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Make It Shorter - Level 1: Rewrite Repeated Multiplication as Powers

Make It Shorter - Level 1: Rewrite Repeated Multiplication as Powers
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2024-04-24 21:32
FunctionSequenceSlider Animation
In collections Potenzen - Einführung
This interactive GeoGebra exercise for middle school students demonstrates how to rewrite repeated multiplication of the same factor (e.g., 2×2×2) into exponential form (e.g., 2³), and checks the learner's understanding of positive integer exponents. The core mathematical concept is the definition of a positive integer exponent as the number of times the base is multiplied by itself, along with reading, writing, and evaluating powers. Construction highlights: the applet uses GeoGebra commands such as Join, Flatten, Sequence, and Textfield to generate random questions, InputBox1 for student answers, and TextToUnicode, If, Numerator, Denominator, Element, and SpeechBubbleRight to parse and compare responses, with buttons (btnValidate, btnNew, btnTryAgain) providing instant feedback and retry options. Suitable for grades 7–8, this exercise supports classroom practice or self-study, helping students transition from repeated multiplication to exponential notation and strengthening algebraic symbol sense.

GeoGebra Commands & Parameters

  1. Join(Sequence[Shuffle[{1, 2}], k, 1, 100]) → CaseList
  2. Flatten(Join[{{1, 1}, Sequence[Shuffle[{1, 2, 3}], k, 1, 67]}]) → NumberCaseList
  3. Sequence(RandomElement[Remove[Sequence[-5 + (0.1 * k), k, 1, 100], {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}]], m, 1, 200) → DecimalList, {3.9000000000000004, 4.700000000000001, -4.1, -4.8, -2.3, 1.7000000000000002, 4.300000000000001, -0.2999999999999998, 3.200000000000001, 2.7, 1.1000000000000005, 4.700000000000001, -4.1, -4.6, 4.600000000000001, -1.1999999999999997, 4.5, 2.1000000000000005, -2.0999999999999996, -2.0999999999999996, -0.7999999999999998, 2.7, -4.4, 4.5, 1.6000000000000005, 0.5, -3.3, -3.9, -2.0999999999999996, -4.7, 3.8000000000000007, -2.6999999999999997, -1.7999999999999998, -1.4, -1.1999999999999997, 0.20000000000000018, 0.40000000000000036, -1.2999999999999998, -4.3, -0.09999999999999964, -3.5999999999999996, 1.5, 4.1, 4.200000000000001, 0.3000000000000007, 3.4000000000000004, 0.40000000000000036, -3.5999999999999996, 4.700000000000001, 1.9000000000000004, -1.6999999999999997, 4.1, -4.2, -4.9, -1.1999999999999997, 2.8000000000000007, -1.4, -0.5999999999999996, -4.3, 3.0999999999999996, -2.9, -1.5, -2.3, -1.4, 2.6000000000000005, -3.5, 0.5, -3.0999999999999996, -1.5, -0.1999999999999993, -0.1999999999999993, 4.5, 0.7000000000000002, -4.9, 3.3000000000000007, 3.5999999999999996, -0.5999999999999996, -4.1, 3.700000000000001, -0.1999999999999993, -1.0999999999999996, 3.9000000000000004, -4.2, 4.5, 1.2000000000000002, 2.2, -1.0999999999999996, 3.9000000000000004, 2.9000000000000004, -0.5, 2.6000000000000005, -1.4, 2.2, 0.7000000000000002, -3.3, -3.7, -1.4, 4.4, -3.5999999999999996, 1.9000000000000004, 3.200000000000001, -2.9, 4.800000000000001, -4.2, 3.0999999999999996, -0.39999999999999947, -4.8, -2.9, -1.5999999999999996, 0.6000000000000005, 3.0999999999999996, -0.09999999999999964, 0.20000000000000018, 3.0999999999999996, -1.2999999999999998, 0.10000000000000053, 0.40000000000000036, 2.8000000000000007, 2.9000000000000004, -1.9, 2.9000000000000004, 1.7000000000000002, -0.39999999999999947, -3.4, -0.7000000000000002, 3.5999999999999996, 1.8000000000000007, 4.9, 0.40000000000000036, -2.4, 0.8000000000000007, -1.5, -0.09999999999999964, 4.4, 2.8000000000000007, 4.300000000000001, -1.5, -1.4, -0.09999999999999964, -4.1, 1.4000000000000004, 4.1, 1.8000000000000007, 2.1000000000000005, -4.7, 0.5, -2.6999999999999997, 4.200000000000001, -2.5, -0.7999999999999998, 1.1000000000000005, -3.8, -2.9, 4.4, 3.5, 3.5, -0.7999999999999998, 3.5, -4.7, -4.5, -0.09999999999999964, 2.5, -2.5, -3.3, 0.5, -1.0999999999999996, 2.6000000000000005, 1.1000000000000005, -2.5, 1.9000000000000004, -3.9, -2.5, -4.5, 0.7000000000000002, 3.9000000000000004, -2.9, -4.6, 1.4000000000000004, 2.2, -0.8999999999999995, 2.6000000000000005, 3.8000000000000007, -3.0999999999999996, -0.8999999999999995, -2.0999999999999996, -0.8999999999999995, -3.7, 2.1000000000000005, -3.0999999999999996, -3.9, 2.4000000000000004, 2.7, 3.5, 0.5, 3.700000000000001, -4.5, -4.5, 3.3000000000000007, 4.9, 4.800000000000001}
  4. Sequence(RandomElement[{1 / 9, 2 / 9, 4 / 9, 5 / 9, 7 / 9, 8 / 9, 1 / 8, 3 / 8, 5 / 8, 7 / 8, 1 / 7, 2 / 7, 3 / 7, 4 / 7, 5 / 7, 6 / 7, 1 / 6, 5 / 6, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1 / 4, 3 / 4, 1 / 3, 2 / 3, 1 / 2}], k, 1, 200) → FractionList, {0.125, 0.6666666666666666, 0.125, 0.6666666666666666, 0.6, 0.5555555555555556, 0.2857142857142857, 0.6666666666666666, 0.3333333333333333, 0.3333333333333333, 0.16666666666666666, 0.875, 0.875, 0.5714285714285714, 0.875, 0.14285714285714285, 0.875, 0.625, 0.2222222222222222, 0.75, 0.7777777777777778, 0.2222222222222222, 0.16666666666666666, 0.75, 0.7777777777777778, 0.8888888888888888, 0.8571428571428571, 0.16666666666666666, 0.16666666666666666, 0.7142857142857143, 0.2857142857142857, 0.4444444444444444, 0.4, 0.625, 0.4, 0.16666666666666666, 0.16666666666666666, 0.125, 0.875, 0.1111111111111111, 0.7777777777777778, 0.5555555555555556, 0.5555555555555556, 0.1111111111111111, 0.4, 0.7142857142857143, 0.7142857142857143, 0.14285714285714285, 0.6666666666666666, 0.42857142857142855, 0.7142857142857143, 0.1111111111111111, 0.125, 0.16666666666666666, 0.625, 0.3333333333333333, 0.8, 0.6666666666666666, 0.5555555555555556, 0.5, 0.2, 0.14285714285714285, 0.8, 0.375, 0.5555555555555556, 0.6, 0.2222222222222222, 0.2222222222222222, 0.5555555555555556, 0.5, 0.5555555555555556, 0.7142857142857143, 0.16666666666666666, 0.3333333333333333, 0.6666666666666666, 0.4, 0.5714285714285714, 0.4444444444444444, 0.2222222222222222, 0.5714285714285714, 0.16666666666666666, 0.125, 0.375, 0.625, 0.875, 0.14285714285714285, 0.7142857142857143, 0.2222222222222222, 0.875, 0.8571428571428571, 0.2222222222222222, 0.5555555555555556, 0.8, 0.6, 0.2222222222222222, 0.6, 0.2222222222222222, 0.5, 0.7777777777777778, 0.14285714285714285, 0.4444444444444444, 0.16666666666666666, 0.8888888888888888, 0.2222222222222222, 0.1111111111111111, 0.8, 0.7142857142857143, 0.875, 0.14285714285714285, 0.7777777777777778, 0.5714285714285714, 0.8, 0.2857142857142857, 0.5714285714285714, 0.5, 0.6, 0.6, 0.5714285714285714, 0.42857142857142855, 0.2222222222222222, 0.75, 0.5714285714285714, 0.7142857142857143, 0.2857142857142857, 0.625, 0.8333333333333334, 0.1111111111111111, 0.8571428571428571, 0.1111111111111111, 0.8333333333333334, 0.2222222222222222, 0.5714285714285714, 0.1111111111111111, 0.5714285714285714, 0.7142857142857143, 0.4444444444444444, 0.16666666666666666, 0.25, 0.2857142857142857, 0.75, 0.8333333333333334, 0.7142857142857143, 0.14285714285714285, 0.14285714285714285, 0.1111111111111111, 0.42857142857142855, 0.8333333333333334, 0.5714285714285714, 0.25, 0.5555555555555556, 0.6666666666666666, 0.75, 0.42857142857142855, 0.5, 0.7777777777777778, 0.1111111111111111, 0.125, 0.5714285714285714, 0.4, 0.375, 0.125, 0.6666666666666666, 0.6, 0.5714285714285714, 0.2857142857142857, 0.4444444444444444, 0.7777777777777778, 0.125, 0.8571428571428571, 0.4, 0.125, 0.7142857142857143, 0.8333333333333334, 0.7777777777777778, 0.375, 0.125, 0.625, 0.16666666666666666, 0.375, 0.4, 0.1111111111111111, 0.5, 0.8333333333333334, 0.5714285714285714, 0.5555555555555556, 0.7142857142857143, 0.2, 0.8571428571428571, 0.2857142857142857, 0.14285714285714285, 0.2222222222222222, 0.4, 0.6666666666666666, 0.5, 0.625, 0.8888888888888888, 0.4444444444444444, 0.42857142857142855, 0.6666666666666666, 0.8}
  5. Textfield(input1) → InputBox1
  6. Join({{RandomElement[2…10], RandomElement[2…10]}, Sequence[RandomElement[{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}], k, 1, 198]}) → IntegerList
  7. Sequence(RandomElement[{2, 3, 4, 5, 6}], k, 1, 200) → FactorExpList, {3, 3, 4, 2, 6, 3, 2, 6, 4, 2, 3, 6, 3, 6, 6, 2, 3, 3, 4, 3, 4, 3, 2, 4, 5, 6, 6, 2, 4, 3, 5, 5, 3, 4, 2, 2, 5, 2, 4, 4, 3, 2, 4, 6, 6, 3, 5, 6, 6, 2, 2, 6, 5, 6, 2, 4, 2, 3, 4, 2, 4, 6, 5, 2, 4, 2, 4, 4, 4, 2, 6, 3, 6, 2, 6, 5, 6, 6, 6, 2, 5, 5, 3, 3, 6, 4, 6, 6, 5, 5, 4, 6, 5, 4, 3, 2, 4, 5, 5, 3, 4, 6, 5, 4, 5, 6, 6, 4, 2, 3, 2, 2, 2, 4, 2, 2, 5, 3, 2, 3, 4, 6, 4, 6, 2, 2, 6, 5, 3, 6, 6, 4, 5, 4, 2, 6, 3, 4, 2, 4, 4, 5, 5, 4, 6, 5, 4, 5, 4, 5, 2, 6, 3, 2, 3, 5, 2, 5, 4, 4, 5, 2, 2, 6, 2, 5, 3, 2, 5, 3, 5, 3, 6, 4, 2, 6, 3, 5, 5, 4, 5, 5, 6, 4, 2, 2, 3, 6, 2, 5, 5, 4, 4, 2, 6, 3, 4, 5, 6, 4}
  8. TextToUnicode((InputBox1 * "")) → uniUser
  9. If(NumberCase ≟ 1, IntegerList(counter), NumberCase ≟ 2, DecimalList(counter), FractionList(counter)) → num
  10. If(Case ≟ 1, (expo * num), num^(expo)) → sol
  11. Numerator(frac) → fracN
  12. Denominator(frac) → fracD
  13. If(NumberCase ≠ 3, TextToUnicode[("" * num)], {LetterToUnicode[("" * fracN)], 47, LetterToUnicode[("" * fracD)]}) → uniNum
  14. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 3, 6, 7, 2, 9, 5, 8, 9, 1}
  15. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  16. TextToUnicode("*") → uniMultList
  17. Join({TextToUnicode["^²³"], {8308, 8309, 8310, 8311, 8312, 8313}}) → uniExpList
  18. If(Case ≟ 1, "+", "\cdot") → symb
  19. If(NumberCase ≟ 1, txtInt, NumberCase ≟ 2, txtDec, txtFrac) → txtNum
  20. SpeechBubbleRight(PosSB, sbwidth, sbheight) → poly1

AI Drawing Prompt Reference

Create a math exercise with 10 random integers, decimals, and fractions, each followed by a random exponent, such as 2^3 or 1.5^4. Connect integers with plus signs, decimals and fractions with multiplication signs, and then convert each expression to exponential form, like 2×2×2 to 2³.
The prompt above was compiled from the original drawing commands and is for reference only.