![]() ![]() This is a great situation to highlight when presented in class. One reduce (red) and the other not (orange). ![]() In the graphic, you can see two forms of the equation.pick either point (2, -7) or (8, -4) to substitute into (x, y).Substitute to solve for the y-intercept: y = mx + b.Use slope formula to calculate the rate of change.Now that the students know the answer, they can use that answer to guide their calculations.Ask students to move the new line (red) so it covers the green segment. ![]() Ask students to enter the equation y = 1/2x.Ask students to press the button to connect the points.Ask them to state an observation for the y-intercept.Ask them to state an observation for the slope.Ask students to enter in the points into the table.Desmos provides a visual! Our visual learners can glean more understanding of linear equations than expected if we incorporate interactive visual tools such as Desmos. I’ll have a hard copy of my notes and then I can share them with multiple people. As I drafted notes, I thought, “Why not write the steps in my blog”. Here’s a little mockup I did for the cue ball shot, but I haven’t added an equation for the ball’s path.One of my teachers asked me to incorporate a different perspective on writing a line in slope-intercept form when given two points. I think you could use sliders to make the vertex a moveable point that would change the path of the ball depending on where it strikes the side of the pool table. “If you want to model it in Desmos, an absolute value function would make the incoming/outgoing angles equal if reflecting off a horizontal or vertical line. Patty Stephens made an awesome improvement to make this more realistic: How can the pool table challenges be improved? Thanks in advance for your feedback. It was still a struggle in the end (more suggestions welcome), but I was much more pleased with the results. Using this strategy helped a lot and allowed more students to truly access the task. Finally, it’s time to launch the putt putt/pool table challenge. Slightly more challenging, but again, most students will be able to get through it and build more confidence. The strugglers are usually able to work with a group member to clear misconceptions. Most of the students are able to get through this and build some confidence. However, I recently tried to ramp the lesson by starting the students with Michael Fenton-esque mini challenges (thanks to Matt’s maze post). It’s been challenging trying to figure out a proper way to launch the task. When using the putt putt version of this game, my students tend to struggle quite a bit. ![]() Speaking of sharing work, Cory Henwood provided a glimpse of an awesome strategy using Nearpod. Each student/group could have a different route to a solution. This also allows students to compare and present work because it isn’t the same presentation every time. I like this setup because there are many options for made shots. In this game, the objective is to draw the path of the white ball hitting and sending another ball into a pocket. My goal is for students to get more practice graphing lines with domain and range restrictions (always a challenge for my kids). That, along with Matt Vaudrey’s maze post and an old putt putt golf Desmos activity led to this. I saw a student playing pool on his phone the other day, and it inspired me to create something in Desmos. ![]()
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