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Änderungen von Dokument Numerische Variablen

Zuletzt geändert von Hendrik Zschocke am 12.01.2024
Von Version 392.1
bearbeitet von Carina Enke
am 22.01.2020
Änderungskommentar: Mittels Scroll Versions veröffentlicht aus dem Bereich ONYXintern und Version 8.9.
Auf Version 400.1
bearbeitet von Carina Enke
am 08.05.2019
Änderungskommentar: Mittels Scroll Versions veröffentlicht aus dem Bereich ONYXintern und Version 8.7.

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
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1 1  {{sv-translation language="de"}}
2 2  {{layout}}
3 3  {{layout-section ac:type="single"}}
4 -{{layout-cell}}
5 -\\
6 -{{/layout-cell}}
4 +{{layout-cell}}{{/layout-cell}}
7 7  {{/layout-section}}
8 8  
9 9  {{layout-section ac:type="two_right_sidebar"}}
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61 61  
62 62   [[image:attach:Editor - Bildvariable Wertsetzung Wertebereich_de.png]]
63 63  
64 -\\
62 +
65 65  
66 66  {{info}}
67 67  Folgende Beispiele zum Einsatz von numerischen Variablen zur Generierung von Zufallswerten zeigen typische Anwendungsszenarien:
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101 101  
102 102   [[image:attach:Editor - Bildvariable Wertsetzung Berechnung Maxima_de.png]]
103 103  
104 -\\
102 +
105 105  
106 106  {{info}}
107 107  Folgendes Beispiele zum Einsatz von numerischen Variablen zur Generierung von Zufallswerten zeigen typische Anwendungsszenarien:
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140 140  {{layout}}
141 141  {{layout-section ac:type="two_right_sidebar"}}
142 142  {{layout-cell}}
143 -For integer or fractional variable values, select the type // **Integer** //or // **Floating point** //.
141 +You can generate integer or fractional variable values. For this purpose, the variable types "**Integer**" and "**Floating Point**" will be available to you.
144 144  
145 -[[image:attach:Editor - Ganzzahlvariable Typauswahl_de.png]]
143 +[[image:attach:image2017-3-23 8:15:49.png]]
146 146  
147 147  To alter the value for the numerical variable, different options are available, which will be explained in the following sections, just as the possibility to define the display accuracy of floating-point numbers. If a numerical variable is not assigned a value, the variable will be initialised with 0.
148 148  
149 -[[image:attach:Editor - Ganzzahlvariable Wertsetzung_de.png]]
147 +[[image:attach:image2017-3-23 8:20:57.png]]
150 150  {{/layout-cell}}
151 151  
152 152  {{layout-cell}}
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155 155  
156 156  
157 157  {{toc/}}
158 -{{/panel}}
159 159  
160 -{{panel title="Application examples"}}
161 -* [[Example "Probability">>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
162 -* [[Example "Hypotenuse">>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
163 -* [[Example "Transport" - Use of random parameters>>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
164 -{{/panel}}
157 +**Related topics**
165 165  
166 -{{panel title="Related topics"}}
167 -* [[Calculation interaction>>url:https://www.bps-system.de/help/display/ONYXintern/.Berechnungsaufgabe+v8.X||shape="rect"]]
168 -* [[Formula comparison>>url:https://www.bps-system.de/help/display/ONYXintern/.Formelvergleich+v8.X||shape="rect"]]
159 +* [[Calculation task>>doc:Berechnungsaufgabe]]
160 +* [[Formula comparison>>url:https://www.bps-system.de/help/display/ONYXintern/.Formelvergleich+v1.11||shape="rect"]]
169 169  {{/panel}}
170 170  
171 171  {{panel borderColor="#ddd" bgColor="#f0f0f0" borderStyle="solid" title="Further information"}}
172 -* [[MAXIMA manual>>url:http://maxima.sourceforge.net/docs/manual/maxima.html||shape="rect"]]
173 -* [[MAXIMA good practice examples>>url:https://bildungsportal.sachsen.de/opal/auth/RepositoryEntry/5499682817/CourseNode/93229879750473/wiki/Index||shape="rect"]]
174 -* [[MAXIMA system information>>url:http://maxima.sourceforge.net/||rel="nofollow" shape="rect" class="external-link"]]
164 +* [[MAXIMA Manual>>url:http://maxima.sourceforge.net/docs/manual/maxima.html||shape="rect"]]
165 +* [[MAXIMA Good-Practice-Beispiele>>url:https://bildungsportal.sachsen.de/opal/auth/RepositoryEntry/5499682817/CourseNode/93229879750473/wiki/Index||shape="rect"]]
166 +* [[MAXIMA Systeminformationen>>url:http://maxima.sourceforge.net/||rel="nofollow" shape="rect" class="external-link"]]
175 175  {{/panel}}
176 176  {{/scroll-ignore}}
177 177  {{/layout-cell}}
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181 181  {{layout-cell}}
182 182  == Range ==
183 183  
184 -For numerical variables, a value range can be defined. The variable value will be randomly determined within the defined value range. Please note that the specified limits are included in the selection. For variables of the type //**Integer** //, the step size (setting steps) can be determined in addition to the limits (setting minimum and maximum).
176 +For numerical variables, a value range can be defined. The variable value will be randomly determined within the defined value range. Please note that the specified limits are included in the selection. For variables of the type "Integer", the step size (setting steps) can be determined in addition to the limits (setting minimum and maximum).
185 185  
186 186  **Possible entries are for example:**
187 187  
188 -* //Range//~:// Minimum=2//,// maximum=11//,// steps=3//: The following values are possible {2, 5, 8, 11}. When the variable is used, a value will be randomly selected, for example 2.
189 -\\[[image:attach:Editor - Bildvariable Wertsetzung Wertebereich_de.png]]
180 +* //Range: Minimum=2, maximum=11, steps=3: //The following values are possible {2, 5, 8, 11}. When the variable is used, a value will be randomly selected, for example 2.
181 +\\[[image:attach:image2017-3-22 14:9:57.png]]
190 190  
191 -{{info}}
192 -The following examples for the use of numerical variables to generate random values show typical application scenarios:
193 -
194 -* [[Example "Probability">>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
195 -* [[Example "Transport" - Use of random parameters>>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
196 -{{/info}}
197 -
198 198  == Value (direct value assignment) ==
199 199  
200 200  You can directly assign a value to all types of variables in order to initialise them. Later on, the value can be changed depending on other variables (cf. conditions).
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201 201  
202 202  **Possible entries are for example:**
203 203  
204 -* //Value//~:// 5//~:// //The variable is assigned the value 5.
205 -* //Value//~:// -2.25//~:// //The variable is assigned the value -2.25.
189 +* //Value: 5: //The variable is assigned the value 5.
190 +* //Value: -2.25: //The variable is assigned the value -2.25.
206 206  
207 207  == Random ==
208 208  
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210 210  
211 211  **Possible entries are for example:**
212 212  
213 -* //Random selection//~:// -5//;// -3//;// 3//;// 5//~:// //One of the specified values will be randomly selected, for example 5.
214 -* //Random selection//~:// 0//;// 12.25//;// 13.5//: One of the specified values will be randomly selected, for example 12.25.
198 +* //Random selection: -5; -3; 3; 5: //One of the specified values will be randomly selected, for example 5.
199 +* //Random selection: 0; 12.25; 13.5: //One of the specified values will be randomly selected, for example 12.25.
215 215  
201 +=== Example "probability" ===
202 +
203 +As an example, a typical task out of probability theory and statistics will be completed. It is to calculate the probability of certain colour combinations, when different coloured spheres are randomly drawn from an urn.
204 +
205 +|(((
206 +[[image:attach:image2017-3-23 8:54:23.png]]
207 +)))|(((
208 +In the example, the numerical variables {BLUE}, {RED}, and {WHITE} are initialised with an integer value between 3 and 15, i.e. in the value range [3,15].
209 +
210 +Based on these random values, the sum of all spheres is determined ({sum}) as well as the probability of pulling a red sphere ({solution}).
211 +)))
212 +|(((
213 +[[image:attach:image2017-3-23 9:0:32.png]]
214 +)))|(((
215 +The variables are included in the task text by typing the variable names {BLUE}, {RED}, and {WHITE}. In the example, the variables are included in a task of the type [[calculation (cloze)>>url:https://www.bps-system.de/help/display/ONYXintern/.Berechnungsaufgabe+v1.11||shape="rect"]].
216 +
217 +The variables and the solutions ({RED}/{sum} and {solution}) are stored for the respective gaps.
218 +)))
219 +|(((
220 +[[image:attach:image2017-3-23 9:7:8.png]]
221 +)))|(((
222 +For the test run, values within the given value ranges are randomly selected for each participant and each test attempt. In the example, the values {BLUE} = 6, {RED} = red, and {WHITE} = 10 are randomly assigned.
223 +
224 +The solutions are automatically determined for each test run on the basis of the defined values and the calculation rule.
225 +)))
226 +
216 216  == Calculation (MAXIMA) ==
217 217  
218 -The ONYX Testsuite is connected with the [[computer algebra system MAXIMA>>url:http://maxima.sourceforge.net/||shape="rect"]], which allows you to calculate variable values on the basis of other variables. To do this, you need to indicate the calculation rule in MAXIMA notation.
229 +The ONYX Testsuite is connected with the [[computer algebra system MAXIMA>>url:http://maxima.sourceforge.net/||shape="rect"]], which allows you to calculate variable values on the basis of other variables. For this purpose, you need to indicate the calculation rule in MAXIMA notation.
219 219  
220 -For further information on the MAXIMA notation, please refer to the [[MAXIMA manual>>url:http://maxima.sourceforge.net/docs/manual/de/maxima.html||shape="rect"]]. A valuable compilation of examples can be found in the form of a wiki under [[MAXIMA good practice examples>>url:https://bildungsportal.sachsen.de/opal/auth/RepositoryEntry/5499682817/CourseNode/93229879750473/wiki/Index||shape="rect"]].
231 +{{info}}
232 +For further information on the MAXIMA notation, please refer to the help pages of the [[computer>>url:http://maxima.sourceforge.net/||shape="rect"]] [[algebra system MAXIMA>>url:http://maxima.sourceforge.net/||shape="rect"]].
233 +{{/info}}
221 221  
222 222  **Possible entries are for example:**
223 223  
224 -* //Calculation (MAXIMA)//~:// 5+{a}//: The sum of 5 and the variable value {a} is calculated. Please note that the variable {a} must have been previously defined.
225 -* //Calculation (MAXIMA)//~:// sqrt({a})/(5+sqrt({b}))//~:// //MAXIMA supports mathematical expressions such as sqrt() for square root.
226 -* //Calculation (MAXIMA)//~:// 2*sin({a})+log({b})//: Further, it is possible to use trigonometric functions or the logarithm function.
227 -\\[[image:attach:Editor - Bildvariable Wertsetzung Berechnung Maxima_de.png]]
237 +* //Calculation (MAXIMA): 5+{a}: //The sum of 5 and the variable value {a} is calculated. Please note that the variable {a} must have been previously defined.
238 +* //Calculation (MAXIMA): sqrt({a})/(5+sqrt({b})): //MAXIMA supports mathematical expressions such as sqrt() for square root.
239 +* //Calculation (MAXIMA): 2*sin({a})+log({b}): //Further, it is possible to use trigonometric functions or the logarithm function.
240 +\\[[image:attach:image2017-3-22 14:38:53.png]]
228 228  
229 -
242 +=== Example "hypotenuse" ===
230 230  
231 -{{info}}
232 -The following examples for the use of numerical variables to generate random values show typical application scenarios:
244 +As an example, a typical task out of geometry will be completed. The understanding of the hypotenuse is to be examined. The solution is supposed to be derivable from the knowledge that the hypotenuse is the longest side of a right triangle. To this end, the participant is given a variety of possible solutions, from which they need to choose the correct solution.
233 233  
234 -* [[Example "Hypotenuse">>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
235 -* [[Example "Transport" - Use of random parameters>>url:https://www.bps-system.de/help/display/ONYXintern/.Beispiele+zum+Einsatz+von+Variablen+v8.X||shape="rect"]]
236 -{{/info}}
246 +|(((
247 +[[image:attach:image2017-3-23 15:6:59.png]]
248 +)))|(((
249 +(% class="WordSection1" %)
250 +(((
251 +The first step in the example is the random determination of the catheti ({k1}, {k2}) of the triangle for the definition of the task.
252 +)))
237 237  
254 +To solve the task correctly, the value for the hypotenuse ({hyp}) needs to be calculated by means of a MAXIMA equation. In addition, further possible answer options ({a}, {b}, {c}) are computed by MAXIMA.
255 +
256 +For all variables of the type floating point, the display accuracy was set to 2 decimal places.
257 +)))
258 +|(((
259 +[[image:attach:image2017-3-23 14:39:27.png]][[image:attach:image2017-3-23 14:51:31.png]]
260 +)))|(((
261 +In the example, the variables are included in a [[selection task>>url:https://www.bps-system.de/help/display/ONYXintern/.Auswahlaufgabe+v1.11||shape="rect"]]. The variables for the task text are integrated into the task by declaring the variable names {k1} and {k2}. The correct solution ({hyp}) and the alternative answers ({a}, {b}, {c}) are additionally provided in the form of answer options.
262 +)))
263 +|(((
264 +[[image:attach:image2017-3-23 14:56:46.png]]
265 +)))|(((
266 +For the test run, the values of the catheti ({k1}, {k2}) are randomly selected for each participant and each test attempt within the given value ranges.
267 +
268 +In the example, the following random values were displayed for the variables: {k1} = 4, {k2} = 13.
269 +
270 +Based on these values and the defined calculation rules, the hypotenuse and the alternative answer options are calculated, and the following values are displayed in the example task: {a} = 17.00, {hyp} = 13.60, {b} = 8.50, and {c} = 5.39 cm.
271 +
272 +Thus, the correct rounded solution for the hypotenuse in the example is 13.60 cm. The answer options {a}, {b}, and {c} can be logically excluded due to the knowledge that the hypotenuse is larger than the respective catheti and smaller than the sum of the catheti.
273 +)))
274 +
275 +
276 +
238 238  == Setting: Format display ==
239 239  
240 -For variables of the type floating point, the **number of decimal places **can be configured for the display. Please note that this setting only affects the display, not the computational accuracy and the solution comparison. This means: If the variable is used for the calculation of additional variables, the complete unrounded value will be used for the calculation. If the variable is stored as a solution for a gap (calculation interaction), the configured number of decimal places will be used for the solution display, but not for the solution comparison.
279 +For variables of the type floating point, the **number of decimal places **can be configured for the display. Please note that this setting only affects the display, not the computational accuracy and the solution comparison. This means: If the variable is used for the calculation of additional variables, the complete unrounded value will be used for the calculation. If the variable is stored as a solution for a gap (calculation task), the configured number of decimal places will be used for the solution display, but not for the solution comparison.
241 241  
242 242  
243 243  
244 -[[image:attach:Editor - Formatierung der Dezimalstellenanzeige_de.png]]
283 +[[image:attach:onyx-variables-float.png]]
245 245  
246 246  
247 247  
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1 +https://www.bps-system.de/help/display/SOV/wiki/spaces/ONYX/pages/226231171/Numerische Variablen