Algorithms are great. They make the modern world work in reliable, predictable and scalable way. Without algorithms your phone wouldn't exist, neither would the transport that you used to get to class today. Algorithms are the back-bone of \emph{Computer Science} and this is the simplest one:

\begin{multicols}{2}
\begin{minipage}{1in}
\begin{tabular}{cccc}
      &$1^1$&5\\
    + &2&7\\
    \hline\\*[-2pt]
    &4&2\\
    \hline
\end{tabular}
\end{minipage}
    \begin{minipage}{4in}
        \Large\textbf{Algorithm:}\vspace*{-0.2cm}
\begin{solutionorbox}[2in]
    \begin{enumerate}
        \item Start with right most column, add downwards
        \item If greater than 10, take the tens unit to next column.
        \item Repeat until no more leftwards columns remaining.
    \end{enumerate}
\end{solutionorbox}
    \end{minipage}
\end{multicols}

\begin{examples}
    \begin{questions}
        \Question[4] Complete the following additions:
        \begin{multicols}{2}
            \begin{parts}
                \part 
                    \begin{tabular}{ccccc}
                        &&9&3&5\\
                        &2&3&8&2\\
                        +&&&9&7\\
                        \hline\\
                        &\fillin[3][0pt]&\fillin[4][0pt]&\fillin[1][0pt]&\fillin[4][0pt]\\
                        \hline\\
                    \end{tabular}
                \part 
                    \begin{tabular}{cccccc}
                        &&7&1&3&6\\
                        +&&8&0&9&5\\
                        \hline\\
                        &\fillin[1][0pt]&\fillin[5][0pt]&\fillin[2][0pt]&\fillin[3][0pt]&\fillin[1][0pt]\\
                        \hline\\
                    \end{tabular}
            \end{parts}
        \end{multicols}
    \end{questions}
\end{examples}

\begin{exercises}
    \begin{questions}
        \Question[10] Work out the answers to these additions by using the standard algorithm.
        \begin{parts}
            \begin{multicols}{2}
            \part \(721+630\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(235+549\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(109+872\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(468+951\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(973+296\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(2107+989\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(1432+3791\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(793+274+473\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(8693+7392\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(9999+32\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
        \end{multicols}
        \end{parts}
        \Question[6] Work out the answers to these additions.
        \begin{parts}
            \part \(37+129+1647\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(9230+839+61\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(829+1083+437\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(72+274+391+28\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(254+194+482+53\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
            \part \(632+106+7+270\)
            \begin{solutionorbox}[1in]
            \end{solutionorbox}
        \end{parts}
        \Question[4] For each of the following, find the missing digits ( \(\star\) ) to make the addition correct.
        \begin{parts}
            \begin{multicols}{2}
            \part
                \begin{tabular}{cccc}
                    &6&$\star$&8\\
                    +&$\star$&3&9\\
                    \hline\\*[-0.4cm]
                    &9&9&7\\
                    \hline\\
                \end{tabular}
            \part 
                \begin{tabular}{cccc}
                    &8&$\star$&4\\
                    +&$\star$&9&$\star$\\
                    \hline\\*[-0.4cm]
                    &$\star$&0&3\\
                    \hline\\
                \end{tabular}
            \part 
                \begin{tabular}{ccccc}
                    &&9&1&9\\
                    +&&8&9&$\star$\\
                    \hline\\*[-0.4cm]
                    &1&$\star$&1&8\\
                    \hline\\
                \end{tabular}
            \part 
                \begin{tabular}{ccccc}
                    &&6&$\star$&3\\
                    +&&$\star$&8&9\\
                    \hline\\*[-0.4cm]
                    &1&2&6&2\\
                    \hline\\
                \end{tabular}
            \end{multicols}
        \end{parts}
        \Question[2] Make six different three-digit numbers from the digits 4,7 and 8 . What is their sum?
        \begin{solutionordottedlines}[2in]
        \end{solutionordottedlines}
        \Question[3] Find the sum of:
        \begin{parts}
            \part three hundred and sixty-seven and six hundred and twenty-seven
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
            \part four hundred and twenty-four and five thousand, three hundred and twenty-six
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \end{parts}
        \Question[2] The odometer of a car read 54987 kilometres at the beginning of a journey of 765 kilometres. What did it read at the end of the journey?
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \Question[2] A shop had three employees. The manager received \(\$ 976\) per week and the senior assistant received \(\$ 654\) per week. The junior assistant earned \(\$ 443\) per week. What was the total weekly wages bill for the shop?
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
        \Question[2] The Amazon River is 6436 kilometres in length and the Nile River is 234 kilometres longer. What is the length of the Nile?
        \begin{solutionordottedlines}[1in]
        \end{solutionordottedlines}
    \end{questions}
\end{exercises}




