A Multisensory Approach to Teaching Slope With Sound

Many middle school math students stumble over a deceptively simple question: What does a negative slope actually mean? By inviting students to not just see a line but hear it, teachers can help connect the visual, verbal, and symbolic aspects of slope into a single, integrated idea.

PRO TIP: Start With Regular Words

Begin with verbal-only exploration before layering in formal vocabulary. Instead of starting with “This is a positive slope,” teachers might prompt, “Listen: The pitch rises steadily,” helping all students make sense of the idea before introducing terms like positive slope, negative slope, or steepness.

Small group discussions can help surface student thinking while encouraging learners to move naturally between what they hear and what they see. Teachers should look for student observations such as,“The pitch rose faster, so the slope must be steeper.”

After each listening activity, ask, “Does the graph confirm what you noticed in the sound?” to strengthen connections across representations.

A multisensory Approach to teaching slope: The Descartes Symphony

Using the Audio Trace feature in the free Desmos app, students can graph a line and listen to its pitch rise or fall as its slope changes. (Full disclosure: I am a Desmos Fellow, though not employed by Desmos Studios.) A slide whistle could also stand in, for a screen-free version of this lesson.

The following three-part sequence moves students from describing lines in their own words, to hearing how slope behaves, to identifying and sketching invisible lines using sound alone. Each phase layers another sensory pathway, helping students internalize slope as something they can see, say, and hear.

1. Lines With a Friend (Explore). This phase begins by immersing pairs of students in a collaborative, language-based challenge. One student is the “Describer,” and the other is the “Drawer.”

First, the Describer examines a sloping line on a graph while their partner faces away with a piece of paper. The Describer must explain the line on the screen without using formal mathematical terms such as slope, rise, run, or intercept.

The Drawer then sketches what they think the line looks like based only on their partner’s description.

Finally, the pair compares the sketch with the original graph and reflects on which words were most helpful and which banned words would have made communication easier.

2. Sound of a Line (Explain). In this next phase, students explore how hearing the slope of a line can deepen their analysis of linear equations.

First, the teacher begins with the parent function (y = x), playing the slope’s sound with the Audio Trace feature in Desmos or by using a slide whistle. With the slide whistle, the teacher produces a smooth, steadily rising pitch (from low to high), mirroring the constant rate of increase of the line. To do this, the teacher starts with the whistle fully retracted and gradually extends it at a uniform speed, creating a clean, linear glide in pitch.

Students then predict how changing the equation will alter the sound. Examples of equation changes might include (y = 2x), (y = 0.5x), or (y = –x + 3).

Questions to prompt student understanding: Will the pitch rise faster? Fall instead? Shift upward?

After sharing their predictions, students play the new line’s audio and reflect on how their expectations compared with reality.

3. I Walk the Line (Elaborate). In this final phase, pairs of students take on a listening challenge designed to classify and reconstruct lines based on sound alone.

Around the classroom, the teacher posts QR codes or links to Desmos graphs where each line has been rendered “invisible” by matching its color to the background. Students access these hidden graphs, listen carefully, and record observations on a thought-catcher: Does the line rise or fall? Is it steep or gentle? How does it compare with the parent function (y = x)?

Using this auditory data, students sketch what they believe the line looks like.

Finally, students or the teacher change the line’s color to reveal the slope, and then students compare their sketches with the actual graphs.

Implementation tips

Classroom setup: Provide students or groups with access to devices with Desmos and headphones for clearer sound. Demonstrate how to activate Audio Trace (Alt + T on Windows, or Option + T on Mac).

Scaffolds: Begin with the simplest parent functions before introducing varied slopes or intercepts. Ask questions such as, “Graph (y = 2x + 1). What happens to the sound as (x) increases?” or “Change the slope to –1. How did the pitch shift?”

Teacher moves: As students investigate, monitor their conversations and prompt reflection: “What did you hear when the line flattened? When it steepened?” Close each activity with reflection on how hearing influenced their visual or symbolic understanding.

The Magic of Music and Math

By merging mathematics, sound, and technology, the Descartes Symphony lesson transforms graphing from a visual exercise into a full sensory experience. Students don’t just see a line—they hear its story. The rising and falling pitch becomes a tangible expression of slope and direction. This blending of sound and visuals builds conceptual depth, accessibility, and student ownership of learning. For educators, it offers a new way to engage students in the beauty of linear relationships, where graphs sing and mathematics becomes music.