I would like to implement a worksheet generator in Latex with the following features:
- It should contain commands to generate addition, subtraction, multiplication and division exercises with random integers. Division exercises should not contain remainders and brackets should be set automatically if necessary.
- Moreover, it should also provide a command to generate multiplication and division exercises with a random decimal and a random multiple of 10 (e. g. 1,52 x 1000).
This is what I have tried so far:
\documentclass{article}
\usepackage{tikz}
\usepackage{tasks}
\settasks{label-width=4ex}
\usepackage{ifthen}
\pgfmathsetseed{\number\pdfrandomseed}
\newcommand*{\NewNumbers}{%
\pgfmathsetmacro{\A}{random(-10, 50)}
\pgfmathsetmacro{\B}{random(-10, 10)}
}
\newcommand{\addition}{
\NewNumbers
\setcounter{firstNumber}{\A}
\setcounter{secondNumber}{\B}
\ifthenelse{\A < 0 \AND \B < 0}{
$(\thefirstNumber) + (\thesecondNumber)$}{}
\ifthenelse{\A < 0 \AND \B > 0}{
$(\thefirstNumber) + \thesecondNumber$}{}
\ifthenelse{\A > 0 \AND \B < 0}{
$\thefirstNumber + (\thesecondNumber)$}{}
\ifthenelse{\A > 0 \AND \B > 0}{
$\thefirstNumber + \thesecondNumber$}{}
}
\newcommand{\division}{
\NewNumbers
\setcounter{firstNumber}{\A}
\setcounter{secondNumber}{\B}
\multiply \value{firstNumber} by \value{secondNumber}
\ifthenelse{\A < 0 \AND \B < 0}{
$(\thefirstNumber) : (\thesecondNumber)$}{}
\ifthenelse{\A < 0 \AND \B > 0}{
$(\thefirstNumber) : \thesecondNumber$}{}
\ifthenelse{\A > 0 \AND \B < 0}{
$\thefirstNumber : (\thesecondNumber)$}{}
\ifthenelse{\A > 0 \AND \B > 0}{
$\thefirstNumber : \thesecondNumber$}{}
}
\newcommand{\subtraction}{
\NewNumbers
\setcounter{firstNumber}{\A}
\setcounter{secondNumber}{\B}
\ifthenelse{\A < 0 \AND \B < 0}{
$(\thefirstNumber) - (\thesecondNumber)$}{}
\ifthenelse{\A < 0 \AND \B > 0}{
$(\thefirstNumber) - \thesecondNumber$}{}
\ifthenelse{\A > 0 \AND \B < 0}{
$\thefirstNumber - (\thesecondNumber)$}{}
\ifthenelse{\A > 0 \AND \B > 0}{
$\thefirstNumber - \thesecondNumber$}{}
}
\newcommand{\multiplication}{
\NewNumbers
\setcounter{firstNumber}{\A}
\setcounter{secondNumber}{\B}
\ifthenelse{\A < 0 \AND \B < 0}{
$(\thefirstNumber) \cdot (\thesecondNumber)$}{}
\ifthenelse{\A < 0 \AND \B > 0}{
$(\thefirstNumber) \cdot \thesecondNumber$}{}
\ifthenelse{\A > 0 \AND \B < 0}{
$\thefirstNumber \cdot (\thesecondNumber)$}{}
\ifthenelse{\A > 0 \AND \B > 0}{
$\thefirstNumber \cdot \thesecondNumber$}{}
}
\newcounter{firstNumber}
\newcounter{secondNumber}
\begin{document}
\begin{tasks}(3)
\task \multiplication
\task \subtraction
\task \addition
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\task \division
\task \multiplication
\task \division
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\task \addition
\task \subtraction
\task \division
\end{tasks}
\end{document}
This approach basically meets the first named requirement. However, there is a problem with the aligment of the actual exercise and the labels generated by the task-command. I cannot change the distance between them by using the options which are provided by the tasks package and I actually would like to align every single exercise flush left at the same point.
I do not see a possible solution when it comes to the second requirement since I could not find any possibility to use decimal variables I can calculate with.
I adapted Mico's version to use negative numbers, too, and to make sure that brackets are placed if necessary. This leads to the following version which is working quite well:
% !TeX program = lualatex
%% First, some code from the original posting, streamlined.
\documentclass[a4paper,landscape,12pt]{article}
\usepackage{newpxtext,newpxmath} % newer than mathpazo
\usepackage[hmargin=2.5cm, tmargin=1.5cm]{geometry}
\usepackage[lastpage]{zref}
\usepackage{fancyhdr,background}
\backgroundsetup{
contents = ,
scale = 1,
color = black,
angle = 0,
opacity = 1,
position = current page.north west,
vshift = -2.02cm,
hshift = 5cm
}
\pagestyle{fancy}
\renewcommand\headrulewidth{0pt}
\setlength\headheight{14.5pt}
\makeatletter
\zref@newprop{numpage}{\the\value{page}}
\zref@addprop{main}{numpage}
\fancyhf{}
\fancyfoot[C]{%
\ifnum \zref@extractdefault{LastPage}{numpage}{0} > 1
\thepage
\fi}
\makeatother
%% Now the new material (mostly Lua code)
\usepackage{array,longtable}
\newcolumntype{R}{>{$}r<{$}} % right-aligned, math mode
\newcolumntype{C}{>{${}}c<{{}$}} % centered, math mode
\setlength\extrarowheight{0.85ex} % extra vert. space
\setlength\tabcolsep{0pt}
\usepackage{luacode}
\begin{luacode}
-- First, some variables and auxiliary functions
n1 = 20 -- max integer in addition and subtract. ops
n3 = -30 -- min integer in addition and subtract. ops
n4 = -10 -- min integer in multiplication ops.
n2 = 9 -- max integer in multiplication ops.
n5 = -30 -- min integer in division ops.
n6 = 10 -- max integer in division ops.
nrows = 40 -- number of rows per longtable (20 rows per page)
xtra_sp = "1.5ex" -- extra whitespace after every 5th row
-- What to place at the _end_ of each table cell?
function cell_terminate(i,j) -- i: 1..nrows; j: 1..5
if j<5 then
tex.sprint ( "&" )
elseif i%5==0 then -- extra space after every 5th row
tex.sprint ( "\\\\[" .. xtra_sp .. "]" )
else
tex.sprint ( "\\\\" )
end
end
-- The following eight functions do the actual work of
-- calculating the cells and outputting them into `longtable` env.'s
-- Addition
function questions_Addition ()
math.randomseed(123456789) -- select a suitable seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "+" .. "(" .. x2 .. ")" .."={}" )
else
tex.sprint ( x1 .. "+" .. x2 .."={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Addition ()
math.randomseed(123456789) -- re-use the same seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "+" .. "(" .. x2 .. ")" .."&=&" .. x1 + x2 )
else
tex.sprint ( x1 .. "+" .. x2 .."&=&" .. x1 + x2 )
end
cell_terminate(i,j)
end
end
end
-- Subtraction
function questions_Subtraction ()
math.randomseed(123456789) -- select a suitable seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "-" .. "(" .. x2 .. ")" .."={}" )
else
tex.sprint ( x1 .. "-" .. x2 .."={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Subtraction ()
math.randomseed(123456789) -- re-use the same seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "-" .. "(" .. x2 .. ")" .."&=&" .. x1 - x2 )
else
tex.sprint ( x1 .. "-" .. x2 .."&=&" .. x1 - x2 )
end
cell_terminate(i,j)
end
end
end
-- Multiplication
function questions_Multiplication ()
math.randomseed(123456789) -- select a suitable seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n4,n2)
x2 = math.random(n4,n2)
if x2<0 then
tex.sprint ( x1 .. "\\cdot" .. "(" .. x2 .. ")" .. "={}" )
else
tex.sprint ( x1 .. "\\cdot" .. x2 .. "={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Multiplication ()
math.randomseed(123456789) -- re-use the same seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n4,n2)
x2 = math.random(n4,n2)
if x2<0 then
tex.sprint ( x1 .. "\\cdot" .. "(" .. x2 .. ")" .. "&=&" .. x1*x2 )
else
tex.sprint ( x1 .. "\\cdot" .. x2 .. "&=&" .. x1*x2 )
end
cell_terminate(i,j)
end
end
end
-- Division
function questions_Division ()
math.randomseed(123456789) -- select a suitable seed
local x1, x2, y
for i=1,nrows do
for j=1,5 do
x1 = math.random(n5,n6) -- divisor
x2 = math.random(n5,n6) -- quotient ("result")
y = x1 * x2
if x1<0 then
tex.sprint ( y..":".. "(" .. x1.. ")" .."={}" )
else
tex.sprint ( y..":"..x1.."={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Division ()
math.randomseed(123456789) -- re-use the same seed
local x1, x2, y
for i=1,nrows do
for j=1,5 do
x1 = math.random(n5,n6) -- divisor
x2 = math.random(n5,n6) -- quotient ("result")
y = x1 * x2
if x1<0 then
tex.sprint ( y.. ":" .. "(" .. x1 .. ")" .. "&=&" .. x2 )
else
tex.sprint ( y.. ":" .. x1 .. "&=&" .. x2 )
end
cell_terminate(i,j)
end
end
end
\end{luacode}
%% Latex code for question and answer longtables
\newcommand\TableQ[1]{%
\begin{longtable}{@{} *{4}{R@{\hspace{2.75cm}}} R @{}}
\bigskip\endfirsthead
\bigskip\bigskip\endhead
\directlua{questions_#1()}
\end{longtable}}
\newcommand\TableA[1]{%
\begin{longtable}{@{} *{4}{RCR@{\hspace{2.25cm}}} RCR @{}}
\bigskip\endfirsthead
\bigskip\bigskip\endhead
\directlua{answers_#1()}
\end{longtable}}
%% Headers above question and answer tables
\newcommand\HeaderQ[1]{%
\clearpage
\noindent
Name: \underline{\hspace{10em}}\hfill%
{\Huge\textbf{Training -- #1}}\hfill%
\phantom{Name: \underline{\hspace{10em}}}}
\newcommand\HeaderA[1]{%
\clearpage
\begin{center}
\Huge\textbf{Answers -- #1}
\end{center}}
\begin{document}
%% the macros \TableQ and \TableA invoke the Lua functions
%%%% Addition
\HeaderQ{Addition}
\TableQ{Addition}
\HeaderA{Addition}
\TableA{Addition}
%%%% Subtraction
\HeaderQ{Subtraction}
\TableQ{Subtraction}
\HeaderA{Subtraction}
\TableA{Subtraction}
%%%% Multiplication
\HeaderQ{Multiplication}
\TableQ{Multiplication}
\HeaderA{Multiplication}
\TableA{Multiplication}
%%%% Division
\HeaderQ{Division}
\TableQ{Division}
\HeaderA{Division}
\TableA{Division}
\end{document}
I also tried to extend the function which generates the division exercises to generate division exercises with decimals and a random multiple of 10. However, since I'm not familiar with Lua at all I can't understand the occuring errors when I use this version:
% !TeX program = lualatex
%% First, some code from the original posting, streamlined.
\documentclass[a4paper,landscape,12pt]{article}
\usepackage{newpxtext,newpxmath} % newer than mathpazo
\usepackage[hmargin=2.5cm, tmargin=1.5cm]{geometry}
\usepackage[lastpage]{zref}
\usepackage{fancyhdr,background}
\backgroundsetup{
contents = ,
scale = 1,
color = black,
angle = 0,
opacity = 1,
position = current page.north west,
vshift = -2.02cm,
hshift = 5cm
}
\pagestyle{fancy}
\renewcommand\headrulewidth{0pt}
\setlength\headheight{14.5pt}
\makeatletter
\zref@newprop{numpage}{\the\value{page}}
\zref@addprop{main}{numpage}
\fancyhf{}
\fancyfoot[C]{%
\ifnum \zref@extractdefault{LastPage}{numpage}{0} > 1
\thepage
\fi}
\makeatother
%% Now the new material (mostly Lua code)
\usepackage{array,longtable}
\newcolumntype{R}{>{$}r<{$}} % right-aligned, math mode
\newcolumntype{C}{>{${}}c<{{}$}} % centered, math mode
\setlength\extrarowheight{0.85ex} % extra vert. space
\setlength\tabcolsep{0pt}
\usepackage{luacode}
\begin{luacode}
-- First, some variables and auxiliary functions
n1 = 20 -- max integer in addition and subtract. ops
n3 = -30 -- min integer in addition and subtract. ops
n4 = -10 -- min integer in multiplication ops.
n2 = 9 -- max integer in multiplication ops.
n5 = -30 -- min integer in division ops.
n6 = 10 -- max integer in division ops.
nrows = 40 -- number of rows per longtable (20 rows per page)
xtra_sp = "1.5ex" -- extra whitespace after every 5th row
-- What to place at the _end_ of each table cell?
function cell_terminate(i,j) -- i: 1..nrows; j: 1..5
if j<5 then
tex.sprint ( "&" )
elseif i%5==0 then -- extra space after every 5th row
tex.sprint ( "\\\\[" .. xtra_sp .. "]" )
else
tex.sprint ( "\\\\" )
end
end
-- The following eight functions do the actual work of
-- calculating the cells and outputting them into `longtable` env.'s
-- Addition
function questions_Addition ()
math.randomseed(123456789) -- select a suitable seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "+" .. "(" .. x2 .. ")" .."={}" )
else
tex.sprint ( x1 .. "+" .. x2 .."={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Addition ()
math.randomseed(123456789) -- re-use the same seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "+" .. "(" .. x2 .. ")" .."&=&" .. x1 + x2 )
else
tex.sprint ( x1 .. "+" .. x2 .."&=&" .. x1 + x2 )
end
cell_terminate(i,j)
end
end
end
-- Subtraction
function questions_Subtraction ()
math.randomseed(123456789) -- select a suitable seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "-" .. "(" .. x2 .. ")" .."={}" )
else
tex.sprint ( x1 .. "-" .. x2 .."={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Subtraction ()
math.randomseed(123456789) -- re-use the same seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n3,n1)
x2 = math.random(n3,n1)
if x2<0 then
tex.sprint ( x1 .. "-" .. "(" .. x2 .. ")" .."&=&" .. x1 - x2 )
else
tex.sprint ( x1 .. "-" .. x2 .."&=&" .. x1 - x2 )
end
cell_terminate(i,j)
end
end
end
-- Multiplication
function questions_Multiplication ()
math.randomseed(123456789) -- select a suitable seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n4,n2)
x2 = math.random(n4,n2)
if x2<0 then
tex.sprint ( x1 .. "\\cdot" .. "(" .. x2 .. ")" .. "={}" )
else
tex.sprint ( x1 .. "\\cdot" .. x2 .. "={}" )
end
cell_terminate(i,j)
end
end
end
function answers_Multiplication ()
math.randomseed(123456789) -- re-use the same seed
for i=1,nrows do
for j=1,5 do
x1 = math.random(n4,n2)
x2 = math.random(n4,n2)
if x2<0 then
tex.sprint ( x1 .. "\\cdot" .. "(" .. x2 .. ")" .. "&=&" .. x1*x2 )
else
tex.sprint ( x1 .. "\\cdot" .. x2 .. "&=&" .. x1*x2 )
end
cell_terminate(i,j)
end
end
end
-- Division
function questions_Division ()
math.randomseed(123456789) -- re-use the same seed
local x1, x2, y, z, w
for i=1,nrows do
for j=1,5 do
w = math.random(0,1)
if w == 1 then
x1 = math.random(n5,n6) -- divisor
x2 = math.random(n5,n6) -- quotient ("result")
y = x1 * x2
else
z = math.random(1,5)
x1 = 10^z -- divisor
x2 = math.random(1, 4000) / 10^z -- quotient ("result")
y = x1 * x2
if x1<0 then
tex.sprint ( y..":".. "(" .. x1.. ")" .."={}" )
else
tex.sprint ( y..":"..x1.."={}" )
end
cell_terminate(i,j)
end
end
end
end
function answers_Division ()
math.randomseed(123456789) -- re-use the same seed
local x1, x2, y, z, w
for i=1,nrows do
for j=1,5 do
w = math.random(0,1)
if w == 1 then
x1 = math.random(n5,n6) -- divisor
x2 = math.random(n5,n6) -- quotient ("result")
y = x1 * x2
else
z = math.random(1,5)
x1 = 10^z -- divisor
x2 = math.random(1, 4000) / 10^z -- quotient ("result")
y = x1 * x2
if x1<0 then
tex.sprint ( y.. ":" .. "(" .. x1 .. ")" .. "&=&" .. x2 )
else
tex.sprint ( y.. ":" .. x1 .. "&=&" .. x2 )
end
cell_terminate(i,j)
end
end
end
end
\end{luacode}
%% Latex code for question and answer longtables
\newcommand\TableQ[1]{%
\begin{longtable}{@{} *{4}{R@{\hspace{2.75cm}}} R @{}}
\bigskip\endfirsthead
\bigskip\bigskip\endhead
\directlua{questions_#1()}
\end{longtable}}
\newcommand\TableA[1]{%
\begin{longtable}{@{} *{4}{RCR@{\hspace{2.25cm}}} RCR @{}}
\bigskip\endfirsthead
\bigskip\bigskip\endhead
\directlua{answers_#1()}
\end{longtable}}
%% Headers above question and answer tables
\newcommand\HeaderQ[1]{%
\clearpage
\noindent
Name: \underline{\hspace{10em}}\hfill%
{\Huge\textbf{Training -- #1}}\hfill%
\phantom{Name: \underline{\hspace{10em}}}}
\newcommand\HeaderA[1]{%
\clearpage
\begin{center}
\Huge\textbf{Answers -- #1}
\end{center}}
\begin{document}
%% the macros \TableQ and \TableA invoke the Lua functions
%%%% Addition
\HeaderQ{Addition}
\TableQ{Addition}
\HeaderA{Addition}
\TableA{Addition}
%%%% Subtraction
\HeaderQ{Subtraction}
\TableQ{Subtraction}
\HeaderA{Subtraction}
\TableA{Subtraction}
%%%% Multiplication
\HeaderQ{Multiplication}
\TableQ{Multiplication}
\HeaderA{Multiplication}
\TableA{Multiplication}
%%%% Division
\HeaderQ{Division}
\TableQ{Division}
\HeaderA{Division}
\TableA{Division}
\end{document}
