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Step-by-Step Algebraic Stamp Cost and Quantity Demo

Step-by-Step Algebraic Stamp Cost and Quantity Demo
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2015-09-25 23:54
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In collections CCSS Support Algebra I Unit 1
This GeoGebra example demonstrates a step-by-step algebraic solution to a stamp-purchase scenario: Easton buys eighteen 49-cent stamps and twenty 34-cent stamps, and the variable f represents the number of 49-cent stamps used. It models expressions for remaining stamps or total cost, reinforcing algebraic expressions, terms, rational-number arithmetic, and linear combinations. The construction uses LaTeX to render formulas, SelectedElement and SelectedIndex to track user choices or current state, and objects such as step, progress, hint, data, prev1, next1, prev2, next2, Refresh, and multiple text objects to create a guided interactive walkthrough. It is suitable for middle-school algebra, word-problem modeling, and GeoGebra interactive lesson design.

GeoGebra Commands & Parameters

  1. LaTeX("\text{Write an expression with parentheses that represents the value of all the stamps Easton has left.}") → text3
  2. LaTeX("\text{We need to find the total value of all of Easton’s remaining stamps, so add these two expressions:}") → text8
  3. LaTeX("\text{Easton has left.}") → text11
  4. LaTeX("\text{Distribute as needed.}") → text13
  5. LaTeX("\text{Original expression}") → text17
  6. LaTeX("\text{Rewritten expression}") → text23
  7. LaTeX("\text{Combine like terms.}") → text29
  8. LaTeX("\text{Rearrange to group like terms.}") → text33
  9. LaTeX("\text{Expression from the previous step}") → text34
  10. SelectedElement(NOS1) → st1
  11. SelectedElement(NOS2) → st2
  12. SelectedElement(ROS1) → sr1
  13. SelectedElement(ROS2) → sr2
  14. LaTeX((((("\text{Multiply \textcolor{#000099}{" * st1) * "} by \textcolor{#000099}{") * sr1) * "}, and}")) → text19
  15. LaTeX((("\text{multiply \textcolor{#000099}{\textendash\;f} by \textcolor{#000099}{" * sr1) * "}.}")) → text20
  16. LaTeX((((((((("\text{\textcolor{#000099}{= " * stsr1) * "\;\textendash\; ") * sr1) * "f + \mathbf{") * stsr2) * "\; \textendash\; ") * sr2) * "p}} }")) → text24
  17. LaTeX((((("\text{Multiply \textcolor{#000099}{" * st2) * "} by \textcolor{#000099}{") * sr2) * "}, and}")) → text25
  18. LaTeX((("\text{multiply \textcolor{#000099}{\textendash\;p} by \textcolor{#000099}{" * sr2) * "}.}")) → text26
  19. LaTeX((((((((((((("\text{In the expression \textcolor{#000099}{" * stsr1) * " \;\textendash\; ") * sr1) * "f + ") * stsr2) * "\; \textendash\; ") * sr2) * "p}, the terms \textcolor{#000099}{") * stsr1) * "} and \textcolor{#000099}{") * stsr2) * "} are like terms.}")) → text30
  20. LaTeX((((((((("\text{\textcolor{#000099}{" * stsr1) * "\;\textendash\; ") * sr1) * "f + ") * stsr2) * "\; \textendash\; ") * sr2) * "p} }")) → text31
  21. LaTeX((((((((("\text{\textcolor{#000099}{= " * stsr1) * "\;+ ") * stsr2) * "\;\textendash\; ") * sr1) * "f \; \textendash\; ") * sr2) * "p} }")) → text32
  22. LaTeX((((((("\text{\textcolor{#000099}{=" * stsr12) * "\; \textendash\;") * sr1) * "f \; \textendash\; ") * sr2) * "p }}")) → text35
  23. LaTeX((((("\text{Add \textcolor{#000099}{" * stsr1) * "} and \textcolor{#000099}{") * stsr2) * "}.}")) → text36
  24. SelectedIndex(NOS1) → Nos_1
  25. SelectedIndex(NOS2) → Nos_2
  26. SelectedIndex(ROS1) → Ros_1
  27. SelectedIndex(ROS2) → Ros_2
  28. LaTeX((((((("\text{A simplified expression for the total value in cents of the stamps Easton has left is \textcolor{#000099}{" * stsr12) * "\; \textendash\;") * sr1) * "f \; \textendash\; ") * sr2) * "p }.}")) → text37
  29. LaTeX((((("\text{\textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)}}")) → text5
  30. LaTeX((((("\text{\textcolor{#000099}{" * sr2) * "(") * st2) * "\; \textendash\; p)}}")) → text7
  31. LaTeX((((((((("\text{The expression \textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\;\textendash\; p)} represents the total value in cents of the stamps}")) → text10
  32. LaTeX((((((((("\text{The expression \textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\;\textendash\; p)} contains two sets of parentheses where distribution can be applied.}")) → text14
  33. LaTeX((((((((("\text{\textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\; \textendash\; p)}}")) → text16
  34. LaTeX("\text{-cent}") → text2_2
  35. LaTeX("\text{-cent}") → text2_3
  36. LaTeX((((((((("\text{\textcolor{#000099}{\mathbf{= " * stsr1) * "\; \textendash\; ") * sr1) * "f} + ") * sr2) * "(") * st2) * " \;\textendash\;p)} }")) → text18
  37. LaTeX((((((((("\text{\textcolor{#000099}{" * stsr1) * " \;\textendash\; ") * sr1) * "f + ") * sr2) * "(") * st2) * "\; \textendash\; p)} }")) → text22
  38. LaTeX((((("\text{Next, distribute \textcolor{#000099}{" * sr2) * "} to \textcolor{#000099}{") * st2) * "} and \textendash\textcolor{#000099}{p}.}")) → text21
  39. LaTeX((((((((("\text{\textcolor{#000099}{" * sr1) * "(") * st1) * "\;\textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\; \textendash\; p)}}")) → text9
  40. LaTeX((((((((((((((((("\text{Once distributed, the expression \textcolor{#000099}{" * sr1) * "(") * st1) * "\; \textendash\; f)} \textcolor{#000099}{+} \textcolor{#000099}{") * sr2) * "(") * st2) * "\; \textendash\; p)\;}is \textcolor{#000099}{") * stsr1) * "\;\textendash\; ") * sr1) * "f + ") * stsr2) * "\; \textendash\; ") * sr2) * "p.}}")) → text27
  41. LaTeX((((("\text{First, distribute \textcolor{#000099}{" * sr1) * "} to \textcolor{#000099}{") * st1) * "} and \;\textcolor{#000099}{\textendash\;f}.}")) → text15
  42. LaTeX((((("\text{\textcolor{#000099}{" * sr1) * "}-cent stamps: Easton bought \textcolor{#000099}{") * st1) * "} and used \textcolor{#000099}{f} of them.")) → text1
  43. LaTeX((((("\text{ \textcolor{#000099}{" * sr2) * "}-cent stamps: Easton bought \textcolor{#000099}{") * st2) * "} and used \textcolor{#000099}{p} of them.}")) → text40
  44. LaTeX("\text{quantities that are not equivalent}") → text38
  45. LaTeX("\text{quantities are equal}") → text28
  46. LaTeX("\text{individual}") → text2_4
  47. LaTeX("\text{stamps}") → text39
  48. LaTeX("\text{individual}") → text2_5
  49. LaTeX("\text{stamps}") → text39_1
  50. LaTeX((((("\text{Easton had \textcolor{#000099}{" * st1) * "} individual \textcolor{#000099}{") * sr1) * "}-cent stamps and used \textcolor{#000099}{f} of them. This is represented as:}")) → text4
  51. LaTeX((((("\text{Easton had \textcolor{#000099}{" * st2) * "} individual \textcolor{#000099}{") * sr2) * "}-cent stamps and used \textcolor{#000099}{p} of them. This is represented as:}")) → text6
  52. LaTeX("\text{\mathbf{equation} a mathematical sentence that uses an equal sign (=) to show that two}") → text42
  53. LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between }") → text49

AI Drawing Prompt Reference

Create a step-by-step algebraic illustration for a stamp purchase problem. Show a scenario where a person buys a number of 49-cent stamps and 34-cent stamps, with variables f and p representing used quantities. Display colored text and formulas that sequentially show the original expression, distribution, combining like terms, and simplified result. Each step includes explanatory text, with arrows or highlights indicating the current operation. Arrange the content in a vertical flow with multiple text boxes and equations, emphasizing the transformation of algebraic expressions.
The prompt above was compiled from the original drawing commands and is for reference only.