The cards are designed to be used digitally, but paper copies can also be used if computer access in not available.
The activity has 5 pages with 15 cards on each page. On each page match the differential equation with its slope field and its description. Write the number of the corresponding slope field in the circle on the differential equation card and the double letter of the corresponding description in the octagon on the bottom of the differential equation card.
Slope fields provide an excellent way to visualize and paint a picture of a differential equation and the family of solutions to the differential equation. Descriptions help you notice the behavior of the differential equation and slope field.
By comparing the cards students should notice:
1. Characteristics of the slope field such as positive slope, negative slope, and zero slope, opposite slopes, existence of a horizontal or vertical asymptote, symmetry, etc.;
2. How the characteristics of a slope field are hidden within the differential equation;
3. How the slope field paints a picture of a family of equations whose derivative is the differential equation.