\begin{student} This is the stage upon which much of the mathematics you will see in High-School is set: \begin{center} \begin{tikzpicture}[scale=0.8] \centering \draw[<-] (-7.5,0) -- (7.5,0) node [left] at (-7.5,0) {$-\infty$}; \draw[->] (-7.5,0) -- (7.5,0) node [right] {$+\infty$}; \foreach \x in {-6,-4,-2,0,2,4,6} \draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt); \foreach \x in {-3,-2,-1,0,1,2,3} \draw[shift={(2*\x,0)},color=black] (0pt,0pt) -- (0pt,-3pt) node[below] {$\x$}; \end{tikzpicture} \end{center} Then if we overlay another axis perpendicular to this one we get: \begin{center} \begin{tikzpicture}[scale=0.4] % Horizontal axis \draw[->] (-7.5,0) -- (7.5,0); \draw[<-] (-7.5,0) -- (7.5,0); \node[left] at (-7.5,0) {$-\infty$}; \node[right] at (7.5,0) {$+\infty$}; \foreach \x in {-6,-4,-2,0,2,4,6} \draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt); \foreach \x in {-3,-2,-1,1,2,3} \draw[shift={(2*\x,0)},color=black] (0pt,0pt) -- (0pt,-3pt) node[below] {$\x$}; % Vertical axis \draw[->] (0,-7.5) -- (0,7.5); \draw[<-] (0,-7.5) -- (0,7.5); \node[below] at (0,-7.5) {$-\infty$}; \node[above] at (0,7.5) {$+\infty$}; \foreach \y in {-6,-4,-2,0,2,4,6} \draw[shift={(0,\y)},color=black] (3pt,0pt) -- (-3pt,0pt); \node[below right] at (0,0) {$0$}; \foreach \y in {-3,-2,-1,1,2,3} \draw[shift={(0,2*\y)},color=black] (0pt,0pt) -- (-3pt,0pt) node[left] {$\y$}; \end{tikzpicture} \end{center} And finally, placing yet \emph{another} axis perpendicular to both of these we spawn 3-Dimensional Space! \begin{center} \begin{tikzpicture}[scale=0.8] \centering % Set up 3D view \tdplotsetmaincoords{60}{110} % Axes \draw[->] (-4,0,0) -- (4,0,0); \draw[<-] (-4,0,0) -- (4,0,0); \draw[->] (0,-4,0) -- (0,4,0); \draw[<-] (0,-4,0) -- (0,4,0); \draw[->] (0,0,-6) -- (0,0,6); \draw[<-] (0,0,-6) -- (0,0,6); % Horizontal axis (x) \foreach \x in {-3,-2,-1,1,2,3} \draw[shift={(\x,0,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {$\x$}; \node[right] at (4,0,0) {$+\infty$}; \node[left] at (-4,0,0) {$-\infty$}; % Vertical axis (y) \foreach \y in {-3,-2,-1,1,2,3} \draw[shift={(0,\y,0)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {$\y$}; \node[above] at (0,4,0) {$+\infty$}; \node[below] at (0,-4,0) {$-\infty$}; % Perpendicular axis (z) \foreach \z in {-5,-4,-3,-2,-1,1,2,3,4,5} \draw[shift={(0,0,\z)},color=black] (2pt,0pt) -- (-2pt,0pt); \node[above right] at (0,0,8) {$+\infty$}; \node[below left] at (0,0,-8) {$-\infty$}; \end{tikzpicture} \end{center} \end{student} \begin{questions} \Question[1] The highest possible dimensional space is \fillin[$\infty$]! \end{questions} \begin{student} \subsection{Less than \& Greater than} On the number line, you can compare 2 quantities: \begin{center} \begin{tikzpicture}[scale=0.8] \draw[->] (-6, 0) -- (6,0); \draw[<-] (-6, 0) -- (6,0); \foreach \x in {-4,-2,0,2,4} \draw[shift={(\x,0)},color=black] (0pt,3pt) -- (0pt,-3pt); \node[above] at (4,0) {$a$}; \node[above] at (-2,0) {$b$}; \node[below] at (0,0) {$0$}; \draw (1,0) circle; \draw (-2,0) circle; \end{tikzpicture} \end{center} \vspace*{-0.3cm} \begin{align*} a &> b\\ b &< a \end{align*} \end{student} \begin{examples} \begin{questions} \Question[1] Draw a number line and on it mark with dots all the whole numbers less than 5. \begin{solutionorbox}[2in] \begin{center} \end{center} \end{solutionorbox} \Question[1] Draw another number line and on it mark all the whole numbers greater than 45 and less than 52. \begin{solutionorbox}[2in] \begin{center} \end{center} \end{solutionorbox} \end{questions} \end{examples} \begin{exercises} \begin{questions} \Question[4] For each of the following, draw a number line from 0 to 10. \begin{parts} \part Mark the numbers 2,4,6 and 8 on it. \begin{solutionorbox}[1in] \end{solutionorbox} \part Mark the numbers 1,3,5 and 7 on it. \begin{solutionorbox}[1in] \end{solutionorbox} \part Mark the whole numbers less than 5 on it. \begin{solutionorbox}[1in] \end{solutionorbox} \part Mark the whole numbers less than 8 and greater than 2 on it. \begin{solutionorbox}[1in] \end{solutionorbox} \end{parts} \Question[2] The manager of an underground railway system decides to save time in the mornings by having one particular train only stop at every third station between stations 1 and 19. The stations are all \(1 \mathrm{~km}\) apart. Show the stations on a number line and mark with a dot each station where the train stops. \begin{solutionorbox}[2in] \end{solutionorbox} \end{questions} \end{exercises}