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\title{Newcomer Math Diagnostic Worksheet (Informal)}
\author{Chris Spackman}
\date{Spring 2021}

\pagestyle{empty}

\begin{document}

%\maketitle

%%% to do
% add geometry?
%%% 


\begin{center}
  \textbf{{\large Newcomer Math Diagnostic Worksheet (Informal)}}
\end{center}

\textbf{{\large Name:}} \rule{10em}{0.02em} \hfill \textbf{Date:} \rule{5em}{0.02em}

\RaggedRight

\subsection*{Addition}

\emph{Answer the questions. Show your work.}

\vspace*{1em}

  \begin{tabular}{ rr rr rr rr rr }
    &2&&7&&12&&18&&24\\
    $+$&2&$+$&$6$&$+$&10&$+$&0&$+$&16\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

      \rule[-5.5em]{0pt}{5.5em}\rule{3em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\
  
    &22&&33&&46&&6&&8\\
    $+$&40&$+$&25&$+$&27&$+$&$-5$&$+$&$-9$\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

      \rule[-5.5em]{0pt}{5.5em}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\

  \end{tabular}
%\end{table}

  \vspace*{-0.5em}
  
\subsection*{Subtraction}

\emph{Answer the questions. Show your work.}

\vspace{1em}

  \begin{tabular}{ rr rr rr rr rr }

    &9&&8&&17&&25&&32\\
    $-$&1&$-$&8&$-$&9&$-$&7&$-$&$13$\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

    \rule[-5.5em]{0pt}{5.5em}\rule{3em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\

    
    &32&&43&&$-5$&&6&&7\\
    $-$&0&$-$&63&$-$&12&$-$&$-3$&$-$&$-8$\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

      \rule[-5.5em]{0pt}{5.5em}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\
    
  \end{tabular}

\subsection*{Multiplication}

\emph{Answer the questions. Show your work.}

\vspace{1em}

  \begin{tabular}{ rr rr rr rr rr }

    &3&&5&&8&&10&&12\\
    $\times$&2&$\times$&1&$\times$&3&$\times$&6&$\times$&4\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

    \rule[-5.5em]{0pt}{5.5em}\rule{3em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\

    
    &9&&13&&7&&$-3$&&$-32$\\
    $\times$&8&$\times$&4&$\times$&0&$\times$&13&$\times$&$-2$\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

    \rule[-5.5em]{0pt}{5.5em}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\

  \end{tabular}

  \vspace*{-0.5em}
  
  \subsection*{Division}

\emph{Answer the questions. Show your work.}

\vspace{1em}

  \begin{tabular}{ rr rr rr rr rr }

    &16&&15&&34&&54&&93\\
    $\div$&4&$\div$&5&$\div$&1&$\div$&9&$\div$&3\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

    \rule[-5.5em]{0pt}{5.5em}\rule{3em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\

    &32&&45&&84&&$-16$&&$-72$\\
    $\div$&8&$\div$&15&$\div$&21&$\div$&2&$\div$&$-6$\\  \cline{2-2} \cline{4-4} \cline{6-6} \cline{8-8} \cline{10-10}

    \rule[-5.5em]{0pt}{5.5em}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&&\rule{4em}{0pt}&\\
    
  \end{tabular}

\clearpage
  
  \subsection*{Long Division}

\emph{Answer the questions. Show your work.}

\vspace{2em}

  \begin{tabular}{ r r }

{\large \longdivision{\rule{0.1em}{0pt}$260$\rule{0.1em}{0pt}}{$4$\rule{0.1em}{0pt}}}&
{\large \longdivision{\rule{0.1em}{0pt}$735$\rule{0.1em}{0pt}}{$5$\rule{0.1em}{0pt}}}\\
\rule{.2\textwidth}{0pt}&\rule{.4\textwidth}{0pt}\\
  \end{tabular}

\vspace*{6em}

\subsection{Number Line}

\emph{Put the numbers in the correct location on the number line.}


\begin{center}
 \textbf{5} \hspace{1em} $\textbf{-3}$ \hspace{1em} \textbf{2} \hspace{1em} \textbf{7.5}
\end{center}



\vspace*{0.5em}

\begin{center}
\begin{tikzpicture}
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\draw (0,0) -- (15,0);
% the ticks and their labels
\foreach \x  in {1,...,15}
  \draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt);% node[below,fill=white] {\the\numexpr\x +1\relax};
  \node[below,fill=white] at (0,0) {-5};
  \node[below,fill=white] at (5,0) {0};
  \node[below,fill=white] at (15,0) {10};
  % \draw[ultra thick] (2.06,0) -- (8.94,0);
% the labels
%\node[fill=white,draw=black,circle,inner sep=2pt,label=above:{$L_1=119.94$}] at (8.9,0) {};
%\node at (5.5,-0.8) {Number Line};
  \node at (5.5,-1.5) {Number Line};
\end{tikzpicture}
\end{center}

\subsection{Simplifying Fractions}

\emph{Simplify the fractions. Show your work.}

\vspace*{1em}

\begin{multicols}{2}
\begin{itemize}
\widelist
\item[] $\dfrac{6}{12} = $

\item[] $\dfrac{7}{14} = $

\item[] $\dfrac{12}{132} = $

\item[] $\dfrac{8}{3} = $

\item[] $\dfrac{-6}{12} = $

\item[] $\dfrac{-18}{-9} = $
\end{itemize}
\end{multicols}

\clearpage

\subsection*{Math with Fractions}

\emph{Find the answer to each quesion. Show your work.}

\begin{multicols}{2}
\begin{itemize}
\superwidelist
\item[] $\dfrac{2}{3} + \dfrac{1}{3} = $

\item[] $\dfrac{3}{5} + \dfrac{4}{5} = $

\item[] $\dfrac{3}{4} - \dfrac{1}{4} = $

\item[] $\dfrac{1}{2} - \dfrac{1}{3}= $

\item[] $\dfrac{1}{2} \times \dfrac{1}{2} = $

\item[] $\dfrac{2}{3} \times \dfrac{3}{4} = $

\item[] $\dfrac{-5}{6} \div \dfrac{3}{-4} = $

\item[] $\dfrac{7}{12} \div \dfrac{3}{16} = $
\end{itemize}
\end{multicols}


\subsection*{Vocabulary}

\emph{Write the number of the terms or examples next to the correct vocabulary word. Each term or example will be used only~1~time.}

\vspace*{1em}

\textbf{Term / Example}

\begin{multicols}{3}
\begin{enumerate}
\item subtraction $(-)$
\item addition $(+)$
\item $a \times a$ or $a^2$
\item multiplication  $(\times)$
\item division $(\div)$
\item $\sqrt{a}$
\end{enumerate}
\end{multicols}

\vspace*{1em}

\textbf{Vocabulary Words}

  \begin{multicols}{3}
  \begin{itemize}[leftmargin=4em]
\item[\rule{2em}{0.02em}] difference \rule{0pt}{1.4em}
\item[\rule{2em}{0.02em}] product \rule{0pt}{1.4em}
\item[\rule{2em}{0.02em}] quotient \rule{0pt}{1.4em}
\item[\rule{2em}{0.02em}] square root \rule{0pt}{1.4em}
\item[\rule{2em}{0.02em}] square \rule{0pt}{1.4em}
\item[\rule{2em}{0.02em}] sum \rule{0pt}{1.4em}
\end{itemize}
\end{multicols}

\clearpage


\subsection*{Factoring}

\emph{Factor the terms below. Show your work.}

%\textbf{Example:} $ 6 = 2 \times 3$ 

\begin{multicols}{2}
  
\begin{itemize}
  \widelist
\item[] $25 = \rule{2em}{0.02em} \times \rule{2em}{0.02em}$
\item[] $12 = \rule{2em}{0.02em} \times \rule{2em}{0.02em} \times \rule{2em}{0.02em}$
\item[] $45 = \rule{2em}{0.02em} \times \rule{2em}{0.02em} \times \rule{2em}{0.02em}$
\item[] $2x^2 = \rule{2em}{0.02em} \times \rule{2em}{0.02em} \times \rule{2em}{0.02em}$
\end{itemize}
\end{multicols}

\vspace*{0.3em}
  
\begin{itemize}
  \widelist
\item[] $x^2+3x+2 = (\rule{2em}{0.02em} + \rule{2em}{0.02em})(\rule{2em}{0.02em} + \rule{2em}{0.02em})$
\end{itemize}

\vspace*{2em}

\subsection*{Algebra}

\emph{Solve for the variable in the questions below.} %directions


\begin{itemize}

\item[] $x + 10 = 25$. What is $x$?

  \vspace*{4em}
  
\item[] $3y - 13 = 8$. What is $y$?

  \vspace*{4.5em}
  
\item[] $6a + 8 = 3a - 10$. What is $a$?

\vspace*{4em}
  
\end{itemize}


\vfill

\subsection*{Copyright}

Copyright \copyright{} 2021 Chris Spackman. Original and editable versions available at {\small \url{https://www.chrisspackman.com/educator-resources/diagnostics/}.} This work is licensed under the \href{http://creativecommons.org/licenses/by-sa/4.0/}{Creative Commons Attribution-ShareAlike 4.0 International License}.

\vspace*{1em}

\hfill {\small Created: Monday, 17 May 2021} \hspace{1.5em} {\small Last Updated: Tuesday, 18 May 2021}

\end{document}


