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Matching Length Units (Level 2)

Matching Length Units (Level 2)
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2021-09-27 22:44
SequenceInequalityGeometric ConstructionSlider Animation
In collections Wiederholung: Längen- und Flächenmaße
This GeoGebra lesson uses an interactive exercise to help students correctly match and verify length units (e.g., mm, cm, dm, m, km) and their conversions. It demonstrates how a unit system works and how proportional relationships between units determine the correct answers. Key math concepts include length measurement, unit conversion based on prefixes, and comparing units by magnitude. Construction and implementation highlights: it generates randomized question data using Sequence and element/number handling (e.g., randomNos1–4, vals/vals1, count), randomizes the order with Shuffle, and uses If logic to control question flow and correctness checks. Geometry/GUI elements are built using Midpoint, Polygon, and Textfield/text objects (e.g., questionElement and answerElement with text objects like text7–9) to present the task and feedback. Correctness is determined through indices and comparison structures (e.g., unitInd, correctInd, numSepText8, answerCorrect, plus listSmallerOrEqual/listBiggerOrEqual). Suitable for grades 5–6, both for in-class conversion practice and for reinforcing measurement and units.

GeoGebra Commands & Parameters

  1. Sequence(Random[0, 1], i, 1, 100) → randomNos4, {1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0}
  2. Sequence(Random[21, 7800000], i, 1, 100) → randomNos2, {5926484, 4183619, 4137953, 5812736, 7496660, 7252599, 6164369, 129410, 1723706, 6086519, 4118023, 1640647, 2136562, 4362710, 5425609, 1589727, 2508144, 246538, 388669, 493387, 2577782, 6904337, 529408, 6554176, 6495693, 5871825, 3136459, 6346921, 6190451, 2193553, 3635394, 6640591, 6119474, 426584, 37228, 3448651, 7607990, 2768743, 1775341, 1361289, 4574165, 1481507, 4584239, 4549068, 3425768, 2143013, 6305592, 733973, 6889863, 601007, 7076081, 7197585, 1685550, 5604432, 726075, 3989680, 3944731, 849660, 4957416, 4452260, 1042863, 4255418, 365689, 2220812, 5637124, 4333519, 1953711, 1446434, 7067993, 3626603, 6900525, 771623, 7718046, 1906370, 4429679, 2083430, 4195036, 5599350, 2992280, 5608254, 2430793, 973233, 4041267, 2209850, 1433809, 1335827, 150769, 3244024, 540044, 2565016, 6822904, 5213671, 3480016, 1001907, 563403, 1973539, 5023943, 3519171, 1664485, 6628461}
  3. Element(randomNos2, Mod[count, 100] + 1) → valMM
  4. NumberSeparationComma(valMM) → valMM1
  5. NumberSeparationComma(valCM) → valCM1
  6. NumberSeparationComma(valDM) → valDM1
  7. NumberSeparationComma(valM) → valM1
  8. NumberSeparationComma(valKM) → valKM1
  9. Sequence(Random[1, Length[units]], i, 1, 100) → randomNos1, {4, 4, 3, 2, 5, 3, 3, 4, 2, 4, 2, 4, 2, 2, 4, 4, 3, 2, 2, 3, 2, 4, 5, 2, 3, 3, 1, 1, 2, 1, 5, 2, 4, 4, 2, 3, 2, 4, 3, 1, 2, 3, 3, 2, 1, 2, 3, 1, 3, 1, 1, 1, 5, 4, 4, 3, 3, 4, 4, 2, 2, 5, 3, 3, 2, 4, 5, 5, 4, 5, 1, 2, 3, 1, 2, 2, 3, 4, 4, 5, 1, 4, 4, 5, 4, 1, 5, 2, 5, 1, 4, 3, 5, 3, 3, 3, 4, 5, 4, 3}
  10. If(unitInd ≟ 1, Random[1, 2], If[unitInd ≟ 2, Random[1, 3], If[unitInd ≟ 3, Random[2, 4], If[unitInd ≟ 4, Random[3, 5], If[unitInd ≟ 5, Random[4, 5]]]]]) → correctInd
  11. If(correctInd > unitInd, 1, If[correctInd ≟ unitInd, 2, If[correctInd < unitInd, 3]]) → version
  12. Shuffle(Flatten[Sequence[Sequence["\textsf{\fcolorbox{#000}{#fff}{" + (Element[vals1, i]) + " " + (Element[units, j]) + "}}", j, 1, If[version ≟ 2, i, If[version ≟ 1, i - 1, If[version ≟ 3 ∧ i ≟ 5, 5, i + 1]]]], i, If[version ≟ 1, 2, 1], 5]]) → listSmallerOrEqual, {"\textsf{\fcolorbox{#000}{#fff}{1 775,341 mm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 mm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 mm}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 dm}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 km}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 m}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 dm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 cm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 dm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 m}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 dm}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 km}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 m}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 mm}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 mm}}"}
  13. Shuffle(Flatten[Sequence[Sequence["\textsf{\fcolorbox{#000}{#fff}{" + (Element[vals1, i]) + " " + (Element[units, j]) + "}}", j, If[version ≟ 2, i, If[version ≟ 3, i + 1, If[version ≟ 1 ∧ i ≟ 1, 1, i - 1]]], 5], i, 1, If[version ≟ 3, 4, 5]]]) → listBiggerOrEqual, {"\textsf{\fcolorbox{#000}{#fff}{17 753,41 km}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 m}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 dm}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 km}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 km}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 km}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 m}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 m}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 dm}}"}
  14. Sequence(RandomElement[(1…5) \ {randomNos1(i)}], i, 1, 100) → randomNos3, {2, 2, 5, 5, 1, 1, 1, 1, 4, 1, 5, 1, 4, 1, 1, 3, 4, 4, 4, 2, 3, 2, 3, 4, 2, 2, 2, 3, 1, 5, 1, 5, 5, 2, 4, 1, 4, 2, 4, 5, 3, 2, 1, 5, 5, 5, 5, 4, 4, 3, 2, 3, 2, 2, 2, 5, 1, 2, 2, 1, 3, 3, 1, 5, 4, 3, 3, 4, 2, 2, 2, 5, 2, 4, 1, 5, 4, 2, 5, 1, 4, 3, 3, 3, 2, 3, 3, 4, 2, 4, 5, 1, 1, 5, 2, 1, 5, 4, 5, 1}
  15. NumberSeparationComma(If[type ≟ 0, vals(correctInd) / 10, (vals(correctInd) * 10)]) → numSepAnswerCorrect
  16. NumberSeparationComma(If[type ≟ 0, (vals(correctInd) * 10), vals(correctInd) / 10]) → numSepText8
  17. Midpoint(Corner[answerCorrect, 1], Corner[answerCorrect, 3]) → M1
  18. Midpoint(Corner[text9, 1], Corner[text9, 3]) → M8
  19. Midpoint(Corner[text8, 1], Corner[text8, 3]) → M7
  20. Midpoint(Corner[text7, 1], Corner[text7, 3]) → M6
  21. Midpoint(Corner[text6, 1], Corner[text6, 3]) → M5
  22. Midpoint(Corner[text5, 1], Corner[text5, 3]) → M4
  23. Midpoint(Corner[text4, 1], Corner[text4, 3]) → M3
  24. Midpoint(Corner[text3, 1], Corner[text3, 3]) → M2
  25. Polygon(C, D, E, F) → box, c, d, e, f
  26. Textfield(aInput) → InputBox1
  27. Textfield(bInput) → InputBox2
  28. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  29. Sequence(Shuffle[Flatten[Sequence[Sequence[G + ((i * dx), (j * dy)), i, 0, 1], j, 0, 3]]], k, 1, 100) → l3, {{(-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379)}, {(-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379)}, {(-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 4.266229595924379)}, {(-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379)}, {(-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 4.266229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379)}, {(-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 6.666229595924379)}, {(-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785)}, {(-4.032814719413515, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379)}, {(-4.032814719413515, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 5.4662295959243785)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 5.4662295959243785)}, {(-4.032814719413515, 6.666229595924379), 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5.4662295959243785), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379)}}
  30. Polygon(Corner[answerCorrect, 1], Corner[answerCorrect, 2], Corner[answerCorrect, 3], Corner[answerCorrect, 4]) → solutionBoxType0, g, h, i, j
  31. Zip(I ∈ box, I, ListM) → inBox

AI Drawing Prompt Reference

Please draw an interactive exercise to help students correctly match and verify length units, such as millimeters, centimeters, decimeters, meters, and kilometers, as well as their conversions. It demonstrates how a unit system works and how proportional relationships between units determine the correct answers. Key math concepts include length measurement, unit conversion based on prefixes, and comparing units by magnitude. The construction and implementation highlights include generating randomized question data using Sequence and element/number handling (e.g., randomNos1–4, vals/vals1, count), randomizing the order with Shuffle, and using If logic to control question flow and correctness checks. Geometry/GUI elements are built using Midpoint, Polygon, and Textfield/text objects (e.g., questionElement and answerElement with text objects like text7–9) to present the task and feedback. Correctness is determined through indices and comparison structures (e.g., unitInd, correctInd, numSepText8, answerCorrect, plus listSmallerOrEqual/listBiggerOrEqual). Suitable for grades 5–6, both for in-class conversion practice and for reinforcing measurement and units.
The prompt above was compiled from the original drawing commands and is for reference only.