5.12 Numeric Questions - Maple T.A. 2016 Help
Maple T.A. Online Help

Instructor
Search Maple T.A. 2016 Help:

5.12 Numeric Questions

Description

A Numeric question compares a student's response to a given number. • The system automatically correctly grades equivalent numeric expressions. This question type accepts:

  • Pure numbers (without physical units) in decimal form or scientific notation
  • Numbers with units

Details:

  • Numeric questions can accept numbers without units as valid answers. The correct answer must be expressed as a number.
  • Numeric responses can also be expressed in decimal form, scientific notation (3.24E4), or as an expression (such as "1+2+3+4").
  • Equivalent numeric expressions and units are recognized. The system recognizes default unit equivalents. You can also create a question bank-specific table of equivalent units.
  • Students are prompted to enter responses in scientific or numeric format, with or without physical units.
  • You specify the inclusion of units in the correct answer using the answer.units question field. If you do not assign a value to the answer.units statement, the correct answer is dimensionless.
  • Using the optional showUnits field, you control whether the system displays the question with the Units Part text field.
  • You can control the precision and tolerance (or margin of error) required in student responses.
  • You can specify whether arithmetic is allowed in student responses.
  • You cannot use equations or algebraic formulas in the correct answer.

Important: When creating questions that have a specific number of significant digits in the correct answer, it is recommended that you use the sig function to create algorithmic variables. By using these variables in the question statement, feedback, hints, and solution, you ensure that values are displayed with the correct number of significant digits.

  • Single or multiple numeric questions can be included, along with other response objects.

Grading

Using the grading mode, you can control the precision or margin of error in the student responses graded correctly.

Precision

    exact_sigd 

The numeric value of the student response must match answer.num.

The number of significant digits in the student response must match digit.

For example, if answer.num = 2.5 and the digit = 3, only 2.50 is correct. In particular, 2.5 is incorrect.

    exact_value 

The numeric value of the student response must match answer.num.

For example, if answer.num = 2.5, 2.50 and 2.5 are correct, but 2.500001 is incorrect.

Margin of Error

    toler_perc

The numeric value of the student response must be within perc % of answer.num.

For example, if perc = 5 and answer.num = 2.5, any response between 2.5 * 0.95 and 2.5 * 1.05 is correct. In particular, 2.38888888 is correct.

    toler_abs

The numeric value of the student response must be within +/- err of answer.num. The error can be specified as a numeric value or algorithmic variable.

For example, if err = 0.25 and answer.num = 2.5, any response between 2.25 and 2.75 (inclusive) is correct. In particular, 2.333333333 is correct.

Precision and Margin of Error

    toler_sigd

The numeric value of the student response must be within +/- err in the digitth significant digit of answer.num (inclusive) and have digit significant digits. The error can be specified as a numeric value or algorithmic variable.

For example, if err = 2, digit = 3, and answer.num = 2.5, the responses 2.48, 2.49, 2.50, 2.51, and 2.52 are correct. All other responses, for example, 2.499 and 2.5, are incorrect.

For example, if err = 1, digit = 3, and answer.num = 27.18, the responses 27.1 and 27.2 are correct. Although 27.3 is within 0.1 of 27.18 rounded to 3 significant digits, it is incorrect because it is not within 0.1 of 27.18.

See Also:

Setting the Answer Format in Numeric Questions

Controlling Answer Format in Numeric Questions

Setting the Answer Tolerance in Numeric Questions

Using a Question Bank-specific Table of Units

To use a table of units, include the following statement:

qu.<topic_number>.<question_number>.units=<tablename>@

where <tablename> is a table of unit definitions in the question bank. For more information, see Using a Table of Units.

See Also:

Controlling Answer Format in Numeric Questions

Controlling Answer Tolerance

Instructions

To create a Numeric question:

  1. From the Class Homepage, click Content Repository in the top menu.
  1. From the Create New drop-down menu, select Question/Text.
  1. The Question Designer screen appears:
  • Enter a title for the question under the Question Name panel.
  • Enter the question in the Question Text.
  1. Click Response Area ().
  1. In the Edit Response Area:
  1. Under Choose Question Type, select Numeric.
  1. Weighting: specify the weight of this response area in the overall question. (By default, the Weighting is set to 1).
  1. In the Numeric Part text field, enter the numeric portion of the correct answer in symbolic math syntax. This is required.
  1. If the correct answer has physical units, in the Units Part text field, enter the units for the correct answer. To use units in addition to the default system units, you must add a custom table of units. If you do not specify units, then the system does not display a units text field in the question.

Note: To display the Units Part text field in a question for which the correct answer has no units, edit the question source to specify showUnits=true. To not display the Units text field in a question for which the correct answer has units, edit the question source to specify showUnits=false.

  • Specify the precision or margin of error for the grading of a student response.

Important: When creating questions that have a specific number of significant digits in the correct answer, it is recommended that you use the sig function to create algorithmic variables. By using these variables in the question statement, feedback, hints, and solution, you ensure that values are displayed with the correct number of significant digits. For more information, see Setting the Answer Tolerance in Numeric Questions and decimal(n, x), sig(n, x), int(x).

  1. (Optional) To add an Algorithm or Feedback to the question, see Adding and Editing Algorithms and Adding and Editing Feedback for more details.
  1. Click Save to save the question, then click Preview to view it.

Setting the Answer Format in Numeric Questions

When working with Numeric questions in the Question Editor, you can specify acceptable formatting for student responses. See Figure 5.45.

Specify Acceptable Answer Format in a Numeric Question

Figure 5.45: Specify Acceptable Answer Format in a Numeric Question


Accept 1000 separator - Student responses containing commas (,) as a separator are graded correctly.

Accept scientific notation - Student responses specified using scientific notation, for example, 2.0E2, are graded correctly.

Accept $ signs - Student responses containing a leading dollar sign ($) are graded correctly.

Accept arithmetic - Student responses specified using the arithmetic operators, that is, +, -, *, /, (), and ^, are graded correctly.

Select the style of negative numbers - Negative responses must be specified by using a negative sign (-), by enclosing in parentheses (()), or by using either notation to be graded correctly. Note: If you select the Accept arithmetic check box, then you cannot allow parentheses to be used to indicate a negative response.

See Also:

Controlling Answer Format in Numeric Questions

Setting the Answer Tolerance in Numeric Questions

When working with Numeric questions in the Question Editor, you can specify the:

  • Precision of student responses (that is, the number of digits)
  • Acceptable margin of error for student responses
  • Precision and margin of error for student responses

See Figure 5.46.

Specify Answer Precision and Tolerance in a Numeric Question

Figure 5.46: Specify Answer Precision and Tolerance in a Numeric Question


Specifying Precision

  • To require that the student response exactly matches the value of the correct answer (to floating-point limits, approximately 8 decimal places), select Require absolute accuracy. For example, if the correct answer is 2.77, the response 2.7701 is graded incorrectly.
  • To require that the student response contains a specific number of significant digits, and exactly matches the value of the correct answer, select # Figures, and then select the number of significant digits from the drop-down menu. Student responses that are correct up to the specified number of significant digits receive 50% credit.

Important: # Figures does not specify a margin of error. If you specify a correct answer value in the answer value text field with more significant digits than the number selected in the # Figures drop-down menu, all student responses are graded incorrectly. For example, if you specify 2.771 as the correct answer value, and select 3 in the # Figures drop-down menu, 2.77 is incorrect (because it does not have the same value as the correct answer value 2.771) and 2.771 is incorrect (because it has more than 3 significant digits).

Example

In a physics problem where the correct answer is 2.70, if you insist that a student enter the correct number of significant digits, you must use the # Figures option. If you select Require absolute accuracy and enter 2.70 in the answer value text field, 2.7, 2.70, and 2.700 are graded correctly, which is not the desired behavior. You must select # Figures, select 3 from the drop-down menu, and enter 2.70 in the answer value text field. In this case, the student responses 2.7 and 2.700 are graded incorrectly.

Setting a Margin of Error

  • To directly specify the margin of error, select Accept +/- err, and then enter the numeric value of the variance (or corresponding algorithmic variable) in the err text field. For example, if the correct answer is 3.142 and err = 0.001, the range of correct responses is between 3.141 and 3.143 (inclusive).
  • To specify the margin of error as a percentage of the correct answer, select Accept +/- perc%, and then enter the percentage in the perc text field. For example, if the correct answer is 3.141592 and perc = 1, the range of correct responses is between 3.11017604 and 3.17300792 (inclusive).

Specifying a Precision and a Margin of Error

  • To specify the margin of error as the tolerance in the value of a significant digit and require that same number of significant digits, select Accept +/- k in the nth place, enter the floating-point value (or corresponding algorithmic variable) of the tolerance in the k text field, and then select the significant digit from the n drop-down menu. Student responses that are correct up to the specified number of significant digits receive 50% credit. For example, if the correct answer is 2.4, k = 2, and n = 3, the correct responses are 2.38, 2.39, 2.40, 2.41, and 2.42. For example, if k = 1, n = 3, and the correct answer is 27.18, the responses 27.1 and 27.2 are correct. Although 27.3 is within 0.1 of 27.18 rounded to 3 significant digits, it is incorrect because it is not within 0.1 of 27.18.

See Also:

Setting a Margin of Error in Non-numeric Questions

Controlling Answer Tolerance

Tutorial: Setting Margin of Tolerance in Non-numeric Questions

Example 1: Creating a Simple Numeric Question

This example describes how to create a simple question that accepts a numeric response.

  1. From the Class Homepage, click Content Repository in the top menu.
  1. From the Create New drop-down menu, select Question/Text.
  1. The Question Designer screen appears:
  • Enter the following for Question Name: Multiplication.
  • Enter the following for the Question Text: What is 326 multiplied by 7?
  1. Click Response Area ().
  1. In the Edit Response Area:
  1. Under Choose Question Type, select Numeric.
  1. Weighting: specify the weight of this response area in the overall question. (By default, the Weighting is set to 1).
  1. Enter the following:
  • In the Numeric Part field, enter: 2282
  • Leave the Units Part field blank since units are not required with this response.
  1. Click OK.
  1. Click Save to save the question, then click Preview to view it. For more details, see Figure 5.47. You can test the question by selecting various responses and clicking Grade.
Numeric Example 1

Figure 5.47: Numeric Example 1


Example 2: Creating a Simple Numeric Question with Units in the Question Designer

This example describes how to create a simple question that accepts a numeric response in decimal form along with the accompanying units. This question is created in the Question Editor as a Numeric question.

  1. From the Class Homepage, select the Content Repository.
  1. From the Create New drop-down menu, select Question/Text.
  1. The Question Designer screen appears:
  1. Enter the following for Question Name: Rounding
  1. Enter the following for the Question Text: Round 2.76789 m to three significant digits.
  1. Click Response Area ().
  1. Enter the following for the Correct answer:
  • In the Number field, enter: 2.77
  • In the Units field, enter: m

Note: To require a unit with the answer, enter the correct unit dimension m (for meters) in the Units Part field. Since units are specified, the students are presented with two cells: one for the number part and one for the unit dimension. Students must enter correct values in both cells to receive full credit for the question. If you do not specify units, students are only presented with one answer cell.

  1. Leave all other fields as their default settings and then click OK.
  1. Click Save to save the question.
  1. In the Question Summary pane, click Preview to view the question as shown in Figure 5.48. You can test the question by selecting various responses.
Numeric Example 2

Figure 5.48: Numeric Example 2


Example 3: Numeric and Algorithmic Variables

  1. From the Class Homepage, select the Content Repository.
  1. From the Create New drop-down menu, select Question/Text.
  1. Enter the following title for the Question Name: Degree of a Polynomial
  1. Enter the following for the Question Text: What is the degree of $displaypoly?
  1. At the bottom of the page, click the add icon () and enter the following Algorithm:

$a=range(2,5);

$poly=maple("randomize(): randpoly(x,degree=$a)");

$displaypoly=maple("printf(MathML[ExportPresentation]($poly))");

  1. Click Refresh algorithm preview to preview the variables you defined, as shown in Figure 5.49.
Numeric Example 3 Algorithm

Figure 5.49: Numeric Example 3 Algorithm


  1. Under Choose Question Type, select Numeric.
  1. Enter the following for the Correct answer:
  • In the Number field, enter: $a
  • Leave the Units field blank since units are not required with this answer.
  1. Leave all other fields as their default settings and then click OK.
  1. Click Save to save the question and end the question authoring process.
  1. In the Question Summary pane, click Preview to view the question as shown in Figure 5.50. You can test the question by selecting various responses.
Numeric Example 3

Figure 5.50: Numeric Example 3


Example 4: Numeric Question with Units and Algorithmic Variables

  1. From the Class Homepage, select the Content Repository.
  1. From the Create New drop-down menu, select Question/Text.
  1. Enter the following title for the Question Name: Area of a Rectangular Solid
  1. Enter the following for Question Text: What is the volume of a rectangular solid $h cm high, $w cm wide, and $d cm deep?
  1. At the bottom of the page, click the add icon () and enter the following Algorithm:

$h=rint(10, 50);

$w=rint(10, 50);

$d=rint(10, 50);

$vol=$h*$w*$d;

  1. Click Refresh algorithm preview to preview the variables you defined, as shown in Figure 5.51.
Numeric Example 4 Algorithm

Figure 5.51: Numeric Example 4 Algorithm


  1. Under Choose Question Type, select Numeric.
  1. Enter the following for the Correct answer:
  • In the Number field, enter: $vol
  • In the Units field, enter: cm^3
  1. Leave all other fields as their default settings and then click OK.
  1. Click Save to save the question and end the question authoring process.
  1. Then, click Preview to view the question as shown in Figure 5.52. You can test the question by selecting various responses.
Numeric Example 4

Figure 5.52: Numeric Example 4


Next Steps

To edit further details in the Content Repository, see Editing Question Details.

See Also:

Authoring Mathematical Questions

Controlling Answer Format in Numeric Questions