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Identifying Patterns in Input-Output Tables - Addition and Subtraction

Identifying Patterns in Input-Output Tables - Addition and Subtraction
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2023-07-18 19:45
FunctionSequenceCoordinate Geometry
This example helps students identify and understand patterns through completing input-output tables for addition and subtraction. Key mathematical concepts include addition and subtraction operations. Using GeoGebra commands such as RandomUniform, TableText, and others, students can dynamically observe the function machine and convert it into algebraic expressions. Suitable for grades 4-5, this resource aids in developing algebraic thinking and pattern recognition skills.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.34031558826858116, 0.4547453883029274, 0.010569607427750684, 0.2666045968943386, 0.15056502300318825, 0.9004282824457688, 0.47524211699839686, 0.7254857581826846, 0.7624345974888892, 0.921321072446213, 0.39125478051992024, 0.6058901548462925, 0.10676265456677773, 0.6960934367609305, 0.31572859784243323, 0.17287153325853555, 0.16655204667792514, 0.9872325927846007, 0.8692480706105891, 0.35760496896140437, 0.6606860773646871, 0.4295096329855696, 0.2195048655501369, 0.14293742559623188, 0.8270994086181175, 0.8161834746189732, 0.735259750222774, 0.6378898404206211, 0.33114231614083833, 0.5952989604421796, 0.3216886646951678, 0.7603177857034479, 0.017015060488353342, 0.7979969765531104, 0.5570353173999487, 0.6019676525801706, 0.07322557976801577, 0.8287514478301145, 0.10528838390830708, 0.08863198069075134, 0.9570370041895659, 0.17388484732230428, 0.5303331896905693, 0.380011662206822, 0.427823311267247, 0.5995858401552764, 0.9236979587959963, 0.41923462198279254, 0.7451391127318963, 0.023963858159292598, 0.6306222770855388, 0.4407600837680156, 0.4341369257810099, 0.7894232163734262, 0.4877198938847939, 0.8576140856079353, 0.4387279655392905, 0.7518249874975513, 0.2799910366818101, 0.9445561548359254, 0.04158411679827892, 0.3715278912027688, 0.9153586646796208, 0.6828692009443648, 0.5397175014890768, 0.2884599467220865, 0.4412608399617749, 0.934993611960027, 0.0849500129254952, 0.4788706825919343, 0.7101267056031043, 0.5831934416592112, 0.8200986631835049, 0.47534960659655323, 0.40879510056406343, 0.43584714124705076, 0.0741546039549301, 0.674068848153582, 0.6811052965364159, 0.0077965611033958705, 0.9031211653818195, 0.6240193007437541, 0.622997177837274, 0.847467681370372, 0.23750335709686496, 0.20225751388713092, 0.6055020447797518, 0.013193323069956226, 0.24270473073957172, 0.06686516012423425, 0.3129885556847828, 0.27432195884584254, 0.6447882134687366, 0.4254475254672035, 0.3119479316235088, 0.4392889972637871, 0.35119687415121503, 0.08155677206124286, 0.7994598177951386, 0.4628562439372413, 0.3841063799046831, 0.9244240069678249, 0.3002753621856852, 0.2981912187580322, 0.4930943501843732, 0.7688205316629427, 0.7871865162282519, 0.6963638619259188, 0.013763818511722056, 0.8117404466578418, 0.23101991479179193, 0.606178020930486, 0.08984554405584379, 0.5909083079673352, 0.9142022552978655, 0.7710362046973434, 0.858130959677117, 0.21686326596041014, 0.7953876342369208, 0.2267516927877597, 0.5383510902874461, 0.5855563163620926, 0.4221209033186445, 0.7748768142594992, 0.9038173417991465, 0.1220211527585571, 0.8639303513000808, 0.29020814477730345, 0.3832797118248614, 0.6677387384679394, 0.739600453312392, 0.4886583495305157, 0.17003297636059916, 0.9548142405329358, 0.869671012995873, 0.3326514118668119, 0.8008165268771975, 0.4290208851488056, 0.3284403641049066, 0.48560216290805197, 0.9545030162239341, 0.5911373038726577, 0.8589212772752982, 0.23488308863222826, 0.9789611629359434, 0.26181652497421415, 0.03930489553191409, 0.32396003979519455, 0.48380337086986264, 0.5894722805036392, 0.7005334968061857, 0.5090963325099495, 0.8469925785555292, 0.8633539598909575, 0.8515645273482036, 0.3641777759628701, 0.4744842816467046, 0.025104386264320322, 0.2918295004426089, 0.6588040750568741, 0.14421805774743024, 0.41165583185719057, 0.8692473633441975, 0.1298205221033472, 0.9388489475466617, 0.10031656521543186, 0.8169479945947109, 0.5349312175193199, 0.88562338821115, 0.8333370872984224, 0.6725932519825896, 0.23893919427501173, 0.2667545612518788, 0.384117109271429, 0.44085317751017583, 0.9485003841697782, 0.7295415923650503, 0.18052578071947065, 0.6322023259052597, 0.3300580787470113, 0.1023028385903615, 0.4525549608819489, 0.8397463075419425, 0.04784110560150394, 0.6399570527506432, 0.8517116090245705, 0.7702704039561882, 0.504462996328626, 0.9117873937685448, 0.15817758478343288, 0.6261229880631212, 0.035751939055235334, 0.9835626736880789, 0.2788267324864312, 0.14090326048963783, 0.19396970475139827, 0.12676475585366406, 0.9146859002210483, 0.48421766669324046, 0.43954522831832304}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element({"+", "-", "\times", "\div"}, randomNum1) → chosenOperation
  4. Zip(kk + randomNum2, kk, ins) → out1
  5. Zip(kk - randomNum2, kk, ins) → out2
  6. Zip((kk * randomNum2), kk, ins) → out3
  7. Zip(kk / randomNum2, kk, ins) → out4
  8. Element({out1, out2, out3, out4}, randomNum1) → outs
  9. If(currentRandomSeeds(9) ≥ 0.5, 0, 1) → showInOut2
  10. If(currentRandomSeeds(8) ≥ 0.5, 0, 1) → showInOut1
  11. Textfield(input1) → InputBox1
  12. Textfield(input2) → InputBox2
  13. Corner(5) → layoutAppSize
  14. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  15. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  16. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  17. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  18. Translate(vGL, Vector[(Vector[Corner[1], Corner[2]] / 800 * 16)]) → vGL'
  19. Text(text1, H, true, true, 0, 1) → text2
  20. If(anim ≤ 2.5, (5, 5.45), (5 + (2 * (anim - 2.5)), 5.45 - ((anim - 2.5)^(0.2) * (5.45 - 4.8)))) → AnimPoint3
  21. Element({AnimPoint1, AnimPoint2, AnimPoint3, AnimPoint3}, floor(anim) + 1) → AnimPoint
  22. Text(text3, AnimPoint, true, true, 0, 0) → text4
  23. Text((chosenOperation * randomNum2), AnimPointDrop, true, true, 0, 0) → text5
  24. Zip(((If[kk, "\bold{", "{"] * nn) * "}"), kk, boldIns, nn, ins) → insText
  25. Zip(((If[kk, "\bold{", "{"] * nn) * "}"), kk, boldOuts, nn, outs) → outsText
  26. TableText(Append["\textsf{Input}", Zip[Text[kk], kk, ({inp1, inp2, inp3, inp4, inp5} * If[randomNum1 ≟ 4, randomNum2, 1])]], Append["\textsf{Output}", Zip[Text[kk], kk, outs]], "c_|v", 100, 46) → table
  27. TableText(Take[insText, 1, Min[animCount, 5]], Sequence[chosenOperation, ii, 1, Min[animCount, 5]], Sequence[randomNum2, ii, 1, Min[animCount, 5]], Sequence["=", ii, 1, Min[animCount, 5]], Take[outsText, 1, Min[animCount, 5] - If[anim ≤ 2.5, 1, 0]], "v,c", 10, 46) → tableSol
  28. Translate(hGL, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → hGL'

AI Drawing Prompt Reference

Create a “function machine” input-output table interface. Place a two-column table titled “Input” on the left and “Output” on the right. Each row should show the same kind of computation: the inputs generate an equation using one selected operation (+, −, ×, ÷) and a random factor, and the resulting output is filled into the Output column. Add two editable text input areas near the interface for entering two numbers. Animate the table to progressively reveal up to five rows of solved steps, where each row displays the equation form and then the corresponding output value. Around the table, include an onboarding style pulsing sector with a small angle display and a nearby guidance text, emphasizing a step-by-step discovery of the pattern.
The prompt above was compiled from the original drawing commands and is for reference only.