Creating a Scatter Plot: DP1B-04-P3-Q3 Interactive Exercise

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2018-05-18 22:51

This GeoGebra example demonstrates how to create a scatter plot by generating random points on a coordinate plane, with an interactive interface for students to determine whether points lie within specified regions. Core mathematical concepts include coordinate geometry, point location, integer coordinates, and random data generation. The construction uses GeoGebra commands such as Random, Sequence, Point to generate random points, Append and Sort to manage point lists, Segment and Polygon to define region boundaries, and Shuffle and Element to randomize answer options. Additional objects like RotateText, PointLocation, TryAnother, and CheckMark provide interactive feedback. Suitable for middle and high school students (e.g., IB DP Mathematics) learning statistical plotting and coordinate geometry in classroom or self-study settings.

GeoGebra Commands & Parameters

Append(Sequence[Sequence[(1 + j, 1 + i), i, 0, 8], j, 0, 10], PointLocation) → GridSpace
LaTeX("Which\ variable\ should\ be\ on\ which\ axis?") → Instructions
Segment(Origin, (x(Origin), yHeight)) → yaxis
Segment(Origin, (xHeight, y(Origin))) → xaxis
LaTeX("Time") → Item1
LaTeX("Money") → Item2
Polygon(Pt1, Pt1 + Corner[Item1, 3] - Corner[Item1, 4], Pt1 + Corner[Item1, 2] - Corner[Item1, 4], Pt1 + Corner[Item1, 1] - Corner[Item1, 4]) → DragSpace1, pt1, f, g, h
Polygon(Pt2, Pt2 + Corner[Item2, 3] - Corner[Item2, 4], Pt2 + Corner[Item2, 2] - Corner[Item2, 4], Pt2 + Corner[Item2, 1] - Corner[Item2, 4]) → DragSpace2, pt2, i, j, k
LaTeX("\checkmark") → CheckMark
LaTeX("\times") → Wrong
Polygon(Origin, (xHeight, y(Origin)), (xHeight, -10), (x(Origin), -10)) → WhiteSpace1, origin, l, m, n
Polygon((x(Origin), yHeight), (xHeight, yHeight), (xHeight, 30), (x(Origin), 30)) → WhiteSpace2, p, q, r, s
Polygon((x(Origin), -10), (x(Origin), 30), (-10, 30), (-10, -10)) → WhiteSpace3, t, a, b, c
Polygon((xHeight, -10), (xHeight, 30), (30, 30), (30, -10)) → WhiteSpace4, d, e, f_1, g_1
Shuffle({Item1lc, Item2lc}) → ItemList
Element(ItemList, 1) → FirstItem
Element(ItemList, 2) → SecondItem
LaTeX("Paired\ data\ was\ collected\ to\ study\ the\ relationship\ between\ " + FirstItem + (("\\ and\ " * SecondItem)) + ". \, Which\ one\ would\ you\ place\ on\ the\ horizontal\ axis?") → InstructionsQ1
LaTeX(("The\ independent\ variable\ affects\ the\\ dependent\ variable.\\ It\ is\ likely\ that\ " * Item1lc) + "\\ affects\ " + Item2lc + "\ so\ we\\ identify\ " + Item1lc + "\ as\ the\\ independent\ variable\ and\ place\ it\\ on\ the\ horizontal\ axis.") → FeedbackQ1
LaTeX("Drag\ a\ variable\ onto\ the\ horizontal\ axis\\ before\ checking\ your\ work.") → FeedbackNotStarted
Sequence((1 + i, 1), i, 1, 10) → XPointLocations
Sequence((1, 1 + i), i, 1, 8) → YPointLocations
Sequence(Text[(ymult * i), Element[YPointLocations, i] - (0.79, 0.2)], i, 1, 9) → YLabels
Sequence(Text[(xmult * i), Element[XPointLocations, i] - (0.18, 0.7)], i, 1, 10) → XLabels
RotateText(LaTeX[Item2], π / 2) → YLabel
LaTeX(Item1) → XLabel
Point(GridSpace) → Point1
Point(GridSpace) → Point2
Point(GridSpace) → Point3
Point(GridSpace) → Point4
Point(GridSpace) → Point6
Point(GridSpace) → Point5
Sort({Point1, Point2, Point3, Point4, Point5, Point6}) → Points
Sort({(x1 / xmult, y1 / ymult), (x2 / xmult, y2 / ymult), (x3 / xmult, y3 / ymult), (x4 / xmult, y4 / ymult), (x5 / xmult, y5 / ymult), (x6 / xmult, y6 / ymult)} + {(1, 1), (1, 1), (1, 1), (1, 1), (1, 1), (1, 1)}) → Answer
Sequence(TLPoint - (0, (i * Height)), i, 1, 7) → LeftPts
Sequence(TRPoint - (0, (i * Height)), i, 1, 7) → RightPts
Segment(TMPoint, BMPoint) → h_1
Segment(TLPoint, Element[LeftPts, 7]) → LeftSegment
Segment(TRPoint, Element[RightPts, 7]) → RightSegment
Sequence(Segment[Element[LeftPts, i], Element[RightPts, i]], i, 1, 7) → Segments
Segment(TLPoint, TRPoint) → TopLine
Element(LeftPts, 1) → PtA
Element(RightPts, 1) → PtB
Polygon(TLPoint, PtA, PtB, TRPoint) → q1, tlpoint, pta, ptb, trpoint
LaTeX("Points\text{:}") → PointText
LaTeX(x1) → x1Text
LaTeX(x2) → x2Text
LaTeX(x3) → x3Text
LaTeX(x4) → x4Text
LaTeX(x5) → x5Text
LaTeX(x6) → x6Text
LaTeX(y1) → y1Text
LaTeX(y2) → y2Text
LaTeX(y3) → y3Text
LaTeX(y4) → y4Text
LaTeX(y5) → y5Text
LaTeX(y6) → y6Text
LaTeX(Item1) → XColLabel
LaTeX(Item2) → YColLabel
Random(1, 5) → qindex
LaTeX("The\ correct\ answer\ is\ shown.\, See\ where\ you\\ made\ mistakes\ and\ try\ again.") → FBAnsShown
LaTeX("Drag\ all\ the\ points\ onto\ the\ grid\ before\\ checking\ your\ work.") → FBNotStarted2
LaTeX("Correct!") → FBCorrect
LaTeX("One\ or\ more\ of\ the\ points\ is\ incorrect.\,\\Please\ try\ again.") → FBWrong
LaTeX("Paired\ data\ was\ collected\ to\ study\ the\ effect\ of\ " + Item1lc + "\ on\ " + Item2lc + ".\\ Graph\ the\ data\ set.") → InstructionsQ2
LaTeX("\textbf{Instructions\text{:}}\ First,\, drag\ the\ correct\ variable\ to\ the\ horizontal\ axis.") → Instructions2S1
LaTeX("\textbf{Instructions\text{:}}\ Drag\ points\ onto\ the\ grid\ to\ graph\ the\ data\ set. ") → Instructions2S2
LaTeX(("The\ \textbf{independent}\ variable\ affects\ the\\ dependent\ variable.\\ The\ \textbf{independent}\ variable\ goes\ on\\ the\ horizontal\ axis.\\This\ study\ looks\ at\ how\ " * Item1lc) + "\\ affects\ " + Item2lc + ".\\ Thus,\, " + Item1lc + "\ is\ the\\ independent\ variable.") → FeedbackQ2

AI Drawing Prompt Reference

Create a coordinate plane with horizontal and vertical axes from the origin, labeled with tick marks. Randomly place six integer-coordinate points in the grid area. Below the plane, show two draggable labels, one saying 'Time' and the other 'Money', for choosing the horizontal axis variable. Display a question text asking which variable should be on the horizontal axis. Include a feedback area with a checkmark and a cross symbol, plus instructional text for checking answers. The layout should be clean and interactive for students.

The prompt above was compiled from the original drawing commands and is for reference only.