Introduction to Graphing
The graphing tool provides a versatile way to explore and analyze mathematical concepts. It supports graphing linear, exponential, and quadratic equations, as well as plotting individual points for custom visualizations. With features like adjustable asymptotes, it offers flexibility and precision, making it suitable for a variety of teaching and learning needs. Use this guide to get started.
Add a Graphing question
1. Click on the blue + button to open the 'Add Item' window
2. Choose Graphing from the Paid Questions list
3. Click the dropdown and choose from linear, quadratic, exponential, or points.
4. Click the graph to plot points to set your answer key. You must plot 2 points to create a line.
To remove a point, simply click the point you would like to remove.
You are also able to drag points even once placed.
Changing the graph type will also change the line.
5. Opening the Graph settings allows you to add up to 4 graphs, as well as toggle on Student settings to manipulate the graph.
If multiple graphs have been added; you will simply click on the graph number to add data.
You can also designate to show tick marks in decimals or fractions format
6. Access the student preview to see how one, or multiple, graphs would look for your students. When a graphing question is added; students will get instructions on how to use the graph.
Adjust question settings
Students will not be able to submit their work without providing an answer
Add a whiteboard style box for your students to showcase their work
Switch scoring method for this question from auto-grading to a rubric based grading.
You can also add hints for your students, and tag the question to standards.
Customizing the Graph View (Axes, Intervals, and Labels)
To ensure your graph precisely reflects the mathematical concepts you are teaching, you now have granular control over the X and Y axes' viewing window and presentation. This feature is crucial for focusing student attention on specific quadrants, domains, or scales relevant to the assessment.
How to Customize the Axes
Access Settings: After adding a Graphing question, click the 'Graph settings' button (often represented by a gear icon).
Navigate to Axes Control: Look for a tab or section titled 'Axis Customization' or 'View Window.'
Setting Function Example Use Case
Minimum (Min) Sets the lowest numerical value displayed on the axis. Setting X-Min to $-5$ and Y-Min to $0$ to focus only on the first two quadrants.
Maximum (Max) Sets the highest numerical value displayed on the axis. Setting X-Max to $10$ for a problem focused on 10 trials or 10 years of data.
Interval Defines the step size between tick marks on the axis. Setting the Y-Axis Interval to $0.5$ to force students to analyze decimal increments, or to $100$ for financial data.
Axis Label Allows you to label the axis with descriptive text. Changing the standard 'x' label to "Time (in seconds)" or the 'y' label to "Population Growth."
Note on Intervals: If you do not specify an Interval, Formative will automatically choose a clean interval based on your set Minimum and Maximum values. By controlling the axes, you eliminate external factors (like poor window scaling) that can confuse students, ensuring they are tested purely on their mathematical understanding of the function or data set.
Graphing inequalities (lines and curves)
You can represent inequalities on the coordinate plane—not just equations—by combining a boundary line or curve with shading that shows the solution region.
Linear, quadratic (parabola), and exponential graphs support inequality shading on the 2D plane.
Plot your boundary the same way you do for an equation: place and adjust points so the line or curve matches the problem you are assessing.
Use a solid boundary when the line or curve is part of the solution (for example, “less than or equal to” / “greater than or equal to”). Use a dashed boundary when the line or curve is not included (for example, strict “less than” / “greater than”). See Dashed boundary lines below.
Dashed boundary lines
For graphs that use a line, parabola, or exponential (not the separate Number Line question type), you can mark the boundary as dashed so it matches standard inequality notation (a dashed line for a strict inequality).
Select the graph tab for the line or curve you are editing (for example, Graph 1, Graph 2).
Enable Dashed line when the boundary should not be included in the solution.
Leave Dashed line off when the boundary should be included.
Students see the same control when they answer, so they can match solid vs dashed as part of their response.
Shading the solution region
Shading shows which side of a line or which region relative to a curve is part of the solution.
Set your shading answer key (teacher)
Open Graph settings (gear) if you need to turn on Require students to shade (see Student settings below).
Click the Shading tab.
Click directly on a line or curve on the graph to add shading for that graph element. (Prompt text in the product is along the lines of “Click on a graph line to add a shading.”)
For each active shading, use Flip shading if students should choose the opposite side of the boundary. Use Remove to delete a shading you no longer want.
If you use multiple graphs, shadings are tied to each graph’s color so you can build systems of inequalities (for example, overlapping regions).
Require shading (optional)
In Graph settings, under the student-facing options for the graph (alongside intercept requirements), turn on Require students to shade when students must submit the correct shaded region as well as the correct graph. When this is off, you can still define shading on your answer key for your own reference or preview, but students are not required to complete a shading step.
Integrated Calculator Experience (Paid Teacher / School & District feature)
Paid Teacher / School & District subscribers will have the option to turn on access to an integrated calculator for their students to use. Click here for full details!
Number Lines and Graphing Compound Inequalities
Number Line questions - through which you an graph compound inequalities - are separate from the Graphing question type. Click the 'Add item' button (plus icon) on your editor page to select Number Line from the available question types. Click here to learn more.