Inspiration

RandomGenerator is one of the functions within Desmos’ computational layer.  As I explored the feature, I began to see the benefits of random generated tasks.  Many experiments later, I’m publicly sharing my first random generated (RG) series.  This one focuses on slope and y-intercepts.

This AB would not have been possible without the help from Jay , Suzanne,  Jocelyn, Serge and last but not least, Eli. Each person either added CL examples to the Desmos Fellows CL Bank of Wonders (that I adapted or used in complete form) or answered my questions when I was completely stumped.

My Intention

As I learn computational layer (CL), I often practice writing the code I’m using.  Let’s take Jay’s example, Sketch and Check Random.  Since the example involves features that I haven’t coded with before, I used Jay’s code for practice activity 11.  I’ll now need to go back and learn the code. Study it.  Figure out the purpose of each line and how the various lines connect with components to achieve the desired outcome.  I’ll then work on replicating the code.  It takes me multiple tries to replicate code.  The rewriting process not only helps me understand the CL language, but also helps me become more efficient when creating future activities.

Throughout the school year, teachers offer a variety of experiences.  There’s definitely a need for exploration activities and tasks that build conceptual understanding.  There’s definitely a need to focus on academic language through mathematical discourse.  There’s also a need to practice a specific concept, similar to when I practice the writing of code to gain fluency.

The random generated aspect of the Random Generated:  Determine Slope and Y-intercept  activity builder allows teachers and students to use the activity as often as they wish without the worry of duplicating problems.  A feedback loop is built into each practice activity, therefore regardless of the example, students will know if they calculated the problem correctly.  Listed below are few suggestions to integrate the AB.

Example 1:  After assessment practice.  Mr. X gave his students an assessment and he noticed that the majority of his students struggled with finding the y-intercept when given two points.  The next day, he could project practice slide 6 for a whole class task.  He could also pass out one computer per group and ask a group member to go to slide 6.  Now each group has their own problem to solve collaboratively and since feedback is provided, students will know if they completed the problem correctly.

Example 2:  Collaborative practice.  If you use #VNPS (vertical non-permanent surfaces aka white boards on the wall), pair up 2 students with 1 computer.  Let the partners work through a few randomly generated problems on the whiteboards while you circulate through the room.  Since the problems never run out, some pairs may complete 2 problems where others finish 3 or 4. A follow up activity could require students to reflect on the strategies used.

Example 3:  Individual practice. Sarah often struggles to determine the slope when the line does not have clearly marked points.  Prior to a test, she could run through a few examples on slide 4.  After she answers the first problem correctly, she can press the button for another example (if necessary). Again, each slide is designed with built in feedback.  Therefore even if Sarah practices at home, she can gauge her progress.

Example 4:  Choice boards and Hyperdocs.  If you provide choice boards for your students, then one or two of the practice activities could be used as an option.  A familiar Hyperdoc format is:  Engage, Explore, Explain, Share and Reflect.  Teachers could find interesting ways to integrate the RG practice activities into a Hyperdoc.

The Random Generator Slope AB

Feedback has been built into each practice activity.

Note:  If a vertical line pops up on a slide where the check depends on a numerical value for slope, then generate a new problem.  Vertical lines are addressed on slide 10.

Slide 1:  Students are asked to acknowledge the individual rise and run and then enter the slope.  The program calculates the y-intercept based on the displayed points and the inputted slope.  Therefore, the line that matches the student’s response is graphed.   If the student enters the correct slope, then the line will pass through the given points. If their slope is incorrect, then the graphed line will not pass through the given points.  Students are encouraged to use the sketch tools.

Slide 2:  Similar to slide 1 but requiring students to calculate slope using 2 points.

Slide 3:  Students practice finding the slope when points are not prominent.  For these examples, the slope values are only integers.

Slide 4:  Same as slide 3, except the slope values can include fractions.

Slide 5:  Students are expected to calculate the y-intercept when given the slope and points.  In order to generate slope values to include fractions, I had to randomly generate a numerator and a denominator.  This method produces slopes in various formats, like the one pictured, -4/-2.

I entertained the idea of simplifying the slope but then made the conscious decision to leave it as is.  In my experience, students often struggle when a fraction contains 2 negatives, a negative in the denominator or is not simplified.  By leaving the slopes “messy”, students have more opportunities to navigate tricky formats.

Slide 6:  This activity requires students to calculate both the slope and y-intercept.  Students can either determine the slope using rise/run or with the given points.

Slide 7:  Similar to slide 6 but without a grid.  Without the grid, students are encouraged to practice calculating slope using the formula.

Slide 8:  Students enter the linear equation in slope-intercept form.  Sketch tools are available.

Slide 9:  Same as slide 8 but without a grid or sketch tools.

Slide 10:  The same as slides 8 & 9 but with vertical lines.

Slide 11:  Using the sketch tools, students draw the line that represents the given equation.  When the button is pressed, the correct line is displayed.

The activity builder:   Random Generator:  Determining Slope and Y-intercept