% backtracking worksheet template
\documentclass[leqno, 12pt]{article}
\usepackage{tikz} 
\usetikzlibrary{positioning}
\usetikzlibrary {arrows.meta}
\usepackage[a4paper, portrait, margin=1cm]{geometry}
\usepackage{multicol}
\pagestyle{empty}

\tikzset{backtrack/.style={rectangle,draw=black,fill=white,
inner sep=2pt,minimum height=32pt, minimum width=20mm}}
\tikzset{backtrackeq/.style={rectangle,draw=black,fill=white,
inner sep=2pt,minimum height=12pt, minimum width=20mm}}
\tikzset{backtrackstep/.style={rectangle,draw=none,fill=white,
inner sep=2pt,minimum height=12pt, minimum width=20mm}}

\def \HeadingAnswers {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{1-step backtracking: Answers} \vspace{1pt}\hrule}

\begin{document}
    \HeadingAnswers
    \vspace{-5mm}
    \begin{multicols}{2}
        \begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$8x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$7$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$56$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times8$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div8$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$7x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$5$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$35$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times7$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div7$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$6x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$9$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$54$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times6$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div6$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$9x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$5$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$45$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times9$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div9$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$7x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$2$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$14$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times7$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div7$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}
    \columnbreak
        \begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$8x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$9$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$72$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times8$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div8$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$6x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$8$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$48$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times6$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div6$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$7x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$2$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$14$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times7$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div7$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$8x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$7$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$56$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times8$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div8$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}\begin{equation}
\begin{tikzpicture}[baseline={([yshift=-1pt]current bounding box.north)}]

    \node[backtrack] (boxA) at (0, 0) {$x$};
    \node[backtrack] (boxB) [right=1cm of boxA] {$8x$};
 
    \node[backtrackeq] (boxAeq) [below=-1pt of boxA] {$=$};
    \node[backtrackeq] (boxBeq) [below=-1pt of boxB] {$=$};

    \node[backtrack] (boxArev) [below=-1pt of boxAeq] {$3$};
    \node[backtrack] (boxBrev) [below=-1pt of boxBeq] {$24$};

    \node(boxAr) at ([yshift=24pt,xshift=5mm]boxA) { };
    \node(boxBl) at ([yshift=24pt,xshift=-5mm]boxB) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxAr)  --node[backtrackstep, above=3.0pt] {$\times8$} (boxBl);
    
    \node(boxBrevl) at ([yshift=-24pt,xshift=-5mm]boxBrev) { };
    \node(boxArevr) at ([yshift=-24pt,xshift=5mm]boxArev) { };
    \draw [line width=0.4pt,-{Stealth[length=2mm]}] (boxBrevl)  --node[backtrackstep, below=3.0pt] {$\div8$} (boxArevr);

\end{tikzpicture}
\end{equation}


\vspace{-2pt}
    \end{multicols}
\end{document}
