Three choices are given at the time of homework retrieval:

So for example, if your source homework has 20 problems and has been posted with multiplicity 3, then any version of it has 10 problems, one from the first 3, one from the second 3, and so forth.  Further, the order of occurence of the problems is scrambled, unless it is turned off by the author.   This allows an author to create a homework with a  large number number of different versions.  based on as few as 10 problems.   Just parameterize 10 problems and create 3 instances of each one in a source homework, and then post it with mulitplicity 3.  There will be     different homeworks.  Of course, many of them will have the same problems; just in a different order.   And too, there are only  possible personal versions.    Actually, if you read the author documentation on mathclass, there is a way to turn off randomization: Put the header tag in with a third argument  of -1.  So H_[3;0;-1]  gives a homework of multiplicity 3 with each retrieved homework in the same order.  If there are  10 problems, there will be only  different versions possible.

Problem:    How many different versions does a 20 question homework of multiplicity 2 have?  How many different personal versions are there?

>

We include these problems as an example of one way  to versioned a versioned homework.    Each problem sits in its own section, which is titled appropriately. Included in the section is at least the problem generator and a number of calls to it.  In addition, any computations made to solve the parameterized problem should be included along with any text comments the author feels appropriate.  

Problem .  A circle is inscribed in a square of side s.  Find the area inside the square but outside the circle.  

Answer:   s^2 - Pi*(s/2)^2

>	pic := proc(s,c1,c2,c3) plots[display](ARRW(tail=[0,-.1],head=[1,-.1],doublearrowtxt=s,color=c1), ARRW(tail=[-.1,0],head=[-.1,1],doublearrowtxt=s,color=c1), plottools[disk]([.5,.5],.5,color=c2), plottools[polygon]([[0,0],[1,0],[1,1],[0,1]],color=c3), scaling=constrained,axes=none) end:

Then we construct the problem generator.  

>

prob1 := proc(s,c1,c2,c3) local ans; ans:=[s^2-(s/2)^2*Pi,s^2*Pi-s^2,s^2-(s/2)^2*Pi+1,(s/2)^2*Pi-(s/2)^2,(s/2)^2*Pi-s^2]; tagit(["A circle is inscribed in a square ",s," inches on a side as shown. What is the area, in square inches, of the region inside the square and outside the circle?"],pic(s,c1,c2,c3),_ALlabels(ans)) end:

>

>	prob1(1,red,pink,grey) ;   #1.1

>	prob1(2,blue,yellow,grey); #1.2

>

>	prob2 := proc(x,a,b,c,d) tagit(Line("Which of the following expressions is a factor of " ,expand(c*(d*x-a)*(x-b)),"?"), _ABlabels([[d*x-a-1],[x-b],d*x + a,x+b,c*x])) end:

>	prob2(x,2,3,2,2);     #2.1;

>	prob2(y,2,3,3,2);     #2.2;

>

Here the list of alternatives was parameterized outside the problem generator.

>	alternatives := proc(x,a,b,c,d)  [a*(x^2-b*x)-c*(x^2-d*x),-a*(x^2-b*x)+c*(x^2-d*x), a*(x^2-b*x)-c*(x^2+d*x),a*(x^2-b*x)-c*(x^2-d/c*x),a*(x^2-b/a*x)-c*(x^2-d*x)]  end:

>	alternatives(x,3,2,5,4);

>

a is converted to a symbol so that it won't be multiplied out.

>	prob3 := proc(x,a,b,c,d) tagit("In simplified form, ",convert(a,symbol)*(x^2-b*x)-convert(c,symbol)*x*(x-d)," = ?",inline=yes,_ALlabels(alternatives(x,a,b,c,d))) end:

>

>	prob3(x,2,3,5,1); #3.1

>	prob3(y,3,2,5,1); #3.2

>

Here is another problem that requires the input parameters be symbolized in order to keep the computation from being made by Maple's parser.

>	prob4 := proc(x,a,b,c) tagit("If the equation ", 1/(x-convert(a,symbol))=convert(b,symbol)/convert(c,symbol),"  is solved for ",x,", then ",x," = ?" ,_ALlabels([(c+b*a)/b,c/(b+a*c),-(b/c+a),c/b-a,b/c-a])) end:

>

>	prob4(x,3,3,5); #4.1

>	prob4(y,5,3,4); #4.2

>

>	mctools(roundto);

MCtools, version June 1 2004.

roundto(x,places=3)  

>

>

prob5 := proc(z) tagit(["A child has x nickles, y dimes and no other coins in her piggy bank. If the total amount of money in the bank is ",z," dollars, which of the following equations is satisfied by x and y?"], _ALlabels([`0.05`*x+`0.10`*y=roundto(z,places=2),5*x+10*y=roundto(z,places=2),x+y=roundto(z,places=2),`0.05`*x+`0.10`*y=ceil(100*z) ,x+y=ceil(100*z)])) end:

>

>	prob5(5.25);#5.1

>	prob5(4.25);#5.2

>

>

This has been used to produce multiple versions of an exam which can be given in latex hardcopy and also given in html on WHS.

>

PRINT_:="yes":PNUM_:=1:SPACES_:=5: mcprint("Algebra I quiz   June 18, 2003   Name________ \n  Instructions:  Show all your work, as unsupported answers will recieve no credit."); print(matrix([[`Problem`,`Possible Points`,`Credit`], [1,10,`________`],[2,10,`________`], [3,10,`________`],[`Total`,30,`________`]])); #1 tagit(  "Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours.  How many hours does it take Bill and Jim to mow the yard together?",_AC(1/(1/3+1/5),txtboxsize=4,"Assume they do not interfere with each other.")): #2 tagit("3 + 4 =",_AC(7),"   5 + 12 =",_AC(17),"   4 + 1 =",_AC(5)): #3 tagit("Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours.  How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer.",_AS([1.875,2.125,4,"None of the others"])): PRINT_:= "no":

Algebra I quiz   June 18, 2003   Name________

 Instructions:  Show all your work, as unsupported answers will recieve no credit.

1.  Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours.  How many hours does it take Bill and Jim to mow the yard together?

__________

Assume they do not interfere with each other.

2.  3 + 4 =

__________

   5 + 12 =

__________

   4 + 1 =

__________

3.  Bill can mow a yard in 3 hours. Jim can mow the same yard in 5 hours.  How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer.

>

quiz1 := proc(dat,a,b,c) global PRINT_,PNUM_,SPACES_; PRINT_:="yes":PNUM_:=1:SPACES_:=5: mcprint("Algebra I quiz   ",dat,", 2003   Name________ \n  Instructions:  Show all your work, as unsupported answers will recieve no credit."); print(matrix([[`Problem`,`Possible Points`,`Credit`], [1,10,`________`],[2,10,`________`], [3,10,`________`],[`Total`,30,`________`]])); #1 tagit(  ["Bill can mow a yard in ",a," hours. Jim can mow the same yard in 5 hours.  How many hours does it take Bill and Jim to mow the yard together?"],_AC(1/(1/a+1/5),txtboxsize=4,"Assume they do not interfere with each other.")): #2 tagit([c," + 4 ="],_AC(c+4),"   5 + 12 =",_AC(17),"   4 + 1 =",_AC(5)): #3 tagit(["Bill can mow a yard in 3 hours. Jim can mow the same yard in ",b," hours.  How many hours does it take Bill and Jim to mow the yard together, assuming they do not interfere with each other? Select the most nearly correct answer."],_AS([evalf(1/(1/3+1/b),4),evalf((1/3+1/b),4),evalf(1/(1/3+1/b),4)+1,"None of the others"],randomize="no")): PRINT_:= "no": NULL: end:

>	quiz1("Makeup  June 21",4,7,6);

>

There are 5 Standards in the Tennessee Setup.

1  Number Sense and Number Theory:   The student will recognize, represent, model, and apply real numbers and operations verbally, physically, symbolically, and graphically.

2  Estimation, Measurement, and Computation The student will apply appropriate tools and units of measurement; develop effective estimation and computation strategies for producing reasonable results; and calculate using appropriate tools such as mental mathematics, technology, manipulatives, and pencil-and-paper.

3 Patterns, Functions, and Algebraic Thinking: The student will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real world problem solving.

4 Statistics and Probability:  The student will collect, organize, represent, and interpret data; make inferences and predictions; present and evaluate inferences and predictions; present and evaluate arguments based on data analysis; and model situations to determine theoretical and experimental probabilities.

5 Spatial Sense and Geometric Concepts: The student will investigate, model, and apply geometric properties and relationships.

The standards are organized by grade (3 thru 8) , then by standard (1 thru 5), then by performance indicator (state or teacher). Each indicator has a number to distinguish it from the others in that category. So each indicator  has a label of the form   x.y.zpi.w   where x is the grade level, y is the standard, zpi is  spi  (state performance indicator) or tpi (teacher performance indicator), and w is the specific indicator number in that branch.  Thus    5.3.tpi.2  is the label for the 5th grade, 3rd standard,  2nd teacher performance indicator..  After you excute the input cell below, you can use   standards=[G53tpi2]  in the tagit line of the  problem generator if the problems it generates test that indicator.  This makes it relatively painless to make your homework standards based.

There are three levels  of expectation in the Tennessee system.  The indicators of any given type are arranged in  or of increasing expectation.  Thus  for the 3rd grade, standard 1, state performance indicators,  3.1.spi.1  is level 1 and 3.1.spi.16 is level 3.  The breakpoint from one level to the next are not part of the labelling scheme, perhaps intentionally.

To see the breakpoints and get more information about the standards, go to the state site.

>

G31spi1 :="3.1.spi.1. count by 10’s, 100’s, and 1000’s": G31spi2 :="3.1.spi.2. identify whole numbers as odd or even": G31spi3 :="3.1.spi.3. add and subtract efficiently and accurately with single-digit whole numbers": G31spi4 :="3.1.spi.4. represent whole numbers to 9999 with models": G31spi5 :="3.1.spi.5. identify the place value of a given digit up to thousands": G31spi6:="3.1.spi.5. recognize the value of combinations of coins and bills up to 5 dollars.": G31spi7:="3.1.spi.7. compare and order whole numbers to 9999 using the appropriate symbol for less than, greater than and equal.":

Standards omitted ..

>

G35tpi2 :="3.5.tpi.2. create tables using tally marks": G35tpi3 :="3.5.tpi.3. pose questions and gather data to answer questions": G35tpi4 :="3.5.tpi.4. develop an appropriate method to collect data": G35tpi5 :="3.5.tpi.5. select an appropriate method to display data": G35tpi6 :="3.5.tpi.6. explain whether an event is certain, possible, or impossible": G35tpi7 :="3.5.tpi.7. explain whether an event is likely or unlikely": G35tpi8 :="3.5.tpi.8. make conjectures based on data gathered and displayed": G35tpi9 :="3.5.tpi.9. predict outcomes of events based on data gathered and displayed":

>

>

G41spi1 :="4.1.spi.1. represent whole numbers to 9999": G41spi2 :="4.1.spi.2. compare and order whole numbers to 9999 using the appropriate symbol for greater than, less than, or equal.": G41spi3 :="4.1.spi.3. solve one-step real-world problems involving addition or subtraction of whole numbers.": G41spi4 :="4.1.spi.4. read and write numbers from hundred-thousands to hundredths":

Standards omitted ...

>

G45spi5 :="4.5.spi.5. determine the median of a data set": G45tpi1 :="4.5.tpi.1. collect data using observations, surveys, and experiments": G45tpi2 :="4.5.tpi.2. construct bar graphs and line graphs from data in a table": G45tpi3 :="4.5.tpi.3. evaluate how well various representations show the collected data.": G45tpi4 :="4.5.tpi.4. understand how data collection methods affect the nature of the data set": G45tpi5 :="4.5.tpi.5. design investigations to address a question": G45tpi6 :="4.5.tpi.6. explain differences in measures of center (mean, median, mode).":

>

>	G51spi1 :="5.1.spi.1. read and write numbers from millions to thousandths": G51spi2 :="5.1.spi.2. connect symbolic representations of proper and improper fractions to models of proper and improper fractions": G51spi3 :="5.1.spi.3. represent whole numbers and two-place decimals in expanded form.":

Standards omitted ..

>

G55tpi6 :="5.5.tpi.6. create a sample space to predict the probability of an event": G55tpi7 :="5.5.tpi.7. explain the importance of sample size in investigations": G55tpi8 :="5.5.tpi.8. examine various representations of data and evaluate how accurately the data is depicted by the graph": G55tpi9 :="5.5.tpi.9. understand how data collection methods affect the nature of the data set": G55tpi10 :="5.5.tpi.10. explain which measure of central tendency best represents a given data set":

>

>

G61spi1 :="6.1.spi.1. identify the place value of a given digit": G61spi2 :="6.1.spi.2. solve one-step real-world problems involving whole numbers and decimals": G61spi3 :="6.1.spi.3. represent numbers using a variety of models and equivalent forms (i.e., whole numbers, mixed numbers, fractions, decimals, and percents)": G61spi4 :="6.1.spi.4. connect whole numbers, mixed numbers, fractions, and decimals to locations on the number line":

Standards omitted ....

>

G65tpi4 :="6.5.tpi.4. determine an appropriate sample to test a hypothesis": G66tpi5 :="6.6.tpi.5. conduct simple experiments to compare theoretical and experimental probabilities": G65tpi6 :="6.5.tpi.6. explain the importance of sample size in surveys and research": G65tpi7 :="6.5.tpi.7. make conjectures from data to formulate new questions for further investigation":

>

>

G71spi1 :="7.1.spi.1. identify prime and composite numbers up to 50": G71spi2 :="7.1.spi.2. compute efficiently and accurately with whole numbers, fractions, and decimals": G71spi3 :="7.1.spi.3. represent numbers using a variety of equivalent forms (i.e., mixed numbers, fractions, decimals, percents, and integers)": G71spi4 :="7.1.spi.4. compare rational numbers using the appropriate symbol for greater than, less than, and equal":

Standards omitted ...

>

G75tpi5 :="7.5.tpi.5. identify appropriate data sources to address questions or hypotheses": G75tpi6 :="7.5.tpi.6. construct tree diagrams to determine outcomes of a simple compound event": G75tpi7 :="7.5.tpi.7. make conjectures to formulate new questions for future studies": G75tpi8 :="7.5.tpi.8. describe why or why not predictions can be made for a population based on survey results for a given sample": G75tpi9 :="7.5.tpi.9. communicate the difference in theoretical and experimental probabilities":

>

>

G81spi1 :="8.1.spi.1. identify the opposite and the reciprocal of a rational number": G81spi2 :="8.1.spi.2. compare rational numbers using the appropriate symbol for greater than, less than and equal": G81spi3 :="8.1.spi.3. use ratios and proportions to represent real-world situations (i.e., scale drawings, probability)":

Standards omitted ...

>

G85tpi5 :="8.5.tpi.5. develop meaning for lines of best fit": G85tpi6 :="8.5.tpi.6. determine an appropriate sample to test a hypothesis": G85tpi7 :="8.5.tpi.7. make conjectures to formulate new questions for future studies": G85tpi8 :="8.5.tpi.8. use a variety of methods to compute probabilities for compound events (i.e., multiplication, organized lists, tree diagrams, area models)": G85tpi9 :="8.5.tpi.9. develop meaning of mutually exclusive events": G85tpi10 :="8.5.tpi.10. find the probability of dependent and independent events":

>

1   Number/Computation

2   Geometry/Measurement

3   Probability/Statistics

4   Algebraic Ideas.

which are divided into 3 types  

1  Concepts

2  Skills

3  Relations

Each strand has a number of individual standards which are grouped by school level into Elementary, Middle, and High School.   So the individual standards have labels of the form MA-X-x.y.z  where X = E, M or H, x = strand number, y = type number, and z is the specific standard in that branch.

So the label  MA-M-1.2.3  denotes the 3rd skills standard in the Geometry/Measurement Strand of Middle School.

>

MAE111:="MA-E-1.1.1:Whole numbers, fractions, mixed numbers, and decimals through thousandths": MAE112:="MA-E-1.1.2:The operations of addition, subtraction, multiplication, and division": MAE113:="MA-E-1.1.3:Odd and even numbers, composite and prime numbers, multiples, and factors": MAE114:="MA-E-1.1.4:Place value, expanded form, number magnitude":

Standards omitted ...

>	MAE424:="MA-E-4.2.4:Locate whole numbers, fractions, and decimals on a number line": MAE425:="MA-E-4.2.5:Graph ordered pairs on a positive coordinate grid": MAE431:="MA-E-4.3.1:How patterns are alike and different": MAE432:="MA-E-4.3.2:How rules involving number patterns can be explained":

>

>

MAM111:="MA-M-1.1.1:Rational numbers (integers, fractions, decimals, percents)": MAM112:="MA-M-1.1.2:Irrational numbers (square roots and   only)": MAM113:="MA-M-1.1.3:Meaning of proportion (equivalent ratios)": MAM114:="MA-M-1.1.4:Place value of whole numbers and decimals": MAM115:="MA-M-1.1.5:Positive whole number exponents":

Standards omitted ...

>

MAM425:="MA-M-4.2.5:Represent and use functions through tables, graphs, verbal rules, and equations": MAM426:="MA-M-4.2.6:Write and solve equations that represent everyday situations": MAM1431="MA-M-4.3.1:How everyday situations, tables, graphs, patterns, verbal rules, and equations relate to each other": MAM1432="MA-M-4.3.2:How the change in one variable affects the change in another variable":

>

>

MAH111:="MA-H-1.1.1:Students will describe properties of, define, give examples of, and apply real numbers, and understand that irrational numbers cannot be represented by terminating or repeating decimals.": MAH112:="MA-H-1.1.2:Students will recognize, define, give examples of, and apply finite arithmetic and geometric sequences and series.": MAH113:="MA-H-1.1.3:Students will understand how matrices are used to represent  data.":

Standards omitted ...

>

MAH433:="MA-H-4.3.3:Students will demonstrate how slope shows rate of change in linear functions arising in problems": MAH434:="MA-H-4.3.4:Students will show how changes in parameters affect graphs of functions [e.g., compare the graphs y = x2,  y = 2x2, y = (x - 4)2 , and y = x2 + 3]": MAH435:="MA-H-4.3.5:Students will show how equations and graphs are models of the relationship between two quantities (e.g., the relationship between degrees Celsius and degrees Fahrenheit)":

>

The source for these standards:

>

I1:="Compute fluently and accurately with rational numbers without a calculator:": I1d1:="Add, subtract, multiply and divide integers, fractions and decimals.":   I1d2:="Calculate and apply ratios, proportions, rates and percentages to solve problems.":   I1d3:="Use the correct order of operations to evaluate arithmetic expressions, including those containing parentheses.":

Standards omitted...

>	I4:="Understand the capabilities and the limitations of calculators and computers in solving problems:": I4d1:="Use calculators appropriately and make estimations without a calculator regularly to detect potential errors.": I4d2:="Use graphing calculators and computer spreadsheets.":

>

J1:="Perform basic operations on algebraic expressions fluently and accurately:": J1d1:="Understand the properties of integer exponents and roots and apply these properties to simplify algebraic expressions.": J1d2:="*Understand the properties of rational exponents and apply these properties to simplify algebraic expressions.": J1d3:="Add, subtract and multiply polynomials: divide a polynomial by a low-degree polynomial.":

Standards omitted ...

>

J5d3:="Recognize and solve problems that can be modeled using a quadratic equation, such as the motion of an object under the force of gravity.":   J5d4:="Recognize and solve problems that can be modeled using an exponential function, such as compound interest problems.": J5d5:="*Recognize and solve problems that can be modeled using an exponential function but whose solution requires facility with logarithms, such as exponential growth and decay problems.":   J5d6:="Recognize and solve problems that can be modeled using a finite geometric series, such as home mortgage problems and other compound interest problems.": J6:= "*Understand the binomial theorem and its connections to combinatorics, Pascal's triangle and probability.":

>

>

K1:="Understand the different roles played by axioms, definitions and theorems in the logical structure of mathematics, especially in geometry:": K1d1:=" Identify, explain the necessity of and give examples of definitions, axioms and theorems.": K1d2:="State and prove key basic theorems in geometry such as the Pythagorean theorem, the sum of the angles of a triangle is 180 degrees, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.":

Standards omitted ...

>

K12d2:="*Know and use the basic trig identities,  and  formulas for sine and cosine, such as addition and double angle formulas.": K12d3:="*Graph sine, cosine and tangent as well as their reciprocals, secant, cosecant and cotangent; identify key characteristics.": K12d4:="*Know and use the law of cosines and the law of sines to find missing sides and angles of a triangle.":

>

L1:="Explain and apply quantitative information:": L1d1:="Organize and display data using appropriate methods (including spreadsheets) to detect patterns and departures from patterns.":   L1d2:="Read and interpret tables, charts and graphs.":   L1d3:="Compute and explain summary statistics for distributions of data including measures of center (mean, median) and spread (range, percentiles, variance, standard deviation).":

Standards omitted ...

>

L4d2:="Explain how the relative frequency of a specified outcome of an event can be used to estimate the probability of the outcome.": L4d3:="Explain how the law of large numbers can be applied in simple examples.": L4d4:="Apply probability concepts such as conditional probability and independent events to calculate simple probabilities.": L4d5:="Apply probability concepts to practical situations to make informed decisions.":

>

>

It is a good idea when aligning problems with standards to have a section at the top of the source worksheet with the standards defined in an input cell.  In this example, we have only put the standards that are cited, but the homework template worksheet should probably have all the standards just in case one is needed.

>

This generator illustrates a way of putting the standards in:  make the standard an argument to the generator.   This way one can quickly switch from one set of standards to another.

>	subtractprob:=proc(a,b,s) tagit(standards=s,["What is ",a," - ",b,"?"],_AS([a-b,b-a,a+b,a-b+1])); end:

Here we have aligned it with the Kentucky standards.

>	subtractprob(5,2,[MAE112]);

Number 6

QM_[0.05;3][MA-E-1.1.2:The operations of addition, subtraction, multiplication, and division]

AH_[0]

What is 5 - 2?

AS_[-3;3;4;7]

SKIP_

Usually, standards homework would be with multiplicity greater than 1, so in the same section with the generator, one would make a fixed number of additional calls to the generator.   Here we have aligned this call with the ADP standards.

>	subtractprob(7,3,[I1d1]);

Number 7

QM_[0.05;4][Add, subtract, multiply and divide integers, fractions and decimals.]

AH_[0]

What is 7 - 3?

AS_[10;-4;5;4]

SKIP_

>

>

Here is a standards problem with a parameterized diagram.  In this case, we have defined the diagram outside the generator.  We could just as well have defined it inside the generator.  However, since we defined and tested the diagram first, it made sense to leave it above the generator.

>

>	pie := proc(center,numslices,clrs) plots[display](seq(plottools[pieslice] (center,1,i*2*Pi/numslices..(i+1)*2*Pi/numslices, color=clrs[i mod nops(clrs) +1]),i=0..numslices),scaling=constrained,axes=none) end:

>

>	oddevenprob:=proc(n,clrs,s) local ans,distractor; if irem(n,2)=1 then ans := "odd":  distractor:= "even" else ans := "even": distractor:="odd" fi: tagit(standards=s, pie([0,0],n,clrs),"The pie has an ",_AS([ans,distractor])," number of slices.",_TP()); end:

>	oddevenprob(6,[yellow,grey],[MAE113]);

QM_[0.05;even][MA-E-1.1.3:Odd and even numbers, composite and prime numbers, multiples, and factors]

AH_[0]

The pie has an

AS_[even;odd]

 number of slices.

SKIP_

>	oddevenprob(5,[wheat,magenta,turquoise],[MAE113]);

>	oddevenprob(7,[yellow,pink,blue,red],[MAE113]);

>

Here is a problem which test's the students knowledge that composing two reflections about parallel lines is a translation in a direction perpendicular to the lines with magnitude twice the distance between the line.   We are using some html pretags to italicize the names of the lines.

>

>	m_ := "lt_i gt_ m lt_/i gt_": n_ := "lt_i gt_ n lt_/i gt_":

>

tagit(standards=[MAH211],["Given: ",m_," || ",n_,".  Point P is reflected about ",m_," onto image P' which is then reflected about ",n_," onto P''.  Then PP'' is "] ,_AW(["perpendicular","PERPENDICULAR","Perpendicular"]),[" to ",m_,". If PP'' = 16, what is the distance between the lines ",l_," and ",m_,"?"],_AS([8,4,16,32]));

QM_[0.05;perpendicular#PERPENDICULAR#Perpendicular;8][MA-H-2.1.1:Students will describe properties of and give examples of geometric transformations and apply geometric transformations (translations, rotations, reflections, dilations), with and without a coordinate plane,.]

AH_[0]

Given: lt_i gt_ m lt_/i gt_ || lt_i gt_ n lt_/i gt_.  Point P is reflected about lt_i gt_ m lt_/i gt_ onto image P' which is then reflected about lt_i gt_ n lt_/i gt_ onto P''.  Then PP'' is

AW_[15]

AH_[0]

 to lt_i gt_ m lt_/i gt_. If PP'' = 16, what is the distance between the lines l_ and lt_i gt_ m lt_/i gt_?

AS_[16;8;32;4]

SKIP_

>

>	mctools(PT);

MCtools, version Oct 15 2003.

PT(Location,txt,fontsize=16,clr=black)

>	mctools(DL);

MCtools, version Oct 15 2003.

DL(A,B,thknss=2, styl=1,clr=blue,leftshrinkfactor=0,rightshrinkfactor=0,hashnum=3,hashlength=.3,hashspacing=.1,hashlocation=.5)  

The first word draws a numberline from a to b and puts the requested tickpoints in.    

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numberline := proc(a,b,eps1,eps2,ticks)   local ba,pba,A,B,len;   len := b-a;   A:=[a,0]:   B:=[b,0]:   ba := B-A;   pba := [-ba[2],ba[1]]:   plots[display](DL(A,B),    seq(op([DL(A+(ticks[i]-a)/len*ba,A+((ticks[i]-a)/len+eps1)*ba,hashnum=1),    PT(A+(ticks[i]-a)/len*ba+eps2*pba,ticks[i])]),i=1..nops(ticks)),    scaling=constrained,axes=none); end:

The second word inserts the point into the diagram that the student will estimate.

>	estimatepic := proc(a,b,eps1,eps2,ticks,x,rad) plots[display](PP([a,0]+x/(b-a)*([b-a,0]),rad),numberline(a,b,eps1,eps2,ticks)); end:

Now the problem generator has the same arguments as estimatepic

>	estimateprob :=proc(a,b,eps1,eps2,ticks,x,rad) tagit(standards=[MAM224],estimatepic(a,b,eps1,eps2,ticks,x,rad),"Estimate the coordinate of the indicated point on the numberline.",_AS([x,x-.1*x,1.2*x,.5*x])) end:

>	estimateprob(0,10,.01,.05,[0,2,3,4,9],2.6,.08);

QM_[0.05;2.6][MA-M-2.2.4:Estimate measurements in standard units]

AH_[0]

Estimate the coordinate of the indicated point on the numberline.

AS_[1.30;2.34;2.6;3.12]

SKIP_

>	estimateprob(0,10,.01,.05,[0,1.5,2,3,4,9],3.6,.08);

>	estimateprob(0,10,.01,.05,[0,1.5,6,7,8,9],6.2,.08);

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Problem sets aligned with a set of standards can and probably should contain hints of all kinds.  In the next example, a video hint is supplied.  Note: If the 5th argument of the homework header is 1, the hint can be put in the top directory of a CD or hard drive and accessed by selecting the appropriate drive letter.  Otherwise, you must put the hint in a directory who name is the number identifier of the homework.  In either case, you can access it from the video server if you upload the hint to the server.

>	angleprob := proc(a,b) tagit(standards=MAM226,["If two angle of a triangle are ",a," and ",b," degrees respectively, what is the third angle?"], _AC(180-(a+b),av_("shelby.wmv"))) end:

>	angleprob(14,57);

QM_[0.05;109][MA-M-2.2.6:Estimate and determine measurement of angles]

AH_[0]

If two angle of a triangle are 14 and 57 degrees respectively, what is the third angle?

AC_[5]

AH_[3;shelby.wmv;Press]

SKIP_

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1.  The group agrees precisely on  standards relative to which  they will develop a collection of diagnostic instruments. It also decides on the scope of the effort. The collection could range from a single problem set (e.g. a  few problems referencing a single course standard - or  to a complete set of instruments for  entire course.  

2. Once the standards and the scope of the project  are selected the various instruments (individual problem sets)  are usually developed sequentially - generally in the order in which they might be studied.  

3.  Individuals or teams are assigned the task of developing various parts of the instrument.  Depending on the organization these smaller units may simply take sets of problems defined by the group (or other working subgroups)  and render them in WHS form. At the other extreme they may have the full responsibility of  taking a subset of the standards, producing the problems, and then the WHS form.  What ever the path the final outcome of the smaller group is a WHS problem set which each problem is expected to be:

a. Complete, well-stated and unambiguous, properly illustrated (if appropriate), in proper English, mathematically correct, and fully tested

b. Contained in its own section which includes not only the problem but  all of the code needed to produce the problem and information on which standards it references. The sectoned problem should have a descriptive title which indicates the mathematical topic (e.g. "Solve two eqns in two unknowns." or the like).

Once each team assigned with part of the project has completed its work the problem then reduces to collecting the individual components in one place and assembling them into a single problem set.  The assumption is that they are not all in the same geographic location and this has to be accomplished via the net.

The problem the is to get the individual problem sets to the collator.  Although there are several ways to do this the following is simple, secure, systematic, and imposes the least on the collator. The process is:

a. The collator creates a WHS class for the project.

b. Each person on the team  adds class, requesting registration.

c.  The collator admits each of the people from part b to the class.  This is done at
Teacher Resources -> Access Records (for the class in question) -> Registration and Passwords

d. Each person with a worksheet for the collator goes to the Assignments screen

Assignments -> Uploads (for the class in question)  and uploads the worksheet

Once everyone has done this the files are all in the  Student Uploads  for the class. The collator goes

Teacher Resources -> Access Records (for the class in question) -> Student Uploads.  All of the files uploaded by the team members are arranged  chronologically in a table which includes a link  to the file and an email link to the person who uploaded it. The collator then downloads each of the files into a convenient directory.

a. The collator then opens a new, blank Maple worksheet, gives it the name of the compiled collection, and saves it in a diectory of the same name, as is customary. The then opens the directory containing each of the downloaded files and  double clicks on one of them. This opens that worksheet in a new copy of Maple. The collator then copies each of the sections (problems) he/she wants to include in the compilation into the new worksheet and when done closes the upload just opened, opens another and does the same thing. When all of the desired  problems have been saved the new, compiled worksheet is saved, exported to html, and installed under an appropriate name.

b.  The collator makes the new worksheet available to the collaboration team by adding it to the class downloads.

Teacher Resources -> Access Records (for the class in question) -> Class Downloads

The new instrument is available for viewing as soon as it is installed. However being viewable is not the same as downloadable (which requires toggling the homework set to permit downloading). The above permits the collator to make the source for the new problem set available to the development team without making it available to the rest of the world.  

Note:    Collaboration classes can also be used to provide source worksheets to a select group.   The standard way to share worksheets in the past has been to toggle the download button on the homework in the Homework Installation table.  However, that makes it available to anonymous people with author priviledges.  Certain worksheet, such as future tests, you would not want to share in this fashion.

Exercise:  Form a two person collaboration team

a.  Everyone should clean his "standards" problem set from Wed.  Section off  the problems, include description of the standard addressed, make sure the answer is correct and problem well-stated, etc.

b. In turn each member of the group should become the collator, using his/her extant class or making a new one. Each of the other two members should register for the collator's class,  the collator should admit them to  the class, each of the "students" should upload their worksheets at the assignment screen in the class, the collator should save each download each of the "student" uploads into a directory and add his/her own to the directory. Then he/she should compile the three into a single set, install it on WHS, and then put the new worksheet in the class downloads for the class.

As we know from experience, not all students have the same knowledge of mathematics coming in to our course.  It is good to have a pre-test   which we could give at the beginning of the course to set a baseline.   

Make a post test for students coming out of middle school.

Make a pre-test for students coming into high school.

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