College Readiness from the NYPSC - Math
http://cr.performanceassessment.org/taxonomy/term/1/0
enPrecalculus/Calculus
http://cr.performanceassessment.org/node/269
<p>In this course, students complete a unique 12-part year-long project ranging from algebra through calculus. This original project begins with students choosing three locations on the Earth and involves using linear equations, creating piece-wise functions to match data, using limits to test for continuity, finding and using first and second derivatives, using integrals to solve problems, and other topics such as average value, arc length, trapezoidal approximations, and even partial derivatives.</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
<div class="field-items">
<div class="field-item odd">
"A Short History of Nearly Everything" </div>
<div class="field-item even">
"Functions in the Real World" </div>
</div>
</div>
<div class="field field-type-text field-field-media">
<div class="field-label">Media Used: </div>
<div class="field-items">
<div class="field-item odd">
TI-83 Graphing Calculator </div>
<div class="field-item even">
Google Earth </div>
</div>
</div>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
<div class="field-items">
<div class="field-item odd">
<p>Create your own homework assignments: Throughout the year, students create their own homework problems to complete and then exchange those problems with other students in the class. Students keep their problems in a safe place so that the final product is like a student-created math textbook they can bring to college.</p>
</div>
<div class="field-item even">
<p>Create your own exams: Students consistently create exams to assess their knowledge about the particular subject we are studying. Students exchange exams and work together to find and correct mistakes. On exam day, students each have their own unique exam.</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-activity">
<div class="field-label">Significant Activities or Projects: </div>
<div class="field-items">
<div class="field-item odd">
<p>The Map Project is a year-long 12-part project ranging from algebra through calculus. This is the main performance-based assessment students complete.</p>
</div>
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<p>The Native Country Project, wherein students collect data from some aspect of their native countries (population, car accidents, disease, etc) and use the data to explore applications in math.</p>
</div>
<div class="field-item odd">
<p>The Products Project, in which students try to save companies money by repackaging their products to use less surface area (keeping the volume constant) or hold more volume (keeping the surface area constant)</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
The Map Project Part One </div>
<div class="field-item even">
The Native Country Project </div>
</div>
</div>
<p><a href="http://cr.performanceassessment.org/node/269" target="_blank">read more</a></p>MathFri, 25 Sep 2009 13:55:16 +0000mrsethmihs269 at http://cr.performanceassessment.orgWriting to Learn Math
http://cr.performanceassessment.org/node/257
<p>Students review fundamental concepts from Algebra, Geometry, and Statistics and demonstrate their understanding via repeated short writing exercises which strengthen students' abilities to describe math operations and processes using words and statements. Students then complete indepth investigations on three topics: 1) Is the Coney Island Coin Toss Game Fair?; 2) How do manufacturers decide to package grocery store items?; and 3) How does the student government of BCS determine the ticket price for a dance?</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
<div class="field-items">
<div class="field-item odd">
Essays using math from trade magazines </div>
<div class="field-item even">
Former students' Math papers </div>
</div>
</div>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
<div class="field-items">
<div class="field-item odd">
<p>Students write out every step involved in factoring a polynomial to extreme detail and compare with other students.</p>
</div>
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<p>Students compare written analyses of a similar problem to see how different styles of writing help a writer to convey his/her point.</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-activity">
<div class="field-label">Significant Activities or Projects: </div>
<div class="field-items">
<div class="field-item odd">
<p>What do we know about carnival games? They may seem so easy to win, but in reality, we don’t win every time. Students investigate the original design of the Coney Island Coin Toss Game and decide if its design gives players a fair chance to win.</p>
</div>
<div class="field-item even">
<p>Walk into any supermarket and look at the shapes lining the shelves. Manufacturers consider dozens of factors before determining which shape will best suit the consumer and boost the company's profits. Students explore package design and uncover some of the reasons for the shapes that manufacturers have chosen. Students use their knowledge of geometry and algebra to investigate different ways to decide whether or not it is better for manufacturers to sell items in “bulk” or to sell individually packaged items and determine if manufacturers are packaging their items as efficiently as possible.</p>
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<p>Suppose you are a student council member who is responsible for planning a BCS student dinner dance. Plans include hiring a DJ and buying and serving dinner. You want to keep the ticket price as low as possible to encourage student attendance. Identify and use systems of equations to analyze costs and make decisions. Then write a report detailing your choice of band, the cost of a catering service, and your ticket price recommendation. Present this report to Student Government.</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
Are carnival games fair? </div>
<div class="field-item even">
How can I plan a student event to maximize profit or minimize cost? </div>
</div>
</div>
<p><a href="http://cr.performanceassessment.org/node/257" target="_blank">read more</a></p>MathSun, 20 Sep 2009 02:27:03 +0000joshuasteckel257 at http://cr.performanceassessment.orgData Analysis
http://cr.performanceassessment.org/node/236
<p>Knowledge of statistics is a valuable asset that will help students make sense of the vast amount of information we are presented with everyday. The goal of this course is to give the student a hands-on ability to apply the fundamentals of statistics to make informed decisions. This will be accomplished by examining the skills required to read data, interpret data and judge others' claims about data. In addition to manual calculations, we will look at the usefulness of technological tools such as the graphing calculator and Microsoft6 Excel in data analysis.</p>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
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<div class="field-item odd">
<p>Analyze the difference between various kinds of studies; apply knowledge of statistics to critique data presented and conclusions reached.</p>
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<p>Determine factors which may affect the outcome of a survey; consider outcomes of various hypothetical situations on outcomes.</p>
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</div>
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<div class="field field-type-text field-field-activity">
<div class="field-label">Significant Activities or Projects: </div>
<div class="field-items">
<div class="field-item odd">
<p>Calculate the measures of a central tendency with group frequency distributions</p>
</div>
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<p>Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
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<div class="field-item odd">
Choose a subject of interest to you that is appropriate for a statistical analysis. Determine the function for the regression model, using appropriate technology, and use the regression function to interpolate and extrapolate from the data. </div>
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MathMon, 06 Jul 2009 15:07:07 +0000szbaida236 at http://cr.performanceassessment.org11th Grade Algebra 2
http://cr.performanceassessment.org/node/232
<p>Algebra 2 is a continuing exploration of algebra for eleventh graders who are preparing for graduation-level Performance Based Assessment Tasks. This course is the second and third part of three-semester series. By the end of this year, all 11th graders should have written a graduation level report and presented her or his project for consideration of graduation PBAT.</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
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<div class="field-item odd">
All About Alice unit in IMP </div>
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Meadows or Malls unit in IMP </div>
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Small World, Isn't It? unit in IMP </div>
<div class="field-item even">
High Dive unit in IMP </div>
</div>
</div>
<div class="field field-type-text field-field-media">
<div class="field-label">Media Used: </div>
<div class="field-items">
<div class="field-item odd">
http://www.cssjbronx.org </div>
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https://sites.google.com/site/hsmathprogram </div>
<div class="field-item odd">
Alice in Wonderland film </div>
</div>
</div>
<div class="field field-type-text field-field-activity">
<div class="field-label">Significant Activities or Projects: </div>
<div class="field-items">
<div class="field-item odd">
<p>All About Alice project: exploring in-depth application of logarithms and scientific notation</p>
</div>
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<p>Parks or Malls project: solving a system of multi-variable (at least 6) linear inequalities using matrices</p>
</div>
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<p>Small World, Isn't It? project: exploring in-depth application of exponential functions and data analysis</p>
</div>
<div class="field-item even">
<p>High Dive project: in-depth application of trigonometric functions, polar coordinates, and parametric functions</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
Multi-constraint linear programming </div>
<div class="field-item even">
Population data analysis and prediction using exponential functions </div>
<div class="field-item odd">
Application of parametric and trigonometric functions in polar coordinates </div>
</div>
</div>
<p><a href="http://cr.performanceassessment.org/node/232" target="_blank">read more</a></p>MathSun, 05 Jul 2009 21:52:45 +0000Lonice232 at http://cr.performanceassessment.orgAdvanced Math
http://cr.performanceassessment.org/node/215
<p>Students will explore content focusing on: Reasoning, Numbers and Numeration, Operations, Modeling/Multiple Representation, Measurement, Uncertainty and Patterns/Functions. </p>
<p>Some of the major topics that are covered include: Geometric Proofs, Circles, Complex Numbers, Quadratics, Functions, Conic Sections, Transformations, Logarithms, Regressions, Trigonometry, Binomial Theory, Probability and Statistics.</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
<div class="field-items">
<div class="field-item odd">
Pearson:// Elementary Statistics </div>
</div>
</div>
<div class="field field-type-text field-field-media">
<div class="field-label">Media Used: </div>
<div class="field-items">
<div class="field-item odd">
www.aw-bc.com/triola </div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
"Texas Tech -vs- Oklahoma" A comparative statistical analysis that exhibits how data can be manipulated to convey a variety of messages. </div>
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"Plinko" Students design their own 'Plinko Board' then use Pascal's Theory to compare their empirical data against expected outcome data. </div>
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"Trigonometry in Aviation" Students test various scenarios in relation to Visual Flight Rules. </div>
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"Calculating the Magnitude of an Earthquake" Students measure Magnitude and other variables using scale developed by Charles Richter. </div>
</div>
</div>
<p><a href="http://cr.performanceassessment.org/node/215" target="_blank">read more</a></p>MathTue, 23 Jun 2009 18:23:43 +0000Dwhite215 at http://cr.performanceassessment.orgCollege Algebra, Trig, & Statistics (with LaGuardia Community College)
http://cr.performanceassessment.org/node/198
<p>Math 115 is College Algebra- Trigonometry. The course will start with a review of basic algebra (factoring, solving linear equations and equalities) then proceed to study polynomials, exponential, logarithmic and trigonometric functions. Students will use this mathematical modeling to improve critical thinking skills in inquiry based activies.</p>
<p>Math 120- Statistics</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
<div class="field-items">
<div class="field-item odd">
Energy Information Administration- http://www.eia.doe.gov </div>
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America's Climate Choices- http://dels.nas/edu/basc/climate-change/ </div>
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Redefining Progress: www.myfootprint.org </div>
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Medline Plus- US National Library of Medicine and National Institutes of Health- http://medlineplus.gov </div>
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Healthy People- http://www.healthypeople.gov </div>
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Center for Disease Control and Prevention- http://www.cdc.gov/datastatistics </div>
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Investopedia- http://investopedia.com </div>
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World Health Organization- Report- http://www.who.int/en </div>
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</div>
<div class="field field-type-text field-field-media">
<div class="field-label">Media Used: </div>
<div class="field-items">
<div class="field-item odd">
E-Portfolio </div>
<div class="field-item even">
MAPLE </div>
</div>
</div>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
<div class="field-items">
<div class="field-item odd">
<p>The first part involves reading information related to CO2 emissions from transportation, followed by data on CO2 emissions by cars and transportation choices by country. Using the data, students will<br />
analyze and make recommendations for environmental performance.- </p>
<p>Co2 Emmisions by Cars - By Sreedevi Ande- Department of Mathematics, Engineering and Computer Science at Laguardia Collmunity College</p>
</div>
<div class="field-item even">
<p>Modeling Unemployment Rate Data- By Denise Carter- Department of Mathematics, Engineering and Computer Science</p>
<p>This project is meant for e-portfolio.<br />
Students use MAPLE to analyze the unemployment rates data for the months January through September</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
Project Quantum Leap--tasks change each year in response to the research conducted by students </div>
</div>
</div>
<p><a href="http://cr.performanceassessment.org/node/198" target="_blank">read more</a></p>MathFri, 19 Jun 2009 03:02:10 +0000kmarsh198 at http://cr.performanceassessment.orgFunctions
http://cr.performanceassessment.org/node/183
<p>This course is based on the following Essential Questions: How can we use functions to make predictions about the world? Should judgments be based on quantified relationships?</p>
<p>Students will learn about and analyze three types of functions: Linear, Quadratic, and Exponential</p>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
<div class="field-items">
<div class="field-item odd">
<p>In this mastery project, you will investigate which kind of function best models your data.</p>
<p>Formulate:<br />
1.Give an in depth description your situation, including any background information and images that make your investigation as clear as possible.<br />
2.Explain which function (linear, quadratic, or exponential) best models your situation.<br />
3.Explain why it makes sense for your data set to be modeled by that function.</p>
<p>Represent:<br />
4.Show and explain in as much detail as possible:<br />
a.Your variables: what do “x” and “y” stand for?<br />
b.Tables: data table and a table that models your data<br />
c.Graph: clearly indicate your scale and units<br />
d.Equation: identify each of the coefficients<br />
e.Your domain and range<br />
5.In your opinion, which representation (table, graph, or equation) best reveals the nature of your function or gives you the most information about your function?</p>
<p>Analyze:<br />
6.Show and explain interpolated and extrapolated predictions for your function.<br />
7.Choose and explain a domain and a range for your function.<br />
8.Explain the meanings of your coefficients: Pick any coefficient. If it were to change, how would your function be affected? Do the same for all coefficients.<br />
9.How do your table, equation and graph help people understand the problem or situation your data describes?<br />
10.Analyze the graph – what do all the intercepts, extreme points, or important points mean in the context of the situation?<br />
11.Each student gets one extension question from their teacher.</p>
<p>Interpret:<br />
12.During a class lesson planned by your teacher, you will make sense about at least one other person’s problem.</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-activity">
<div class="field-label">Significant Activities or Projects: </div>
<div class="field-items">
<div class="field-item odd">
<p>Identify patterns in a variety of forms (stories, geometric patterns, linear patterns).<br />
Represent patterns (xy-relationshps) using words, tables, graphs and equations.<br />
Describe growth that either increases or decreases by a constant amount.<br />
Write an equation of a linear function in slope-intercept form.<br />
Identify the slope and the y-intercept from the equation of linear function.<br />
Use a variety of situations to collect and organize data (Barbie bungee, counting beats, balloon drop).<br />
Use linear regression to model real-world data.<br />
Use a linear regression to make predictions about linearly modeled situations.<br />
Given a situation that can be modeled using a step function (postage rates, etc…), create a graph to model the situation.<br />
Recognize non-integer values within an interval of values.<br />
Use inequalities to describe intervals.<br />
Come up with situations that can be modeled using step functions.</p>
</div>
<div class="field-item even">
<p>Identify more than one way of describing the “change” in the Step Change pattern.<br />
Identify one way of describing the change as linear and another way as “non-linear.”<br />
Describe the nature of the change of the non-linear.<br />
In their own words, explain the idea that the quadratic growth means that the difference is linear.<br />
Develop a strategy for the “chip-swap” game.<br />
Using the standard form of the quadratic equation, identify how far a runner is after various amounts of time running.<br />
Plug in x-values to find y-values in quadratic functions.<br />
Find out how far the runner is after further amounts of time by following the pattern (similar to Step Change and Chip Swap).<br />
Identify the standard form of a quadratic equation.<br />
Make up quadratic equations in standard form.<br />
Identify the a, b and c-coeffieients of quadratic equations in standard form.<br />
Develop rules for the effect of the a- and b-coefficients on the graph of the equation.<br />
Apply –b/2a as the x-value of the turning point on the graph.<br />
Given an equation for a quadratic equation in standard form, shift the parabola up/down, right/left, make it skinnier/wider, and flip it.<br />
Determine an object’s height off the ground after various seconds using an equation (with factors for speed, initial height off the ground, and gravitational pull back towards the earth).<br />
Given an object’s initial speed, initial height off the ground, and gravitational pull back towards the earth, write an equation for the object’s position as a function of time.<br />
Determine the amount of time it will take an object to rise and then land in a well below the surface of the earth.<br />
Given data for the relationship between time and an object’s position off the ground, write a quadratic equation.<br />
Create a reasonable pricing system for pizzas based on square units of area in the pizza and another based on diameter.<br />
Discuss the differences in the relationships between “size” and “price.”<br />
Given a specific amount of fencing, sketch various rectangles with perimeter equal to the amount of fence. (for various amounts of fencing).<br />
Determine the dimensions that provide the largest area for each.<br />
Create a generalization for the dimensions with largest area with perimeter P.<br />
Create a rulebook for the rules of exponents.<br />
Identify the growth pattern of exponential functions.</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
Coffee Cooling: How Long is Too Long? </div>
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Additional PBAT questions grow out of the activities listed above </div>
</div>
</div>
MathThu, 11 Jun 2009 14:28:55 +0000emilys183 at http://cr.performanceassessment.org12th Grade Math Analysis
http://cr.performanceassessment.org/node/165
<p>12th Grade Math Analysis Course Description</p>
<p>In this course, students study Pre-Calculus using the College Preparatory Mathematics program www.cpm.org This is an advanced, challenging course where we will explore mathematical ideas such as Problem Solving, Analysis of Models, Trigonometry, Advanced Functions, and Algebraic Fluency and Accuracy. Students will learn a variety of approaches to problem solve and use math in real life contexts.</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
<div class="field-items">
<div class="field-item odd">
CPM College Peparatory Mathematics </div>
</div>
</div>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
<div class="field-items">
<div class="field-item odd">
<p>Polynomial Functions: How does this connect to linear and quadratic functions</p>
</div>
<div class="field-item even">
<p>Trigonometric Functions: How can we model this relationship (ie height over time, etc.) using a trigonometirc funciton?<br />
How does the unit circle connect to the graph ofthe sine/cosine curve/<br />
How are the trigonometric functions related to each other</p>
</div>
<div class="field-item odd">
<p>Law of Sines/Cosines: How do you know which formula you should use?<br />
How does this connect to right triangle trigonometry and trigonometric functions?</p>
</div>
<div class="field-item even">
<p>Probability: How can you use probability to predict outcomes?<br />
How can you use probability to make policy decisions and analyze the world around you? Is that a fair situation/game? Why or why not?</p>
</div>
<div class="field-item odd">
<p>Combinatorics: How many choices are there?</p>
</div>
<div class="field-item even">
<p>Statistics: How can you use statistics to advocate for social justice? What do these statistics tell you about the situation, is there a bias? How does statustics help you seek significvance in the study of mathematics? How can you use statistics to provide evidence and reinforce your argument?</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-activity">
<div class="field-label">Significant Activities or Projects: </div>
<div class="field-items">
<div class="field-item odd">
<p>Using trigonometric functions analyze the height, distance and speed of amusement rides at Six Flags.</p>
</div>
<div class="field-item even">
<p>By analyzing Vanguard's data distribution determine if the data distribution is "normal"</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
Vanguard Six Flags: Trigonometric Functions </div>
<div class="field-item even">
Skywalker: Law of Sines and Cosines </div>
<div class="field-item odd">
Your Game: Polynomial Functions, Probability, Combinations and Permutations </div>
<div class="field-item even">
Is Vanguard Normal--Statistics Analysis </div>
</div>
</div>
MathTue, 09 Jun 2009 15:00:41 +0000apurdy2165 at http://cr.performanceassessment.orgStatistics
http://cr.performanceassessment.org/node/152
<p>This one semester course will provide experience in collecting data, analyzing data, and writing statistical reports. Students will study statistical concepts through activities and projects that involve the collecting and analyzing of data. Techniques for summarizing, analyzing and interpreting large sets of data will also be discussed. Emphasis will be on practical problem-solving with real data sets using appropriate computer software packages. This course culminates in a math portfolio presentation. </p>
<p>Prerequisite: Both Algebra & Geometry portfolios with at least a “Competent” rating</p>
<div class="field field-type-text field-field-reading">
<div class="field-label">Readings: </div>
<div class="field-items">
<div class="field-item odd">
College Preparatory Mathematics (CPM) </div>
</div>
</div>
<div class="field field-type-text field-field-assignment">
<div class="field-label">Significant Assignments: </div>
<div class="field-items">
<div class="field-item odd">
<p>Portfolio/Panel Presentation: Social Justice Statistics Research and Analysis using single variable regression</p>
</div>
</div>
</div>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
“Prison Populations and Race” </div>
<div class="field-item even">
“Relationship Abuse and Gender” </div>
</div>
</div>
<p><a href="http://cr.performanceassessment.org/node/152" target="_blank">read more</a></p>MathMon, 08 Jun 2009 14:24:06 +0000ofeckt152 at http://cr.performanceassessment.orgFoundations of Pre-calculus
http://cr.performanceassessment.org/node/147
<p>A year-long course designed to strengthen and expand the concepts and skills learned in algebra and provide further development of the concept of a function. Students will expand their knowledge and understanding of linear, quadratic, and exponential functions and be introduced to logarithmic and trigonometric functions. Students will analyze and identify relationships among functions using multiple representations (verbal, numeric, graphic, and algebraic). Students will apply mathematical skills to make meaningful connections to the physical world and write about their conclusions.</p>
<div class="field field-type-text field-field-pbat">
<div class="field-label">Sample PBATs: </div>
<div class="field-items">
<div class="field-item odd">
How can Matrices be used to solve multivariable mathematical situations? </div>
<div class="field-item even">
How can linear and quadratic functions be used to maximize a company's profits? </div>
<div class="field-item odd">
How can exponential functions be used to predict the future value of investments? </div>
</div>
</div>
MathFri, 05 Jun 2009 18:54:41 +0000sof_felixshen147 at http://cr.performanceassessment.org