Example "Hypotenuse"
As an example, a typical geometry task to examine the understanding of the hypotenuse will be completed. The solution is supposed to be derived from the knowledge that the hypotenuse is the longest side of a right triangle. To do this, the participant is given a variety of possible solutions, from which they need to choose the correct one.
| The first step in the example is the random determination of the catheti ({k1}, {k2}) of the triangle for the definition of the task. The correct solution, which is the value for the hypotenuse ({hyp}), will be calculated using a MAXIMA equation. In addition, further possible answer options ({a}, {b}, {c}) will also be computed by MAXIMA. For all variables of the type floating point, the display accuracy was set to 2 decimal places. |
| In the example, the variables will be included in a choice interaction. The variables for the task text can be integrated into the task by entering the variable names {k1} and {k2}. The correct solution ({hyp}) and the alternative answers ({a}, {b}, {c}) can be additionally provided in the form of answer options. |
| The values for the catheti ({k1}, {k2}) will be randomly selected for each participant and each test attempt within the given value ranges. In the example, the following random values were displayed for the variables: {k1} = 4, {k2} = 13. Based on these values and the defined calculation rules, the hypotenuse and the alternative answer options will be calculated, and the following values displayed in the example task: {a} = 17.00, {hyp} = 13.60, {b} = 8.50, and {c} = 5.39 cm. In the example, the correctly rounded solution for the hypotenuse 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. |
