Desmos Math Journey: Representations of Linear Relations

Using Desmos to Create Interactive Math Investigations

Jump Into a Desmos Math Journey: Representations of Linear Relations

Just recently, I have really been extending the effectiveness of inquiry/discovery based learning in my classroom by having students work at the whiteboards around my room. Students in grade 9 applied math are usually disengaged in math class because they have likely struggled with mathematics in elementary school. While I’m thoroughly enjoying the learning environment and collaborative culture that is developing in my classroom, I also want to ensure I give students access to some great explorations that may not be so easy on a blank whiteboard.

After recently checking out Michael Fenton’s “Match My Line” activity and seeing an innovative way to break an investigation down into a series of Desmos graphs by Jon Orr, I thought I’d try to do something similar with linear relations:

Desmos Math Journey - Representing Linear Relations Investigation

Begin Journey

Scaffold Students Along, Linking From Graph-to-Graph

In the activity, students begin using their understanding of linear relations and constant growth to determine missing values in a table:

Desmos Math Journey: Representations of Linear Relations - Find Missing Values

After students have found the missing values in the table and plotted those points, they can now begin using the sliders for ‘m’ (slope/rate of change) and ‘b’ (initial value). It is important to note here that I will not discuss what these values are – that’s why we’re doing the investigation. Hopefully, as a group, we can consolidate later and settle on what these values might be called based on their characteristics.

Desmos Math Journey: Representations of Linear Relations - Use Sliders to Find Equation

Students can then write their equation. While this is a bit redundant, I want to expose my students to as many tools throughout the investigation as possible as this is the first time we are using Desmos this semester. They are also asked to write an explanation/reflection to see if they can recognize what ‘m’ and ‘b’ really do and where we can find them in the table.

Desmos Math Journey: Representations of Linear Relations - Create an Equation and Make Connections

After they have completed the first part, they click on the link and move on to the next portion of the Desmos Math Journey:

Desmos Math Journey: Representations of Linear Relations - Move Along to Next Graph in the Journey

Start Your Desmos Math Journey Here

Click on the graph below to start this Desmos Math Journey:

Begin Journey

Here are some direct links to each of the six parts:

Have any Desmos Math Journeys to Share?

Toss the links in the comments!


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About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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