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Like Terms within a Group

Like Terms within a Group
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2020-11-25 10:19
FunctionGeometric Construction
This example demonstrates the concept of combining like terms. Key mathematical concepts include algebraic like terms and their combination. Using GeoGebra commands such as Zip, LaTeX, and Polygon, it dynamically shows how to combine like terms. Suitable for middle school math education.

GeoGebra Commands & Parameters

  1. Zip(A ≟ Text[B], A, {textBasket3apples, textBasket3oranges, textBasket3bananas}, B, {numBasket3apples, numBasket3oranges, numBasket3bananas}) → basket3correctness
  2. Zip(A ≟ Text[B], A, {textBasket2apples, textBasket2oranges, textBasket2bananas}, B, {numBasket2apples, numBasket2oranges, numBasket2bananas}) → basket2correctness
  3. Zip(A ≟ Text[B], A, {textBasket1apples, textBasket1oranges, textBasket1bananas}, B, {numBasket1apples, numBasket1oranges, numBasket1bananas}) → basket1correctness
  4. LaTeX(UnicodeToLetter[10003]) → cmark
  5. LaTeX(UnicodeToLetter[10007]) → xmark
  6. Polygon({(-8, 2), (-8, 6.5), (1.5, 6.5), (1.5, 2)}) → basket1quad
  7. PointIn(basket1quad) → basket1apple1
  8. PointIn(basket1quad) → basket1apple2
  9. PointIn(basket1quad) → basket1apple3
  10. PointIn(basket1quad) → basket1apple4
  11. PointIn(basket1quad) → basket1apple5
  12. PointIn(basket1quad) → basket1orange1
  13. PointIn(basket1quad) → basket1orange2
  14. PointIn(basket1quad) → basket1orange3
  15. PointIn(basket1quad) → basket1banana1
  16. PointIn(basket1quad) → basket1banana2
  17. PointIn(basket1quad) → basket1banana3
  18. PointIn(basket1quad) → basket1banana4
  19. Polygon({(22, 2), (22, 6.5), (31.5, 6.5), (31.5, 2)}) → basket3quad
  20. PointIn(basket3quad) → basket3apple1
  21. PointIn(basket3quad) → basket3apple2
  22. PointIn(basket3quad) → basket3apple3
  23. PointIn(basket3quad) → basket3apple4
  24. PointIn(basket3quad) → basket3banana1
  25. PointIn(basket3quad) → basket3banana2
  26. PointIn(basket3quad) → basket3banana3
  27. PointIn(basket3quad) → basket3orange1
  28. Textfield(textBasket1apples) → ansBoxBasket1apples
  29. Textfield(textBasket1oranges) → ansBoxBasket1oranges
  30. Textfield(textBasket1bananas) → ansBoxBasket1bananas
  31. Textfield(textBasket2apples) → ansBoxBasket2apples
  32. Textfield(textBasket2oranges) → ansBoxBasket2oranges
  33. Textfield(textBasket2bananas) → ansBoxBasket2bananas
  34. Textfield(textBasket3apples) → ansBoxBasket3apples
  35. Textfield(textBasket3oranges) → ansBoxBasket3oranges
  36. Textfield(textBasket3bananas) → ansBoxBasket3bananas
  37. 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
  38. 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
  39. 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
  40. Polygon({(7, 2), (7, 6.5), (16.5, 6.5), (16.5, 2)}) → basket2quad
  41. PointIn(basket2quad) → basket2apple1
  42. PointIn(basket2quad) → basket2apple2
  43. PointIn(basket2quad) → basket2banana1
  44. PointIn(basket2quad) → basket2banana2
  45. PointIn(basket2quad) → basket2orange1
  46. PointIn(basket2quad) → basket2orange2
  47. PointIn(basket2quad) → basket2orange3
  48. PointIn(basket2quad) → basket2orange4
  49. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  50. LaTeX("\textbf{Basket 1 contains:}") → basket1Header
  51. LaTeX("\textbf{Basket 2 contains:}") → basket2Header
  52. LaTeX("\textbf{Basket 3 contains:}") → basket3Header
  53. TableText({numBasket1apples, numBasket1oranges, numBasket1bananas}, {"\text{\vphantom{\dfrac{1}{2}}apple(s)}", "\text{\vphantom{\dfrac{1}{2}}orange(s)}", "\text{\vphantom{\dfrac{1}{2}}banana(s)}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, basket1correctness], {}], "v") → basket1Table
  54. TableText({numBasket2apples, numBasket2oranges, numBasket2bananas}, {"\text{\vphantom{\dfrac{1}{2}}apple(s)}", "\text{\vphantom{\dfrac{1}{2}}orange(s)}", "\text{\vphantom{\dfrac{1}{2}}banana(s)}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, basket2correctness], {}], "v") → basket2Table
  55. TableText({numBasket3apples, numBasket3oranges, numBasket3bananas}, {"\text{\vphantom{\dfrac{1}{2}}apple(s)}", "\text{\vphantom{\dfrac{1}{2}}orange(s)}", "\text{\vphantom{\dfrac{1}{2}}banana(s)}"}, If[isChecked, Zip[If[A, (("\textcolor{#254117}{" * cmark) * "}"), (("\textcolor{#e41b17}{" * xmark) * "}")], A, basket3correctness], {}], "v") → basket3Table

AI Drawing Prompt Reference

Draw three separate enclosed quadrilateral “baskets” on a coordinate plane, shaped as rectangles: one on the left roughly from (-8,2) to (1.5,6.5), one in the middle from (7,2) to (16.5,6.5), and one on the right from (22,2) to (31.5,6.5). Inside each rectangle, place multiple interior points to represent three groups of items (apples, oranges, bananas), with a different count for each group as indicated by the number of points used. Add a text input box next to each basket for the quantity of apples, oranges, and bananas, so the user can read or enter the counts for each basket.
The prompt above was compiled from the original drawing commands and is for reference only.