2. Number Lines - manual

The LaTeX in this section is for one number line diagram.
The values in the diagram can be entered manually into the LaTeX code.

2.1. A number line diagram with answers

question

png pdf tex

number_lines_mq

answer

png pdf tex

number_lines_mans

2.2. number lines LaTeX

A LaTeX .tex file consists of two parts, the preamble and the main document.

2.3. LaTeX preamble

In the preamble, set the document class, and import required packages and set their options.
Macro definitions, such as those for the variables to hold the diagram values, are also in the preamble.
% numberline
\documentclass[preview,12pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary {arrows.meta}
\usetikzlibrary{bending}
\usepackage[a4paper, portrait, margin=1cm]{geometry}

\def\jumpheight{10}
% \def\qgap{\rule[-1pt]{1.0em}{.25pt}}

defqgap{raisebox{-1pt}{dotuline{phantom{X}}}}

% modify values for number lines defstartval{-3} defendval{2} % values for display defstartvaltxt{startval} defendvaltxt{endval} defchangevaltxt{+5} defequtxt{-3 + 5 = 2} % end modify values for number lines

2.3.1. Document class

The code \documentclass[preview,12pt]{standalone} is used to define a document that can be used to create graphics that are self-contained and can be easily included in other documents.
The argument [12pt] specifies the base font size of the document.
See: https://mirror.cse.unsw.edu.au/pub/CTAN/macros/LaTeX/contrib/standalone/standalone.pdf

2.3.2. tikz package

The code \usepackage{tikz} imports the TikZ package which allows you to create diagrams and graphics programmatically, such as points, lines and paths, circles, ellipses and rectangles.
The code \usetikzlibrary{positioning} is used to import the positioning library which provides advanced positioning options for nodes (points in a diagram that can be referenced and used to draw lines or shapes).
The code \usetikzlibrary{arrows.meta} loads the arrows.meta library, which provides more options for customizing the appearance of arrows in tikz diagrams. This library allows you to use different arrow tip styles and to adjust the size and shape of arrow tips.
The code \usetikzlibrary{bending} loads the bending library, which improves the appearance of arrows that are attached to curved lines. This library makes the arrow tips follow the curvature of the line, resulting in a more natural-looking bend.
For docs on the tikz package see: https://tikz.dev/

2.3.3. arrows

Use \usetikzlibrary {arrows.meta} and \usetikzlibrary{bending} to create various types of arrows with TikZ.
The arrows.meta library provides a flexible way to customize the appearance of arrow tips, such as their shape, size, color, and orientation.
The bending library allows curved paths with arrows to be drawn without distortion.

2.3.4. Macro definitions

The macro \def\jumpheight{10} is used for consistency and easy adjustment of the height that the arrow goes up from the points in the number line.
The macro ``% defqgap{rule[-1pt]{1.0em}{.25pt}}

defqgap{raisebox{-1pt}{dotuline{phantom{X}}}}`` is used for placing an underline for space to write answers on a number line used in a question.

The variables to be used are shown below in the Macro definitions.
These will be used in creating the number line diagram.
This allows a user to replace the values that show on the number line diagram, here, in one place, instead of in the LaTeX code for the diagram itself.
% modify values for number lines
\def\startval{-3}
\def\endval{2}
% values for display
\def\startvaltxt{\startval}
\def\endvaltxt{\endval}
\def\changevaltxt{+5}
\def\equtxt{-3 + 5 = 2}
% end modify values for number lines

2.3.5. Macro definitions and Variables

The command \def is used to define new commands in LaTeX.
The syntax for defining a new command is \def\commandname{replacement text}.
When the command is used in the document, LaTeX replaces it with the replacement text.
The command \def\startval{-3} defines a new command named, \startval, that takes no arguments and expands to the text -3.
Later in the code, this will be used to mark the point at -3 on the number line.
The number line diagram shows the names of the variables used for each part of the diagram.
../../_images/number_lines_variables.png

2.3.5.1. The document environment

The tikzpicture part of the document environment is below.
It contains nodes with names to identify each position used to the points on a number line, the arrow above it connecting the 2 points and the equation it represents.
\begin{document}
\begin{tikzpicture}[scale=0.67]
    % axis, arrow style to-to
    \draw[{To[scale=1.3]}-{To[scale=1.3]}, line width=1pt] (-10.4, 0) -- (10.4, 0);
    % tick marks
    \foreach \x in {-10,-9,...,10}
        \draw[shift={(\x,0)},color=black, line width=1pt] (0pt,-14pt) -- (0pt,0pt);
    % numbers along each axis
    \foreach \x in {-10,0,10}
        \draw[shift={(\x,-0.8)},color=black] node[font=\large,text height=12pt] {$\x$};
    % to display variables
    \draw[shift={(\startval,-0.8)},color=black] node[font=\large,text height=12pt] {$\startvaltxt$};
    \draw[shift={(\endval,-0.8)},color=black] node[font=\large,text height=12pt] {$\endvaltxt$};
    % dots
    \filldraw[black] (\startval,0) circle (4pt) node[above,yshift=-2pt] (a) {};
    \filldraw[black] (\endval,0) circle (4pt) node[above,yshift=-2pt] (b) {};
    % arrow
    \draw[-{To[scale=1.3, bend]},line width=1pt, color=black] (a.north)  .. controls  +(north:\jumpheight mm) and +(north:\jumpheight mm) .. node[above=2pt,text height=12pt,font=\large]{$\changevaltxt$} (b.north);
    % equation at right end
    \node [font=\large, anchor=east] at (15,1.65){$\equtxt$};
\end{tikzpicture}
\end{document}

2.3.6. Document

The command \begin{document} starts the body of the document. It is used to indicate the beginning of the text that will be typeset to appear in the output pdf.
The \end{document} command marks the end of the document

2.3.7. tikzpicture

\begin{tikzpicture} is a command in LaTeX that creates a new picture environment.

2.3.8. Diagram parts

These LaTeX lines create a graphic element using the tikzpicture environment, which is part of the TikZ package for creating diagrams. The lines do the following:

  • \begin{tikzpicture}[scale=0.67] starts the tikzpicture environment and sets the scale option to 0.80, which means that the graphic will be scaled down by 20%. This enables the line to be drawn with one tick every 1 cm before scaling it to fit on an A4 page.

  • ``draw[{To[scale=1.3]}-{To[scale=1.3]}, line width=1pt] (-10.4, 0) – (10.4, 0)``draws a horizontal line from (-10.4, 0) to (10.4, 0) with a thickness of 1pt and arrow tips at both ends. The arrow tips are customized using the arrows.meta library and the To shape with a scale of 1.3.

  • \foreach \x in {-10,-9,...,10} starts a loop that assigns values to the variable x from -10 to 10 with increments of 1.

  • \draw[shift={(\x,0)},color=black, line width=1pt] (0pt,-14pt) -- (0pt,0pt) draws a vertical line segment from (0pt,-14pt) to (0pt,0pt) for each value of x, shifting the origin to (x,0) and using black color and 1pt thickness.

  • \foreach \x in {-10,0,10} starts another loop that assigns values to the variable x for -10, 0 and 10.

  • \draw[shift={(\x,-0.8)},color=black] node[font=\large,text height=12pt] {$\x$} places a node with the value of x below each tick mark on the horizontal axis, using a large font and a text height of 12pt.

  • \draw[shift={(\startval,-0.8)},color=black] node[font=\large,text height=12pt] {$\startvaltxt$} places a node with the value of \startvaltxt below the tick mark corresponding to \startval on the horizontal axis, using a large font and a text height of 12pt.

  • \draw[shift={(\endval,-0.8)},color=black] node[font=\large,text height=12pt] {$\endvaltxt$} places a node with the value of \endvaltxt below the tick mark corresponding to \endval on the horizontal axis, using a large font and a text height of 12pt.

  • \filldraw[black] (\startval,0) circle (4pt) node[above,yshift=-2pt] (a) {} fills and draws a black circle with a radius of 4pt at (\startval,0) and names it (a). It also places an empty node above the circle with a vertical shift of -2pt.

  • \filldraw[black] (\endval,0) circle (4pt) node[above,yshift=-2pt] (b) {} fills and draws a black circle with a radius of 4pt at (\endval,0) and names it (b). It also places an empty node above the circle with a vertical shift of -2pt.

  • \draw[-{To[scale=1.3, bend]},line width=1pt, color=black] (a.north) .. controls +(north:\jumpheight mm) and +(north:\jumpheight mm) .. node[above=2pt,text height=12pt,font=\large]{$\changevaltxt$} (b.north) draws a curved line from the north anchor of node (a) to the north anchor of node (b), using an arrow tip at the end with a scale of 1.3 and a bend option that makes it follow the curvature of the path. The line has a thickness of 1pt and a black color. The curve is controlled by two points that are relative to the start and end points, using the + notation (see: https://en.wikibooks.org/wiki/LaTeX/PGF/TikZ#Specifying_coordinates). The points are shifted north by \jumpheight mm. The line also has a node above it with a vertical shift of 2pt, a text height of 12pt, a large font, and the text \changevaltxt.

2.4. number lines LaTeX

The number lines LaTeX for the incomplete diagram is below.
Some variable values have been commented out and replaced with empty values.
 1% numberline
 2\documentclass[preview,12pt]{standalone}
 3\usepackage{tikz}
 4\usetikzlibrary{positioning}
 5\usetikzlibrary {arrows.meta}
 6\usetikzlibrary{bending}
 7\usepackage{ulem}
 8\usepackage[a4paper, portrait, margin=1cm]{geometry}
 9
10\def\jumpheight{10}
11% \def\qgap{\rule[-1pt]{1.0em}{.25pt}}
12\def\qgap{\raisebox{-1pt}{\dotuline{\phantom{X}}}}
13
14% modify values for number lines
15\def\minval{-10}
16\def\midval{0}
17\def\maxval{10}
18% modify values for number lines
19\def\startval{-3}
20\def\endval{2}
21
22% values for display
23\def\startvaltxt{\qgap}
24\def\endvaltxt{\qgap}
25\def\changevaltxt{\qgap}
26\def\equtxt{\qgap + \qgap=\qgap}
27% end modify values for number lines
28
29\begin{document}
30\begin{tikzpicture}[scale=0.67]
31    % axis, arrow style to-to
32    \draw[{To[scale=1.3]}-{To[scale=1.3]}, line width=1pt] (\minval-0.4, 0) -- (\maxval+0.4, 0);
33
34    % % tick marks
35    \pgfmathtruncatemacro{\nextmin}{\minval+1}
36    \foreach \x in {\minval,\nextmin,...,\maxval}
37        \draw[shift={(\x,0)},color=black, line width=1pt] (0pt,-14pt) -- (0pt,0pt);
38
39
40    % % numbers along each axis
41    \foreach \x in {\minval,\midval,\maxval} {
42        \pgfmathtruncatemacro\result{\x<0} % Converts boolean to 1 or 0
43        \ifnum\result=1
44            \draw[shift={(\x-0.3,-0.8)},color=black] node[font=\large,text height=12pt] {$\x$};
45        \else
46            \draw[shift={(\x,-0.8)},color=black] node[font=\large,text height=12pt] {$\x$};
47        \fi
48    }
49
50    % Start and end value labels
51    \draw[shift={(\startval,-0.8)},color=black] node[font=\large,text height=12pt] {$\startvaltxt$};
52    \draw[shift={(\endval,-0.8)},color=black] node[font=\large,text height=12pt] {$\endvaltxt$};
53
54    % dots
55    \filldraw[black] (\startval,0) circle (4pt) node[above,yshift=-2pt] (a) {};
56    \filldraw[black] (\endval,0) circle (4pt) node[above,yshift=-2pt] (b) {};
57
58    % arrow
59    \draw[-{To[scale=1.3, bend]},line width=1pt, color=black] (a.north)
60        .. controls  +(north:\jumpheight mm) and +(north:\jumpheight mm) ..
61        node[above=2pt,xshift=-6pt,font=\large,text height=10pt] {$\changevaltxt$} (b.north); % for addition
62
63    % equation at right end
64    \node [font=\large, anchor=west] at (\maxval+3,1.65){$\equtxt$};
65\end{tikzpicture}
66\end{document}
The number lines LaTeX for the complete diagram is below.
 1% numberline
 2\documentclass[preview,12pt]{standalone}
 3\usepackage{tikz}
 4\usetikzlibrary{positioning}
 5\usetikzlibrary {arrows.meta}
 6\usetikzlibrary{bending}
 7\usepackage{ulem}
 8\usepackage[a4paper, portrait, margin=1cm]{geometry}
 9
10\def\jumpheight{10}
11% \def\qgap{\rule[-1pt]{1.0em}{.25pt}}
12\def\qgap{\raisebox{-1pt}{\dotuline{\phantom{X}}}}
13
14% modify values for number lines
15\def\minval{-10}
16\def\midval{0}
17\def\maxval{10}
18% modify values for number lines
19\def\startval{-3}
20\def\endval{2}
21% values for display
22\def\startvaltxt{\startval}
23\def\endvaltxt{\endval}
24\def\changevaltxt{\the\numexpr\endval-\startval\relax} % Automatically computes the change
25\def\equtxt{\the\numexpr\startval\relax + \the\numexpr\changevaltxt\relax = \the\numexpr\endval\relax} % Computes full equation
26% end modify values for number lines
27
28\begin{document}
29\begin{tikzpicture}[scale=0.67]
30    % axis, arrow style to-to
31    \draw[{To[scale=1.3]}-{To[scale=1.3]}, line width=1pt] (\minval-0.4, 0) -- (\maxval+0.4, 0);
32
33    % % tick marks
34    \pgfmathtruncatemacro{\nextmin}{\minval+1}
35    \foreach \x in {\minval,\nextmin,...,\maxval}
36        \draw[shift={(\x,0)},color=black, line width=1pt] (0pt,-14pt) -- (0pt,0pt);
37
38
39    % % numbers along each axis
40    \foreach \x in {\minval,\midval,\maxval} {
41        \pgfmathtruncatemacro\result{\x<0} % Converts boolean to 1 or 0
42        \ifnum\result=1
43            \draw[shift={(\x-0.3,-0.8)},color=black] node[font=\large,text height=12pt] {$\x$};
44        \else
45            \draw[shift={(\x,-0.8)},color=black] node[font=\large,text height=12pt] {$\x$};
46        \fi
47    }
48
49    % Start and end value labels
50    \draw[shift={(\startval,-0.8)},color=black] node[font=\large,text height=12pt] {$\startvaltxt$};
51    \draw[shift={(\endval,-0.8)},color=black] node[font=\large,text height=12pt] {$\endvaltxt$};
52
53    % dots
54    \filldraw[black] (\startval,0) circle (4pt) node[above,yshift=-2pt] (a) {};
55    \filldraw[black] (\endval,0) circle (4pt) node[above,yshift=-2pt] (b) {};
56
57    % arrow
58    \draw[-{To[scale=1.3, bend]},line width=1pt, color=black] (a.north)
59        .. controls  +(north:\jumpheight mm) and +(north:\jumpheight mm) ..
60        node[above=2pt,xshift=-6pt,font=\large,text height=10pt] {$\changevaltxt$} (b.north); % for addition
61
62    % equation at right end
63    \node [font=\large, anchor=west] at (\maxval+3,1.65){$\equtxt$};
64\end{tikzpicture}
65\end{document}