5.2 Question Designer Questions - Maple T.A. 10 Help

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5.2 Question Designer Questions

Description

Question Designer questions are a more flexible and extensible form of free response questions, which can include multiple question types and response areas. It also provides a flexible layout environment, making it easy to include images, tables, and so on in your question. In this way, Question Designer questions are similar to multipart questions in that they provide a shell structure in which to embed other questions.

Question Designer questions support the following features:

  • Questions can contain multiple response cells, for example, Fill in the Blanks questions.
  • Any number of response areas. Parts of your question can require text, numeric or formula answers while other parts can require multiple choice, essay answers—all in a single question. You can even create a question designer question without any response areas. This allows you to have questions that are purely informational.
  • Response areas can anywhere in the body of a question.
  • Standard HTML elements. You can include character formatting, HTML tables, embedded images and media objects. (To import an entire HTML page as a base for creating a question, see Importing HTML Content.)
  • Any number of images, tables, algorithmic variables and inline math expressions as required.

Similar to a multipart question, each subpart of the Question Designer question must itself be a well-formed question. The only exception is that when used to define a blank inside a Question Designer question, any of the above question types may omit the question field (because this is actually defined inline in the body of the larger question statement).

Note: The Question Designer question type supersedes the Blanks and Inline question types.

See Also:

Question Types Supported in the Question Designer

Authoring in the Question Designer

Introduction: Question Types Supported in the Question Designer

  1. Essay Questions in the Question Designer can be used for a long answer response.
  1. Free Body Diagram Questions in the Question Designer can be used to ask a student to draw forces from one or more starting points (called "control points") over a background image. These forces are automatically graded.
  1. List Questions in the Question Designer are fill-in-the-blanks questions with options for text or menu input styles, exact or relaxed graders, and the ability to specify multiple correct or incorrect responses as well as partial credit for each response.
  1. Math App Questions in the Question Designer allow an instructor embed a worksheet that a student will interact with. The worksheet itself will be graded by the final state the student leaves it in.
  1. Mathematical Formula Questions in the Question Designer provide full access to the formula mode math grading behaviors, including configurable grading of equivalent symbolic algebraic and equation expressions. The six sub-modes within the Question Designer are:

Note: For specific information on each subtype, see Mathematical Formula Question Types Comparison Table.

  1. Maple-graded Questions in the Question Designer include facilities for algebra, calculus, differential equations, discrete mathematics, graphics, numerical computation, and many other areas of mathematics. You also have access to the plotting capabilities of Maple. You can plot a student response (or a function derived from a student response, for example, the definite integral of the student response) for a Maple-graded question type or display a plot for any question type. You can also use functions and routines that are contained in a separate Maple Repository (Maple Library). You can access your personal Maple library archives from within your Maple questions.
  1. Multiple Choice Questions in the Question Designer (one answer) can be authored in a fixed order or randomized. Answer choices can also be displayed horizontally or vertically.
  1. Numeric Questions in the Question Designer can be defined to require a number and a unit dimension or simply a number as the answer. You can set grading tolerance and answer precision using one of four methods.
  1. Sketch Questions in the Question Designer can be used to create and/or operate on various sketch types.

Using the Question Designer, you can enter the question text and the correct answers wherever they appear. Questions can contain multiple response cells that may all be different types. For more details on authoring each question type in Question Designer, see Authoring in the Question Designer.

Grading

Question Designer questions are graded individually, depending on the types of questions embedded. The Question Designer supports all the features offered with that individual question type (for example, margin of error, significant figures, and tolerance). For more details, see the grading policies for the respective questions within the Question Designer.

Authoring Tips

Formatting Tips

The Question Designer makes it easy to apply formatting to your question in many of the same ways you use your word processor. There are a few limitations and requirements unique to the editor. These tips are offered to help you achieve the best results.

As with other web content, you may observe differences in the display of your question in various operating systems and browsers.

Character Formatting
  • Use the toolbar buttons to apply character formatting.
  • HTML tags are allowed and will be rendered as HTML
Math expressions in Questions
  • Use the Equation Editor to enter expressions by clicking the () icon, as shown in Figure 5.1.
  • Right-click (Control-click, Macintosh) in the input field to display palettes. See Figure 5.2.

Access the Equation Editor in the Question Designer

Figure 5.1: Access the Equation Editor in the Question Designer


Equation Editor Palettes

Figure 5.2: Equation Editor Palettes


Algorithmic Variables in Questions
  • Insert variables by typing their name. Use the required "$" at the beginning of the variable name: $variable.
Displaying the $ Sign and the @ Symbol in Questions
  • Insert the "$" sign by using the escape sequence "\", as follows: \$.
  • Insert the "@" symbol by using the escape sequence "\" as follows: \@.

Important: When saving elements, remember to click Finish to save changes. If you change a value by simply typing content and do not click Finish, your changes will be lost.

Authoring in the Question Designer

Instructions

To create a Question Designer question:

  1. From the Class Homepage, select the Questions menu.
  1. Click New Question.
  1. On the Question Type list, click Question Designer.
  1. It is recommended that you enter a description in the Question Description text field. (The description is used to label the question in the topic. If excluded, the question type is used.)
  1. You can add algorithms or feedback. For more details, see Adding and Editing Algorithms and Adding and Editing Feedback.
  1. To proceed to the Question Details screen, click Finish.
  1. On the Question Details screen,
  1. In the text box, enter the question statement.
  1. Click Insert/Edit Response Area ().
  1. Select a question type and define the properties for that question type. Click OK.
  1. The properties are now displayed in the Text of the question panel.
  1. You can add multiple parts to a question using the Question Designer by inserting additional response areas.
Editing Information Fields, Hints, Feedback, or Algorithms
  1. Click Finish to place a copy of your question in the web site cache and preview your question.

Essay Question

To create an Essay question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter the essay question in the Question Text.
  1. Click Insert/Edit Response Area ().
  1. Select the Essay question type in the Edit Response Area dialog.
  1. Indicate the number of rows and columns (length) of the response area for the essay question and click OK.
  • You can define the size of the essay blank using rows and columns. A typical screen-width size is 65-70 columns wide. Rows directly correspond to the lines of text you want to provide in a typical response.
  • If a student enters more text than will fit in the preconfigured text window, the cell will automatically insert a scroll bar and allow the student to continue his or her response.
  1. Click OK and then Finish to save and preview the question.

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

Free Body Diagram Question

To create a Free Body Diagram question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text.
  1. Click Insert/Edit Response Area ().
  1. On the Choose Question Type list, select Free Body Diagram.
  1. Complete the following fields:
  1. Click OK and then Finish to save and preview the question.

See Also:

List Question

Description

A List question is a Fill in the Blanks question offered in the Question Designer exclusively. It offers some advanced features, including the ability to give partial credit to certain answers. List questions can be used to present a drop-down list or a free response area. In both cases, you set a single response object in the question. To include multiple response areas in a single question, use the Question Designer question type.

List questions provide the following features:

  • You can define multiple correct (and even incorrect but expected) answers.
  • For each specified answer, you can control the amount of credit awarded for each specified answer.
  • For each specified incorrect answer, you can define response-specific feedback.
  • You can define the display style for the student response input cells - either text or menu style display for student response objects (entry cells).
  • Graders can be set to exact or the more lenient relaxed style.
Grading
Graders
  • Default grader: "exact"
  • Option: "relaxed" (set grader=relaxed)
  • Option: "regex" (set grader=regex) (This provides access to the student response set as a regular expression, for interacting with custom graders.)
Input Display Style
  • Default display: "textbox"
  • Option: "menu" To change the order of menu entries, set display.permute = false
Sizing of Textbox Blanks
  • Blanks sizing: based on max of answer length
Full and Partial Credit
  • At least one answer field must give full credit
  • All other answers can be set for credit from 0-1 (specified in decimal numbers)
Grading Algorithm

Grading is done by comparing the student response with each answer in order until a match is found, and the corresponding credit is then returned. If no match is found, the credit is zero. The emphasis on comparing in order is necessary because someone writing regular expression questions might start with a very specific criteria for full credit and then allow more vague criteria for low credit.

Updating Example 1 on List Question Source Script, if the answers and credits are changed to:

qu.1.1.answer.1=(E|e)instein@
qu.1.1.credit.1=1.0@
qu.1.1.answer.2=(E|e).*@
qu.1.1.credit.2=0.1@

then "Einstein" and "einstein" receive full credit and any other response beginning with "E" or "e" receives 10%. If the order of the two criteria is reversed, it is impossible to receive full credit.

See Also:

Rules for Grading Fill in the Blanks Questions

Fill in the Blanks Questions

List Question Source Script

Instructions

To create a List question:

  1. Select the Questions menu, then New Question. The Question Editor is displayed.
  1. On the Question Type screen, select Question Designer.
  1. Enter the Question Name.
  1. Enter your question in the Question Text.
  1. Click Insert/Edit Response Area ().

In the Edit Response Area dialog:

a. Under Choose Question Type, select List.

b. Weighting: specify the weight of this response area in the overall question.

c. Matching Type:

  • To apply strict grading, case-sensitive, and literal string-matching as your grading mode, set the matching type to Exact text match.
  • To invoke a less stringent grader that ignores case sensitivity and punctuation, select Ignore case text match.
  • You can also select Regular expression match to customize the grading routine.

When the display type is Text field, you can set the grading standards.

d. Display Type:

  • The default Display Type is Text field, which presents students with a blank response area and allows you to set the grading standards.
  • Select Drop-down menu to present students with a drop-down menu of choices. Note: Permute list will create a different order each time the drop-down list is generated.

e. Enter the answer choices in the Item fields. To add additional choices, click Add Item. To delete items, click Delete Item.

f. Edit the Weight in the table as desired, using 1 (fully correct) or any decimal value between 0 and 1 for partially correct answers.

  1. Click OK.
  1. To add an Algorithm or Feedback, see Adding and Editing Algorithms and

Adding and Editing Information Fields.

8. Click Finish to save the question.

9. In order to view the question and test it by selecting various responses, click Preview.

Example

In this example, you are guided through the creation of a list question using the Question Designer. List questions serve two purposes: to ask students to select from a list of entries, or to fill in the blanks. This example uses a list of entries.

This question is created in the Question Editor as a Question Designer question.

To create a List question:

  1. Select the Questions menu, then New Question. The Question Editor is displayed.
  1. On the Question Type screen, select Question Designer.
  1. Enter the Question Name: Question Designer List
  1. In the Question Text field, enter the following: Who introduced the Arabic number system to Europe?
  1. Click Insert/Edit Response Area ().

In the Edit Response Area dialog:

a. Under Choose Question Type, select List.

b. Weighting: specify the weight of this response area in the overall question.

c. Under Matching Type, select Ignore case text match.

d. Under Display Type, choose Drop-down Menu.

e. Enter the following answer choices in the Item and Weight fields, as shown in Figure 5.3 below.

Item

Weight

Rene Descartes

0.0

Leonardo Fibonacci

1.0

Marcel Duchamps

0.0

Note: As you add expected answers the system assigns them a default credit value of "0.0" in the right column. Edit the Weight as desired, using 1.0 (fully correct) or any decimal value between 0.0 and 1.0 for partially correct answers. See Figure

List Response Area in the Question Designer

Figure 5.3: List Response Area in the Question Designer


6. Click OK, to see Figure 5.4:

List Question in the Question Designer

Figure 5.4: List Question in the Question Designer


7. To add an Algorithm or Feedback, see Adding and Editing Algorithms and

Adding and Editing Information Fields.

8. Click Finish to save the question.

9. Click Preview to view the question and test it by selecting various responses.

Next Steps

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

See Also:

Rules for Grading Fill in the Blanks Questions

Question Designer Question Example using Various Embedded Questions

Algorithmic Multiple Selection Question Source Script

Multiple Selection Question Source Script

Maple-graded

To create a Maple-graded question:

  1. Enter a question in the Question Text panel.
  1. Click Insert/Edit Response Area ().
  1. Select the Maple-graded question type in the Edit Response Area dialog.
  1. Select an Expression type: Formula or Maple Syntax.
  1. Using Maple code, enter the correct answer in the Answer field. For example, if the question is find the indefinite integral of sin(x), then the Answer field must contain the Maple code int(sin(x),x);
  1. By default, the Maple code to grade the student answer is given as: is(($ANSWER)-($RESPONSE) = 0);
  1. Click OK and then Finish to save and preview the question.

Maple-graded Response Area in the Question Designer

Figure 5.5: Maple-graded Response Area in the Question Designer


Options

  • You can enter Maple code to plot the student answer. For example, enter an expression in x. The Maple grading code is plot($RESPONSE, x=0..10);
  • You can access your personal Maple library archives from within your Maple questions. You must first upload your archive files into the class file space on the server. When you create a Maple-graded question, you specify the location of the archive as part of the question definition. When executing the Maple code associated with that question, the Maple libname variable is set automatically to access the archive files specified. Click the blank field in the Maple repository row and enter the library location.

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

Math App

To create a Math App question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text. Optionally, enter the question using symbolic math by clicking the Equation Editor ()icon. The Equation Editor opens. See Formatting Tips.
  1. Click Insert/Edit Response Area ().
  1. Select the Math App question type in the Edit Response Area dialog:
  • In the Choose Worksheet section, click the button to choose or upload a new worksheet to use in the question.
  • In the Initialization Parameters section, declare any variables that you want the worksheet you chose above to initialize when the question loads. This is not a requirement, you can leave it blank if there are no variables to initialize in the worksheet.
  • In the Select the type of grading used section, choose which type of grading is going to be used to grade the final state of the worksheet.
  • Click OK and then Finish to save and preview the question.

For more details on Math App questions, see Math App Questions.

Mathematical Formula

To create a Mathematical Formula question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text. Optionally, enter the question using symbolic math by clicking the Equation Editor ()icon. The Equation Editor opens. See Formatting Tips.
  1. Click Insert/Edit Response Area ().
  1. Select the Formula question type in the Edit Response Area dialog.
  1. Select a formula math grader by clicking Sub-type drop-down list.
  1. Enter the answer in the Answer field.
  1. Click OK and then Finish to save and preview the question.

Formula without Simplification

There is one subtype of Mathematical Formula question that can only be authored in the Question Designer. This is called Formula without Simplification, where the answer must be left in its unsimplified form to be graded correctly. In other words, if the instructor states that they would like the answer to be left in unsimplified form, the student would leave their answer in the form , rather than simplify to

Example

To create a Formula without Simplifcation subtype question:

  1. From the Class Homepage, click the Questions menu.
  1. Click New Question.
  1. In the Question Type list, click Question Designer.
  1. Click Insert/Edit Response Area ().

In the Edit Response Area dialog:

a. Weighting: specify the weight of this response area in the overall question.

b. Under Sub-type, select Formula without Simplification.

c. Answer: enter the correct answer. See Figure 5.6 below.

Formula without Simplification in Question Designer

Figure 5.6: Formula without Simplification in Question Designer


d. Click OK.

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text. Optionally, enter the question using symbolic math by clicking the Equation Editor ()icon. The Equation Editor opens. See Formatting Tips.
  1. To add an Algorithm or Feedback to the question, see Adding and Editing Algorithms and Adding and Editing Feedback.
  1. To proceed to the Question Details screen, click Finish.
  1. To view and test the question, click Preview.
Next Steps

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

See Also:

Mathematical Formula Question Types Comparison Table

Multiple Choice

To create a Multiple Choice question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text.
  1. Click Insert/Edit Response Area ().
  1. Select the Multiple Choice question type in the Edit Response Area dialog.

Multiple Choice Response Area in the Question Designer

Figure 5.7: Multiple Choice Response Area in the Question Designer


  1. Select Single for one correct answer or Multiple for multiple correct answers.
  1. To rearrange the order of the displayed choices, select Permuting.
  1. Select the display format of the choices in a table: Vertical or Horizontal.
  1. For Choices: enter the text that defines the choices for the question.

  1. Click OK. The Edit Response Area dialog opens. Select the correct values.

  1. Click OK.

  1. Click Finish to save and preview the question.

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

Numeric (with or without required unit dimensions)

To create a Numeric question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text.
  1. Click Insert/Edit Response Area ().
  1. Select the Numeric question type in the Edit Response Area dialog.
  • Numeric questions can accept numbers without units as valid responses. The correct answer must be expressed as a number. The student response can be an expression (such as "1+2+3+4").
  • Numeric responses can be expressed in decimal form or scientific notation (for example, 3.24E4).
  • To require units, enter a unit in the Units Part field (for example, m for meters). If you do not enter a required unit dimension, the system displays only a single response cell that accepts only numbers. If you do enter a unit dimension, students are presented two cells, one for the number part and one for the unit part. The student must enter correct values in both cells to receive full credit.
  • Correct answers can be specified with a margin of error or range of tolerance.
  • Algorithmic variables can be created for use in the question statement, answer, hint, feedback, and solution fields.
  • The system automatically grades equivalent numeric expressions correct
  1. Click Finish to save and preview the question.

Numeric Response Area in the Question Designer

Figure 5.8: Numeric Response Area in the Question Designer


To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

See Also:

Question Types Supported in the Question Designer

Sketch

To create a Sketch question:

  1. Enter a title for the question under the Question Name panel.
  1. Enter a question in the Question Text.
  1. Click Insert/Edit Response Area ().
  1. Select the Sketch question type.
  1. Complete the fields in the Edit Response Area dialog. For more information on each entry, see the following:
  1. For Correct Answer, use the sketch tools provided to plot the correct response.
  1. Click OK and then Finish to save and preview the question.

See Also:

Free Body Diagram Questions

Description

Free Body Diagram questions can be used to ask a student to draw forces from one or more starting points (called control points) over a background image.

Grading

Students are graded on their ability to correctly answer:

  1. The type of force
  1. The number of forces
  1. The control point or points
  1. The correct angle or angles

No partial marks are assigned, however, you can specify a question-wide tolerance on the angles. By default, this tolerance is five degrees. You can also customize how angles are matched on a per-force basis. For more details, see Customizing How Angles Are Matched.

Customizing how angles are matched

When comparing the angles of a student’s force and a correct answer force, Maple checks whether the angles agree to within the question-wide angle tolerance described above. This default behavior can be overridden for each force. There are three angle tolerance options available to each correct answer force. They are as follows:

  • default: specifies a question-wide tolerance on the angles, which is five degrees by default.
  • collinear: ensures that the student’s forces lie along the same line as the answer force, within the question-wide angle tolerance.
  • any: matches the name of any student force against the name of the answer force, regardless of angle.

The author specifies how angles are matched by:

1. Click Edit Source.

2. Complete the angleCriteria field by specifying default, collinear, or any.

For example, suppose the correct answer consists of three forces: a default angle matching for the first, collinear for the second, and any for the third. This would be specified as:

angleCriteria = ["default", "collinear", "any"]@

Alternatively, the instructor could supply their own Maple comparison procedure rather than saying collinear or any. This procedure must accept exactly three input arguments: two angle values in the range from 0 to 360, followed by a nonnegative tolerance value, and it must return either true (meaning that the angles are considered equivalent) or false. For example, the following procedure checks if two angles are in the same quadrant:

proc(a1, a2, tol) evalb(a1>=-tol and a2>=-tol and a1<=90+tol and a2<=90+tol or a1>=90-tol and a2>=90-tol and a1<=180+tol and a2<=180+tol or a1>=180-tol and a2>=180-tol and a1<=270+tol and a2<=270+tol or a1>=270-tol and a2>=270-tol); end proc

Maple will replace the third argument with the question’s angle tolerance value.

Instructions

To create a Free Body Diagram question:

  1. From the Class Homepage, select the Questions menu.
  1. Click New Question.
  1. On the Question Type list, click Question Designer.
  1. Enter the question in the text box.
  1. Click Insert/Edit Response Area ().
  1. Under the menu options Choose Question Type, select Free Body Diagram. The Edit Response Area window is shown in Figure 5.9.
Free Body Diagram Authoring

Figure 5.9: Free Body Diagram Authoring


Edit Response Area:

Weighting

Specify the weight of this question in the overall assignment.

Angle tolerance

Define the angle of tolerance (in degrees). When the question is graded, the acceptable answer is within a tolerance range of whatever is specified. The default is 5.0 degrees.

Background Image

This is mandatory. To upload a background image, click Browse to select an image from the Class File Manager.

Creating a subfolder
  1. Right click on Files to create a subfolder.

2. Enter a name for the new folder and click OK.

3. Click Upload to load new images into the folder.

4. Double click on the image to select it.

5. Scroll down to confirm that the image was added to the diagram.

Note: The drawing board is 600 by 450 pixels. If you upload a background image whose width exceeds 600 pixels or whose height exceeds 450 pixels, the image will be scaled down (aspect ratio preserved) to fit the drawing board.

Show instructions

Specify whether Maple T.A. should display its default introductory instructions for this tool to students, by choosing Yes (the default) or No from the drop-down menu.

Select forces

Select the check boxes beside the forces you want to include in the free body diagram.

To add a force that is not listed, define a new type of force by assigning it an abbreviation (Abbr.) and a force name (Name). Click Add Force Type to have the customized force added to the bottom of the list.

Once you have finished adding forces, click Update force selection list below.

Add control points

Enter the Control Point Label and then click Add. Automatically, the control point will be added to your free body diagram. To move it, click the control point and drag it to its new location. Once the control point label has been added, click Update Label to modify it or Delete to delete it. Multiple control points can be added to the free body diagram, from which multiple forces can be drawn.

Add a force

Select a force from the drop-down menu. A force can be selected multiple times. Assign an Angle (in degrees) and if applicable, a control point as its Origin, to each force and click to add the force to the free body diagram preview.

Note: Valid angles are between -180 and 360 degrees, inclusive. Half angles are accepted as well; for example, 100.5 degrees.

List of forces

All forces added to the diagram appear in a table at the bottom.

Selecting a force

To select a force, use one of the following methods:

  • Click the force in the diagram.
  • Click the force within the table.

Both options result in the force being highlighted blue. Also, a blue point, or handle, appears at the tip of the drawn force.

To change the angle of a selected force
  1. Drag its handle on the diagram. This approach also affects the arrow's length. This, however, has no impact on the grading since force magnitudes are not considered.
  1. Enter an angle (in degrees) on the table and press Enter.

To change the type of a selected force or to move that force to a different control point (if applicable), use the corresponding drop-down menus in the table row. To delete forces, click Delete Force. Also, the entire list of forces can be deleted by clicking Clear All.

Examples

To view Free Body Diagram question examples:

  1. From the System Homepage, select the class called Maple T.A. Readiness Class.
  1. From the Assignments panel, click Free Body Diagram Questions, as shown in Figure 5.10 below.

Note: Alternatively, you can view Free Body Diagram questions individually through the Question Repository by selecting the group called Free Body Diagram Questions.

Free Body Diagram Questions in the Readiness Class

Figure 5.10: Free Body Diagram Questions in the Readiness Class


Next Steps

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository.

Sketch Questions

Description

Sketch questions can be used to ask students to:

  • Graph one or multiple lines or curves.
  • Indicate which region represents the solution set (cases: single line or curve; multiple lines or curves).
  • Make the line solid or dashed to indicate whether the line is in the solution set.
  • Remove the portion of the line or curve that does not belong.
  • Use an open or closed circle to indicate whether the endpoints belong.
  • Add asymptotes to logarithmic and exponential curves.

Sketch questions do not currently support algorithmically generated sketches.

Grading

When one curve is graded, Sketch questions are graded correct or incorrect. No partial credit is assigned.

However, if there are multiple curves graphed, the student may receive partial credit for having a partially correct response. For example, partial grading of inequalities as follows:

  • If there are n lines, then n+1 points are given.
  • One point is given for each line, assuming both the slope and the strict/nonstrict property are correct.
  • One point is given for the region if all the lines are correct.
  • These points are summed and divided by n+1 to produce a number from 0 to 1.

Partial credit is also applied to exponential and logarithmic curves. They are each graded out of two points: one point for the curve and one point for the asymptote. The final result is divided by two to achieve the final grade.

Customizing tolerance in Sketch questions

For Sketch questions, Maple T.A. uses a built-in tolerance to determine how close the instructor and the student's curves must be to one another for the response to be deemed correct. The closer the value is to zero, the more accurate the response must be to be graded correct.

Note: After the question has been created, the grading code can be modified by clicking Edit Source and adding a tolerance option to the command Grading:-GradePlot.

The default grade code is:

op(1,[Grading:-GradePlot($ANSWER, $RESPONSE, $PLOTVIEW)]);

To specify the tolerance, change the grading code to:

op(1,[Grading:-GradePlot($ANSWER, $RESPONSE, $PLOTVIEW, tolerance=__)]);

where __ is a numeric value between 0.0 and 1.0, with 1.0 being the most lenient.

For more details on this option, refer to the Grading:-GradePlot help page in the Maple help system.

Instructions

To create a Sketch question:

  1. From the Class Homepage, select the Questions menu.
  1. Click New Question.
  1. On the Question Type list, click Question Designer.
  1. Enter the question in the text box.
  1. Click Insert/Edit Response Area ().
  1. Under the menu options Choose Question Type, select Sketch. The Edit Response Area window appears.

Edit Response Area:

The Edit Response Area is shown below in Figure 5.11.

Edit Response Area for a Sketch Question

Figure 5.11: Edit Response Area for a Sketch Question


Weight

Specify the weight of this response area in the overall question.

Axes

Define the ranges for the x-axis and y-axis in the Axes field. Numerically these numbers represent the x-axis minimum value, x-axis maximum value, y-axis minimum value, and y-axis maximum value, respectively.

Tickmarks

These values define the tickmarks on both axes. Numerically these numbers represent x-axis major tickmarks, x-axis minor tickmarks, y-axis major tickmarks, and y-axis minor tickmarks, respectively. Labels are placed at major tickmarks. When gridlines are drawn, they are drawn through all the tickmarks.

Example setting tickmarks

Therefore, setting the axes to -20, 20,-10, 10 and tickmarks to 4,5,4,5 would result in the following:

x-axis:

The x-range is from -20 to 20;

It is divided into four equally-spaced intervals, resulting in major tickmarks and labels at -20, -10, 0, 10, and 20; and

Each interval is further divided into five equally-spaced subintervals, resulting in a minor tickmark every two units.

y-axis:

The y-range is from -10 to 10;

It is divided into four equally-spaced intervals, resulting in major tickmarks and labels at -10, -5, 0, 5, and 10; and

Each interval is further divided into five equally-spaced subintervals, resulting in a minor tickmark every (one) unit.

Grid

Define whether the gridlines are displayed (true) or not displayed (false).

Background functions

This allows the author to pre-populate the sketch board with some curves drawn in the background, purely for display purposes. Background functions are not graded.

Example setting background functions

For instance, if you would like to show the sine curve and the main diagonal (as dashed), then set the background functions to the following:

x:dashed; Math.sin(x)

Important: Use a semicolon-separated list. In addition, functions need to be in JavaScript syntax (e.g. Math.pow(x,2) as opposed to x^2).

Group plots

Use the drop-down menu options, Yes or No, to specify whether all your curves belong to one mathematical relation (for example, a piecewise function) or separate functions. See Adding Multiple Graphs to the Sketch Board for more information.

Important: The Axes, Tickmarks, Grid, and Background functions properties can be changed or updated by clicking Update. The exception is Group plots, which should be specified before sketching questions using the sketch board.

Correct answer

You must graph the correct response in the sketch section provided in Figure 5.12.

Sketching the Correct Response

Figure 5.12: Sketching the Correct Response


Creating Basic Sketch Questions

The sketch board is a set of tools that can be used to create and/or operate on various sketch types. Table 5.2 summarizes the different types of graphs available in Maple T.A.

Table 5.2: Different Types of Graphs Available in Maple T.A.

Graph Type

Tool(s) Used

How to Use Them

Line

Draw two points.

Parabolic function

Draw the vertex and then a second point.

Absolute value function

Draw the vertex and then a second point.

Exponential function

Draw two points and then the horizontal asymptote.

Logarithmic function

Draw two points and then the vertical asymptote.

Solution set (region) for a system of linear inequalities

, ,

Draw the line(s), make certain line(s) dashed as needed, and finally specify the correct region by clicking inside it.


Note: Currently, a region can be created with at most two lines drawn on the sketch board. To remove any unwanted graphs, click Delete (). At any point in the creation of a graph, you can abort by simply clicking in the toolbar.

Graph types and graphing instructions

This section provides detail on each graph type and how to specifically graph it.

To graph a line
  1. Click Draw a Line (). This enables you to plot points on the coordinate grid.
  1. Plot two points on the coordinate grid. After you plot two points on the grid, a line is drawn through these points.
  1. To change the line, you can move either of the two points anywhere on the grid. You can also move the entire line by clicking and dragging on the line.
  1. To delete the line, click Delete () and then click the object you want to delete.
  1. To save changes in the Edit Response Area, click OK.
To graph a parabola
  1. Click Draw Parabola (). This enables you to plot points on the coordinate grid that can be moved to shape and position the parabola.
  1. On the coordinate grid, plot the vertex first followed by another point on the parabola.
  1. You can change the parabola by dragging either of the two points anywhere on the grid. This will stretch, compress, reflect, or translate the parabola.
  1. To delete the parabola, click Delete () and then click on the object you want to delete.
  1. To save changes in the Edit Response Area, click OK.
To graph an absolute value
  1. Click Draw Absolute Value (). This enables you to plot the vertex and an additional point on the coordinate grid.
  1. Plot the vertex first followed by an additional point on the grid. The absolute value graph is drawn automatically.
  1. You can change the absolute value graph by dragging either of the two points anywhere on the grid. This will stretch, compress, reflect, or translate the absolute value.
  1. To delete the absolute value graph, click Delete () and then click on the object you want to delete.
  1. To save changes in the Edit Response Area, click OK.
To graph an exponential curve
  1. Click Draw Exponential (). This enables you to plot two points and a horizontal asymptote.
  1. Plot two points on the exponential curve.
  1. Plot the horizontal asymptote for the curve: Click the location on the coordinate grid where you want to place the horizontal asymptote. A dashed, horizontal line is automatically drawn through the point on the grid where you clicked. If you would like to move this horizontal asymptote, simply drag it to its new location.
  1. To delete the exponential curve, click Delete () and then click on the object you want to delete.
  1. To save changes in the Edit Response Area, click OK.
To graph a logarithmic curve
  1. Click Draw Logarithmic (). This enables you to plot two points and a vertical asymptote.
  1. Plot two points on the logarithmic curve.
  1. Plot the vertical asymptote for the curve: Click the location on the coordinate grid where you want to place the vertical asymptote. A dashed, vertical line is automatically drawn through the point on the grid where you clicked. If you would like to move this vertical asymptote, simply drag it to its new location.
  1. To delete the logarithmic curve, click Delete () and then click on the object you want to delete.
  1. To save changes in the Edit Response Area, click OK.
Indicating a region of the graph

To indicate which region on the graph represents the solution set:

  1. Click Choose Region (). This enables you to select a region on either side of a single line or select a region bounded by two lines.
  1. Click anywhere inside the region that represents the solution set to the problem. The region is automatically shaded.
  1. To delete this shaded region, click Delete () and then click anywhere in the shaded area that you want to delete.
  1. To save changes in the Edit Response Area, click OK.
Using solid or dashed lines
  1. Click Toggle Solid/Dashed (). This enables to you to switch between solid and dashed lines interchangeably.
  1. Click on a line. If the line was solid, then the entire line becomes dashed. To change the line back to solid, click the line again and it will revert back to its original state.
  1. To delete the solid or dashed line, click Delete () and then click on the line you want to delete.
  1. To save changes in the Edit Response Area, click OK.

Adding Multiple Graphs to the Sketch Board

More than one graph can be placed on the sketch board, for instance two lines and a parabola. By default, each graph added is treated as a separate mathematical relation and drawn with a different color.

To treat multiple graphs as belonging to the same relation:

  1. In the Group Plots drop-down menu, select Yes.
  1. Click Update.

Use this option in particular when constructing a sketch that represents a piecewise function. The pieces themselves can be created as subcurves as described in CreatingSubcurves.

Important: Whenever you are specifying the Group Plots option, you must do so before adding any graphs to the sketch board.

Controlling the drawing tools (buttons) students receive

As you add graphs to the sketch board, Maple T.A. automatically decides on an appropriate set of drawing tools (buttons) for students to work with, and how many of any given curve type they can draw. This is done to prevent students from cheating by drawing more of a given type of graph compared to what the the author has drawn. For example, if you draw two lines then students will be given the line tool and be able to draw up to two lines. Students are also given the Delete () icon. Maple T.A. stores this information in Options under Visible buttons. In the rare case where you want to override this setting, click Edit source, Options and then change the Visible buttons.

Creating Subcurves

The graph of any line or parabola can be restricted either to an interval or to a pair of half-bounded subintervals. Endpoint(s) of the resulting subcurve(s) can be filled or open circles to indicate whether they are included or excluded.Table 5.3 describes the different options available.

Table 5.3: Subcurves Available in Maple T.A.

Subcurve Construction

Tool(s) Used

How to Use Them

Restrict a curve to a half-bounded interval that is bounded to the left

Click at any location on the parabola (not necessarily on a point that was used to define the curve) to discard what lies left of it.

Restrict a curve to a half-bounded interval that is bounded to the right

Click at any location on the parabola (not necessarily on a point that was used to define the curve) to discard what lies right of it.

Restrict a curve to a fully-bounded interval

,

Perform a Snip-Left operation at one location on the curve and a Snip-Right at another.

Restrict a curve to a pair of half-bounded intervals

Click at two locations on the curve to discard what lies in between.

Indicate whether an endpoint is itself included in the subcurve

Click on an endpoint to toggle between open and filled.


Subcurve types and graphing instructions

This section provides detail on each subcurve type and how to specifically use it.

Removing a Portion of a Line or Parabola to the Left or Right of a Point

To remove a portion of a line or parabola:

1. Click Snip Left () or Snip Right (). These tools enable you to remove a portion to the left or right (respectively) of a location on the parabola.

2. Click on the portion of the parabola you want to keep. If you selected Snip Left in the previous step, the portion of the parabola to the left of your cursor is removed. Similarly, if you selected Snip Right in the previous step, the portion of the parabola to the right of your cursor is removed.

3. To save changes in the Edit Response Area, click OK.

Removing a Portion of a Line or Parabola between Two Points

To remove the portion of a line or parabola between two points:

1. Click Snip Between (). This enables you to remove a portion of a parabola between two selected points.

2. Select two points on the parabola by clicking on them. A solid, green point indicates each selected location. The portion of the parabola between these two solid, green points is automatically removed.

3. To save changes in the Edit Response Area, click OK.

Note: The operation creates two graphs or subcurves. Recall that two graphs are treated as two separate mathematical relations by default. To have them treated as belonging to one relation instead (such as a piecewise function); choose Yes under the Group plots option as described in Adding Multiple Graphs to the Sketch Board.

Including or Excluding Endpoints

To indicate the position of endpoints on the graph:

1. Click Toggle Filled/Hollow (). This enables you to toggle back and forth between filled (included) and open (excluded) endpoints.

2. Click on the endpoint that you want to include or exclude. If the endpoint is filled (included), click on it to make it open (excluded). Similarly, if the endpoint is open (excluded), click on it to make it filled (included).

3. To save changes in the Edit Response Area, click OK.

Examples

To view Sketch question examples:

  1. From the System Homepage, select the class called Maple T.A. Readiness Class.
  1. From the Assignments panel, click Sketching Questions, as shown in Figure 5.13 below.

Note: Alternatively, you can view Free Body Diagram questions individually through the Question Repository by selecting the group called Sketching Questions.

Sketching Questions in the Readiness Class

Figure 5.13: Sketching Questions in the Readiness Class


Next Steps

To edit further details in the Question Repository within the Question Designer, see Editing Question Details in the Question Respository

See Also:

Question Designer Question Example using Various Embedded Questions

Adaptive Question Designer Questions

Plotting Using Maple