## Amazing STEM lesson

**Title**: Apply concept of slope and y-intercept in a real-life, distance-time problem situation.

**Context**: Students will have been introduced to the slope formula and slope-intercept form, but do not know how it could be used to model a real-life situation.

**Preparation**: A calculator or computer based range-finder is set-up and firmly affixed to a desk or table at roughly waist height for an average student. A graphical image of a distance-time graph showing the walker’s distance from the range-finder is projected onto the wall. Desks are arranged in such a way that there is a pathway allowing a walker to walk back and forth up to 10 feet away from the range-finder. One foot square floor tiles, or lines taped one foot apart on the floor, provide a reference for measurement. Student groups receive a handout with a series of blank graph templates: distance is marked on the y-axis and time is marked on the x-axis; there is space for students to write down the problem scenario, make a prediction, record the actual result, and to reflect.

**Lesson**: Explain that the motion detector emits an ultrasonic wave which bounces off any object in front of the detector and back to the detector. The computer multiplies the elapsed time it takes for the sound to travel between the object and the detector by the speed of sound to find the distance the object is from the detector. The object’s distance from the detector is then displayed on the distance-time graph projected on the wall.

A volunteer walker is asked to stand a fixed distance from the detector. The whole class is then asked to predict what they think the graph will look like if the detector is turned on and the walker stands a fixed distance away for a fixed time before the detector is shut off. When every group has made a prediction, the detector is turned on and an actual distance-time graph is produced. The students compare their predictions with the actual result. The students then discuss with groups and then whole-class with the teacher before filling in the analysis section of their handouts explaining why the actual graph looks the way it does, correcting any misconceptions they may have had.

Additional scenarios of increasing complexity are proposed with new volunteer walkers from each group and the same procedure followed: a question is proposed, the class predicts, actual results are produced, compared, and reflected on. Questions that might be asked are: When does a graph “slant down”? When does a graph “slant up”? When does a graph of a line start at the origin? When does a graph of a line start on the y-axis? What does a graph indicate if it is steep? What does a graph indicate if it is less steep? What is the meaning of a horizontal line? Is it possible to walk in a way that you could create a vertical line?

Another motion detector may be added to the system, so the graphs made by two walkers walking simultaneously can be compared, and so steepness and its meaning in this problem context can be compared directly. It might be asked about two walkers what the scenario might be when lines never meet and when they meet in a single point. Questions that cross into other fields –speed versus velocity versus acceleration– can be discussed and it is possible to head toward calculus in discussions of the meaning of non-linear graphs that are concave up or concave down.

**Conclusion: **The physical meaning of slope, its sign, and steepness; the meaning of the y-intercept, the difference between undefined and 0, the importance of the definition of a function; and with two walkers, the difference between consistent and inconsistent systems, can all find a concrete meaning through use of the motion detector. Giving students the chance to make predictions and immediately compare them to actual results elicits higher order ‘what if’ analysis that comes directly from the students with little teacher prompting. This lesson arrangement has enough flexibility that many of the important questions can come from the students with little prompting! Finally, there is access for all students, as the lesson is not computationally intensive, students get to get up and move, and there is concrete, immediate, visual feedback.

Big 5 Amazing STEM Juno TOP 5 COMMONALITIES

Student Generated Questions – When crafting questions themselves, students become invested and examples are authentic. Students develop confidence in new topics when able to step into the teacher role.

Real World Examples and Applications – Lessons include concrete examples students have been exposed to in their day-to-day environment. This hooks the students and assists conceptual understanding.

Kinesthetic Component – STEM learning incorporates movement or other types of hands-on activities which deepen understanding of a concept.

Cooperative Learning – STEM learning requires different opinions and views for discussion. A cooperative group of students with different backgrounds will provide the different views.

Multiple Modalities – Involves providing diverse presentations and experiences of the content so that students use different senses and different skills during a single lesson.