a distribution by dynamically finding the balance point of the histogram. Preloaded or user-entered data sets can be analyzed.Estimate Center and Spread:Estimate the mean of a distribution as in the Estimate Center app, and estimate the spread of a distribution by estimating a proportion (such as two-thirds) of the data within a distance of the mean. Preloaded or user-entered data sets can be analyzed.Modeling:Estimate a curve of “best-fit” on a scatterplot and compare to the regression equation. Features include a movable “best fit” curve and display of the estimate function equation with the regression equation. Available models are linear, exponential, power, logarithmic, quadratic, cubic, quartic, polynomial, and sinusoidal. Alternatively, users can enter an algebraic function model.Randomization Distribution:Create an approximate sampling distribution of possible differences in means, medians, or standard deviations of two treatments by re-randomizing and, then, identify extreme events. Features include adjusting histogram settings and displaying the count or relative frequency of resampling results in each bar of the histogram.Distribution of a Sample:Explore the shape, mean, and standard deviation of distributions of sample means, medians, or standard deviations for various sample sizes. Results are displayed in a histogram as counts or relative frequencies. Summary statistics are available.Binomial Distributions:Vary the number of trials and the probability of a success on each trial to see how the shape, center, and spread of binomial distributions are affected. Conduct experiments and compare theoretical models of distributions to simulation results. Features include moveable sliders forpandn, comparison of simulation results with theoretical binomial or normal distributions, and simultaneous display of multiple distributions.## Advanced Apps

:Create andanalyze a vertex-edge graph—a collection of vertices and edges. Add color, weight, and direction to a graph; run tests and algorithms to find spanning trees, circuits, critical paths or colorings; and investigate the adjacency matrix or other matrices for a vertex-edge graph.:Examine the run chart for a chosen data set and enter the desired mean and standard deviation. Then test for out-of-control behavior using one or more of eight tests commonly used in industry.Ranked Choice Voting:Determine voting outcomes based on various ranked choice voting methods. Voting methods include plurality, majority, runoff, pairwise-comparison, points-for-preference, and instant runoff.Weighted Voting:Investigate a voting situation with the Banzhaf power index; measure the weight of a voter and determine if the voter is critical or not.Codes and Cryptography:Encode and decrypt messages using ciphers and cryptography. Features include the Rot13, Caesar, affine, matrix (Hill) ciphers, and the RSA public-key cryptosystem.Contour Diagrams:Represent elevation or other data with contour lines. Simultaneously view 3-D and relief lines. Contour diagrams can be modeled from pre-set or user-generated rectangular array of data or spreadsheet. See also 3-D graphing in CAS.## Evaluation