The National Council of Teachers of Mathematics, through the Illuminations Project, has released a manipulative online tool that allows students to test their understanding of algebraic functions:
- Linear, quadratic (2nd order), 3rd and 4th order polynomials
- Exponential and logarithmic functions
- Periodic functions including sine, cosine, and tangent
The way it works is that once the function type is selected, a blue graph is drawn on a coordinate plane. A red graph is also drawn on the same axes. Through changing the coefficients in the function below the graph, the red graph changes.
The object is to make the red graph match the given graph, which is the blue one. Students who know how functions work can just type in the correct coefficients; others can use trial and error to learn how changes in the coefficients affect the graph of a function.
The manipulative (toy) doesn’t require a login and seems to be mobile-friendly, so students will be able to access it from anywhere. It seems to be intended for students at the high school level, such as those in an Algebra II class.
For example, Common Core math standard HSF-LE.A.2 maintains that students should be able to “construct linear and exponential functions … given a graph …,” and HSF-LE.A.3 says students should be able to “observe using graphs … that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.”
Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation. NCTM serves as a content partner for Thinkfinity, the Verizon Foundation’s free online professional learning community, where Illuminations is the primary contributor of resources for teaching and learning mathematics for grades pre-K—12. Connect and collaborate with over 70,000 educators though Thinkfinity! Share resources, join discussions and participate in special interest groups.
