5.14 Sketch Questions - Maple T.A. 2016 Help
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5.14 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 correctly or incorrectly. 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 correctly.

Note: After the question has been created, the grading code can be modified by clicking Edit > 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, click the Content Repository.
  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. Under Choose Question Type, select Sketch.
  1. The Edit Response Area window appears, which is shown below in Figure 5.53.
Edit Response Area for a Sketch Question

Figure 5.53: Edit Response Area for a Sketch Question


7. To complete the fields in the Edit Response Area window, see the section Defining a Sketch Question below for more information:

8. Click OK.

9. Then click Save to save the question.

Defining a Sketch Question

Weighting

Specify the weight of this response area in the overall question. By default, the Weighting is set to 1.

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

Using the sketch tools, plot the correct response in the sketch section provided. Figure 5.54.

Sketching the Correct Response

Figure 5.54: 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 5.5 summarizes the different types of graphs available in Maple T.A.

Table 5.5: 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.
To create drag and drop curves (supply and demand curves)
  1. Click Three-point parabola segment (). This will activate ‘Draw three-point PARABOLA SEGMENT’ mode. The button will light up in red to indicate that you are now in this mode.

TIP: This is not to be confused with the adjacent ‘Draw three-point PARABOLA’ button which would have the curve extend beyond your control points and to the edges of the sketch board, which is not necessarily ideal for supply/demand questions.

  1. Now exactly as the button’s tooltip describes, click at three locations on the sketch board to define the control points. Upon adding the third and final point, the points will be interpolated quadratically.
  1. Adjust the supply curve to your liking, by dragging the curve and/or its control points.
  1. Draw the demand curve, by repeating the procedure described in steps 1 and 2.

  1. Draw the equilibrium point. Click to activate ‘Plot DROPLINE POINT’ mode, which in general lets you place a point anywhere on the sketch board. The button will light up in red to indicate that you are now in this mode.
  1. Click where the supply and demand curves intersect to place the point at that location, thereby representing the equilibrium point as depicted in the following figure.

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 Creating Subcurves.

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 (icons) 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 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 5.6 describes the different options available.

Table 5.6: 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 5.55 below.

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

Sketching Questions in the Readiness Class

Figure 5.55: Sketching Questions in the Readiness Class


Next Steps

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

See Also:

Plotting Using Maple