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PR2-07-ET2: Like Terms Across Groups

PR2-07-ET2: Like Terms Across Groups
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2021-07-21 03:25
PolygonFunctionProbability & StatisticsSlider AnimationGraphing
① This example demonstrates how to identify and combine like terms across different groups using three baskets of fruits (apples, oranges, bananas) as a visual metaphor. ② The core mathematical concept is algebraic simplification, focusing on combining like terms (same variable and exponent) from multiple groups, with additional statistical concepts like random variables and standard deviation as background context. ③ Construction details: Uses GeoGebra commands such as Polygon to draw basket shapes, PointIn and Join to place fruit images, Zip and Textfield for interactive input, TableText to display results; objects include variables like numBasket1/2/3bananas/oranges/apples and image objects like imgBasket*; LaTeX formulas show algebraic expressions. ④ Suitable for middle school to high school students learning algebraic simplification, and useful for teachers in classroom demonstrations or for self-paced practice, making abstract like-term rules tangible through visual grouping.

GeoGebra Commands & Parameters

  1. LaTeX(UnicodeToLetter[10003]) → cmark
  2. LaTeX(UnicodeToLetter[10007]) → xmark
  3. Polygon({(-8, 2), (-8, 6.5), (1.5, 6.5), (1.5, 2)}) → basket1quad
  4. PointIn(basket1quad) → basket1apple1
  5. PointIn(basket1quad) → basket1apple2
  6. PointIn(basket1quad) → basket1apple3
  7. PointIn(basket1quad) → basket1apple4
  8. PointIn(basket1quad) → basket1apple5
  9. PointIn(basket1quad) → basket1orange1
  10. PointIn(basket1quad) → basket1orange2
  11. PointIn(basket1quad) → basket1orange3
  12. PointIn(basket1quad) → basket1banana1
  13. PointIn(basket1quad) → basket1banana2
  14. PointIn(basket1quad) → basket1banana3
  15. PointIn(basket1quad) → basket1banana4
  16. Polygon({(22, 2), (22, 6.5), (31.5, 6.5), (31.5, 2)}) → basket3quad
  17. PointIn(basket3quad) → basket3apple1
  18. PointIn(basket3quad) → basket3apple2
  19. PointIn(basket3quad) → basket3apple3
  20. PointIn(basket3quad) → basket3apple4
  21. PointIn(basket3quad) → basket3banana1
  22. PointIn(basket3quad) → basket3banana2
  23. PointIn(basket3quad) → basket3banana3
  24. PointIn(basket3quad) → basket3orange1
  25. Join({Sequence[(("SetLayer(imgBasket1apple" * q) * ", 8)"), q, 1, numBasket1apples], Sequence[(("SetLayer(imgBasket1orange" * q) * ", 8)"), q, 1, numBasket1oranges], Sequence[(("SetLayer(imgBasket1banana" * q) * ", 8)"), q, 1, numBasket1bananas]}) → basket1LayerCommands
  26. Join({Sequence[(("SetLayer(imgBasket2apple" * q) * ", 8)"), q, 1, numBasket2apples], Sequence[(("SetLayer(imgBasket2orange" * q) * ", 8)"), q, 1, numBasket2oranges], Sequence[(("SetLayer(imgBasket2banana" * q) * ", 8)"), q, 1, numBasket2bananas]}) → basket2LayerCommands
  27. Join({Sequence[(("SetLayer(imgBasket3apple" * q) * ", 8)"), q, 1, numBasket3apples], Sequence[(("SetLayer(imgBasket3orange" * q) * ", 8)"), q, 1, numBasket3oranges], Sequence[(("SetLayer(imgBasket3banana" * q) * ", 8)"), q, 1, numBasket3bananas]}) → basket3LayerCommands
  28. Polygon({(7, 2), (7, 6.5), (16.5, 6.5), (16.5, 2)}) → basket2quad
  29. PointIn(basket2quad) → basket2apple1
  30. PointIn(basket2quad) → basket2apple2
  31. PointIn(basket2quad) → basket2banana1
  32. PointIn(basket2quad) → basket2banana2
  33. PointIn(basket2quad) → basket2orange1
  34. PointIn(basket2quad) → basket2orange2
  35. PointIn(basket2quad) → basket2orange3
  36. PointIn(basket2quad) → basket2orange4
  37. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  38. Zip(A ≟ Text[B], A, {textApples, textOranges, textBananas}, B, {totalApples, totalOranges, totalBananas}) → totalCorrectness
  39. LaTeX("\textbf{In total there are:}") → header
  40. Textfield(textApples) → ansBoxApples
  41. Textfield(textBananas) → ansBoxBananas
  42. Textfield(textOranges) → ansBoxOranges
  43. TableText({totalApples, totalOranges, totalBananas}, {"\text{\vphantom{\dfrac{1}{2}}apples}", "\text{\vphantom{\dfrac{1}{2}}oranges}", "\text{\vphantom{\dfrac{1}{2}}bananas}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, totalCorrectness]], "v") → table

AI Drawing Prompt Reference

Draw three fruit baskets, each represented by a quadrilateral, containing different quantities and types of fruits: apples, oranges, and bananas. Use points to represent each fruit, randomly placed inside the baskets. Add text labels to show the total count of each fruit, highlighting correct and incorrect counts with different colors. Finally, present a table summarizing the total number of fruits in all baskets, with the title 'In total there are:'.
The prompt above was compiled from the original drawing commands and is for reference only.