Points on a Number Line
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CCSS Support Algebra I Unit 3
This example demonstrates plotting a set of numbers on a number line. Key mathematical concepts include the number line, real number set, and point position. Commands used include Point, Segment, Sort, Sequence, etc. Suitable for middle school and above students to learn about the real number set.
GeoGebra Commands & Parameters
Point(xAxis) → BPoint(xAxis) → CSegment(B, C) → aSegment((0, 0), (0, 1)) → iLaTeX("\text{Plot the set of numbers on the same number line.}") → Quest1LaTeX("\text{Identify the least and greatest number in the set of numbers.}") → Pg1ALaTeX("\text{Use the results to determine the scale.}") → Pg1ESort(list3) → AsortElement(Asort, 1) → sort1Element(Asort, 5) → sort2LaTeX((((((((((("\text{ \textcolor{#000099}{\left\{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * ",") * P5) * "\right\}}")) → Question1BLaTeX("\text{line that are less than the least number and greater than the}") → Pg2GLaTeX("\text{greatest number.For this number line,include tick marks from}") → Pg2HSequence(Segment[A + (i, 0), A + (i, 0.5)], i, -3, 7) → list1Sequence(Segment[A + (i, 0), A + (i, (-0.5))], i, -3, 7) → list2LaTeX("\text{\textcolor{#000099}{–3} to \textcolor{#000099}{7}.Including these values,there are \textcolor{#000099}{11} integers between}") → Pg2ILaTeX("\text{\textcolor{#000099}{–3} and \textcolor{#000099}{7}.Place \textcolor{#000099}{11} tick marks on the number line and label from}") → Pg2JLaTeX("\text{\textcolor{#000099}{–3} to \textcolor{#000099}{7},with enough space in between to allow for marking the “half”}") → Pg2KLaTeX("\text{and “quarter” values in the set.Note that,in this case,labeling the tick}") → Pg2LLaTeX("\text{marks in increments of \textcolor{#000099}{0.5} or \textcolor{#000099}{0.25} instead of \textcolor{#000099}{1} would make the number}") → Pg2MLaTeX("\text{line harder to read.}") → Pg2NLaTeX("\text{Plot each point.}") → Pg3ALaTeX("\text{Place a point at the location of each number.}") → Pg3BLaTeX((((((((((("\text{The values given are \textcolor{#000099}{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * "\;and\;") * P5) * "}.}")) → Pg3CLaTeX((((("\text{Plot the points at the whole-number values \textcolor{#000099}{" * P1) * "} and \textcolor{#000099}{") * P5) * "}.The three}")) → Pg3DLaTeX("\text{remaining values are either decimals or fractions,so use estimation}") → Pg3ELaTeX("\text{to plot them between the tick marks on the number line.Estimate}") → Pg3FLaTeX((((((((((("\text{halfway between\textcolor{#000099}{" * CP2) * "} and\textcolor{#000099}{") * FP2) * "} for \textcolor{#000099}{") * P2) * "},halfway between \textcolor{#000099}{") * FP3) * "} and \textcolor{#000099}{") * CP3) * "}}")) → Pg3GIf(P4 ≟ 2, LaTeX[(((((((((("\text{ \textcolor{#000099}{\left\{" * P1) * ",") * P2) * ",") * P3) * ",-") * 2) * ",") * P5) * "\right\}}")], LaTeX[(((((((((("\text{ \textcolor{#000099}{\left\{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * ",") * P5) * "\right\}}")]) → IF1If(P4 ≠ 2, LaTeX[(((("\text{(Recall that\textcolor{#000099}{-" * CM) * "} is equal to \textcolor{#000099}{–") * P4) * "}.)}")]) → Pg3IIf(P4 ≠ 2, LaTeX[(((("\text{Plot the points at the whole-number values \textcolor{#000099}{" * P1) * "} and \textcolor{#000099}{") * P5) * "}.The three}")], LaTeX[(((("\text{Plot the points at the whole-number values \textcolor{#000099}{" * P1) * "},\textcolor{#000099}{") * P5) * "} and\textcolor{#000099}{-2}.The two}")]) → Ifpg3DIf(P4 ≟ 1.25, LaTeX[(((((((("\text{for \textcolor{#000099}{" * P3) * "},and one-fourth of the way between \textcolor{#000099}{–") * FP4) * "} and \textcolor{#000099}{–") * CP4) * "} for\textcolor{#000099}{- ") * CM) * "}.}")]) → Pg3HIfIf(P4 ≟ 1.5, LaTeX[(((((((("\text{for \textcolor{#000099}{" * P3) * "},and half of the way between \textcolor{#000099}{–") * FP4) * "} and \textcolor{#000099}{–") * CP4) * "} for\textcolor{#000099}{- ") * CM) * "}.}")]) → Pg3H1f2If(P4 ≟ 1.75, LaTeX[(((((((("\text{for \textcolor{#000099}{" * P3) * "},and three-fourth of the way between \textcolor{#000099}{–") * FP4) * "} and \textcolor{#000099}{–") * CP4) * "} for\textcolor{#000099}{- ") * CM) * "}.}")]) → Pg3Hif3If(P4 ≟ 2, LaTeX[(("\text{for \textcolor{#000099}{" * P3) * "}.}")]) → Pg3HIf4If(P4 ≟ 2.25, LaTeX[(((((((("\text{for \textcolor{#000099}{" * P3) * "},and one-fourth of the way between \textcolor{#000099}{–") * CP4) * "} and \textcolor{#000099}{–") * FP4) * "} for\textcolor{#000099}{- ") * CM) * "}.}")]) → Pg3Hif5If(P4 ≟ 2.5, LaTeX[(((((((("\text{for \textcolor{#000099}{" * P3) * "},and half of the way between \textcolor{#000099}{–") * CP4) * "} and \textcolor{#000099}{–") * FP4) * "} for\textcolor{#000099}{- ") * CM) * "}.}")]) → Pg3Hif6LaTeX("\text{\mathbf{Domain} the set of all input values (\textcolor{#000099}{x}-values) that satisfy the given function}") → WTk1LaTeX("\text{without restriction.}") → WTK2If(P4 ≟ 2 ∧ (P2 ≟ (-2.5) ∨ P2 ≟ (-3.5)), LaTeX[(((("\text{The least number is\textcolor{#000099}{" * sort1) * "} and the greatest number is \textcolor{#000099}{") * sort2) * "}.Therefore,}")], LaTeX[(((("\text{The least number is\textcolor{#000099}{" * sort1) * "} and the greatest number is \textcolor{#000099}{") * sort2) * "}.Therefore,}")]) → Pg1BIf(P4 ≟ 2 ∧ (P2 ≟ (-2.5) ∨ P2 ≟ (-3.5)), LaTeX[(((("\text{The data ranges from\textcolor{#000099}{" * sort1) * "} to \textcolor{#000099}{") * sort2) * "}.Include numbers on the number}")], LaTeX[(((("\text{The data ranges from\textcolor{#000099}{" * sort1) * "} to \textcolor{#000099}{") * sort2) * "}.Include numbers on the number}")]) → Pg2FIf(P4 ≟ 2 ∧ (P2 ≟ (-2.5) ∨ P2 ≟ (-3.5)), LaTeX[(((("\text{the number line must include numbers ranging from\textcolor{#000099}{" * sort1) * "} to \textcolor{#000099}{") * sort2) * "}.}")], LaTeX[(((("\text{the number line must include numbers ranging from\textcolor{#000099}{" * sort1) * "} to \textcolor{#000099}{") * sort2) * "}.}")]) → Pg1CIf(P4 ≟ 2, LaTeX[(((((((((("\text{The values given are \textcolor{#000099}{" * P1) * ",") * P2) * ",") * P3) * ",-") * 2) * "},and \textcolor{#000099}{") * P5) * "}.}")], LaTeX[(((((((((("\text{The values given are \textcolor{#000099}{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * "},and \textcolor{#000099}{") * P5) * "}.}")]) → IfPg3c