Points on a Number Line

Points on a Number Line
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2015-11-09 23:59
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

  1. Point(xAxis) → B
  2. Point(xAxis) → C
  3. Segment(B, C) → a
  4. Segment((0, 0), (0, 1)) → i
  5. LaTeX("\text{Plot the set of numbers on the same number line.}") → Quest1
  6. LaTeX("\text{Identify the least and greatest number in the set of numbers.}") → Pg1A
  7. LaTeX("\text{Use the results to determine the scale.}") → Pg1E
  8. Sort(list3) → Asort
  9. Element(Asort, 1) → sort1
  10. Element(Asort, 5) → sort2
  11. LaTeX((((((((((("\text{ \textcolor{#000099}{\left\{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * ",") * P5) * "\right\}}")) → Question1B
  12. LaTeX("\text{line that are less than the least number and greater than the}") → Pg2G
  13. LaTeX("\text{greatest number.For this number line,include tick marks from}") → Pg2H
  14. Sequence(Segment[A + (i, 0), A + (i, 0.5)], i, -3, 7) → list1
  15. Sequence(Segment[A + (i, 0), A + (i, (-0.5))], i, -3, 7) → list2
  16. LaTeX("\text{\textcolor{#000099}{–3} to \textcolor{#000099}{7}.Including these values,there are \textcolor{#000099}{11} integers between}") → Pg2I
  17. LaTeX("\text{\textcolor{#000099}{–3} and \textcolor{#000099}{7}.Place \textcolor{#000099}{11} tick marks on the number line and label from}") → Pg2J
  18. LaTeX("\text{\textcolor{#000099}{–3} to \textcolor{#000099}{7},with enough space in between to allow for marking the “half”}") → Pg2K
  19. LaTeX("\text{and “quarter” values in the set.Note that,in this case,labeling the tick}") → Pg2L
  20. LaTeX("\text{marks in increments of \textcolor{#000099}{0.5} or \textcolor{#000099}{0.25} instead of \textcolor{#000099}{1} would make the number}") → Pg2M
  21. LaTeX("\text{line harder to read.}") → Pg2N
  22. LaTeX("\text{Plot each point.}") → Pg3A
  23. LaTeX("\text{Place a point at the location of each number.}") → Pg3B
  24. LaTeX((((((((((("\text{The values given are \textcolor{#000099}{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * "\;and\;") * P5) * "}.}")) → Pg3C
  25. LaTeX((((("\text{Plot the points at the whole-number values \textcolor{#000099}{" * P1) * "} and \textcolor{#000099}{") * P5) * "}.The three}")) → Pg3D
  26. LaTeX("\text{remaining values are either decimals or fractions,so use estimation}") → Pg3E
  27. LaTeX("\text{to plot them between the tick marks on the number line.Estimate}") → Pg3F
  28. LaTeX((((((((((("\text{halfway between\textcolor{#000099}{" * CP2) * "} and\textcolor{#000099}{") * FP2) * "} for \textcolor{#000099}{") * P2) * "},halfway between \textcolor{#000099}{") * FP3) * "} and \textcolor{#000099}{") * CP3) * "}}")) → Pg3G
  29. If(P4 ≟ 2, LaTeX[(((((((((("\text{ \textcolor{#000099}{\left\{" * P1) * ",") * P2) * ",") * P3) * ",-") * 2) * ",") * P5) * "\right\}}")], LaTeX[(((((((((("\text{ \textcolor{#000099}{\left\{" * P1) * ",") * P2) * ",") * P3) * ",-") * CM) * ",") * P5) * "\right\}}")]) → IF1
  30. If(P4 ≠ 2, LaTeX[(((("\text{(Recall that\textcolor{#000099}{-" * CM) * "} is equal to \textcolor{#000099}{–") * P4) * "}.)}")]) → Pg3I
  31. If(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}")]) → Ifpg3D
  32. If(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) * "}.}")]) → Pg3HIf
  33. If(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) * "}.}")]) → Pg3H1f2
  34. If(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) * "}.}")]) → Pg3Hif3
  35. If(P4 ≟ 2, LaTeX[(("\text{for \textcolor{#000099}{" * P3) * "}.}")]) → Pg3HIf4
  36. If(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) * "}.}")]) → Pg3Hif5
  37. If(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) * "}.}")]) → Pg3Hif6
  38. LaTeX("\text{\mathbf{Domain} the set of all input values (\textcolor{#000099}{x}-values) that satisfy the given function}") → WTk1
  39. LaTeX("\text{without restriction.}") → WTK2
  40. If(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,}")]) → Pg1B
  41. If(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}")]) → Pg2F
  42. If(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) * "}.}")]) → Pg1C
  43. If(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