Slope is the rate of change associated with a line. This is a challenging topic especially when presented in the context of a real life application like the one shown in the photo. The graphed function has different sections each with a respective slope.
One aspect of slope problems that is challenging is the different contexts of the numbers:
- The yellow numbers represent time
- The orange numbers represent altitude
- The pink numbers represent the slopes of the lines (the one on the far right is missing a negative)
Before having students find or compute slope I present the problem as shown in the photo above and discuss the meaning of the different numbers. What I find is that students get the different numbers confused and teachers often overlook this challenge. This approach is part of a task analysis approach in which the math topic is broken into smaller, manageable parts for the student to consume. Once the different types of numbers are established for the students we can focus on actually computing and interpreting the slope.
This instructional strategy is useful for all grade levels and all math topics.