After sifting through a seemingly endless list of math apps and online math games recently, we were pleasantly surprised and energized to discover Illuminations. While much of the content we viewed on other websites was more of the same, Illuminations was, well, illuminating. A resource developed by the National Council of Teachers of Mathematics is bound to be impressive and insightful, and Illuminations, we discovered, is both.
Illuminations offers 108 online activities that teach a multitude of skills, from counting to calculus. With material for students in, and teachers of, kindergarten through 12th grade, there is almost certainly something here for everyone. Illuminations’s resources cleverly meld the “why” and the “how” of math so that students will not only understand what to do but understand the reasons they’re doing it.
Some activities are very simple, geared toward helping students to internalize a single concept. For example, Geometric Solids invites students to explore the relationship between the number of a solid figure’s faces, edges, and vertices by tallying up the numbers of those features on different three-dimensional shapes (all of which can be rotated by dragging the mouse and made to appear either opaque or transparent). Half Angle provides a simple, visual explanation for why bisecting the angles of a triangle can reveal the location of the center of a circle inscribed within that triangle. For the most part, though, the tools focus more on the exploration of broader concepts and skill building. Here are a few more examples of activities found on Illuminations:
Young students mastering money can move coins around the screen as they count them, practice trading coins for other coins of equivalent value (for example, five pennies can be exchanged for a nickel), and drag coins onto a grid with 100 squares to help with making change from a dollar. The coins even make a satisfying clinking noise as they are moved!
To teach why a number can have multiple pairs of factors, Factorization provides a 100 square grid and invites students to draw rectangles. The number of squares within the rectangle (i.e. its area) is displayed as the rectangle grows or shrinks, and when students get the number they want they can count the squares on each side of the rectangle to find the factors of the number. The activity indicates how many factorizations there are for each number so students will know when to keep drawing for more solutions. For example, if the number to be factored is 18, the game will prompt the student to draw three different rectangles as they work to factor it (i.e. 18x1, 9x2, 6x3)
This insightful activity allows students to represent algebraic expressions visually using colored squares and rectangles for terms. Once students have set up the expression (Illuminations will check to be sure they’re right), they can move terms from one side of equation to the other and change colors to indicate whether terms are negative or positive. The “cancel out zero pairs” button makes instructions like “subtract from both sides” concrete and visible.
One big caveat applies to this wonderful site, however. The activities are fantastic teaching tools, but most students will have trouble using them independently. This is the kind of site that a frustrated parent or teacher could turn to when the umpteenth explanation of a concept doesn't sink in, but they’ll likely need to sit next to the student and explain how to use the activities and the relationship between the activities on the screen and the paper math work the student must complete. But please, don’t be deterred. We are enormously impressed with the astute instruction provided by Illuminations and recommend it without reservation for both instruction and practice.