Learning how to graph linear equations and predict linear trends is one of the foundational tasks learned in basic algebra. Many hands-on projects dealing with linear equations have to do with predicting linear trends. Algebra Lab has a project called "Egg Drop Soup," in which students put an egg into a plastic sandwich bag and measure the distance that the egg will drop in the bag if one rubber band is holding the bag from above, and they release the bag. Then, they add a rubber band, increasing the slack, and drop again, and then they add as many rubber bands as they need to develop a reliable trend line.
Finally, the teacher gives them a distance that the egg must drop, and the students use trend lines to estimate how many rubber bands they need to drop that distance without breaking. The winning group is the one that can get the closest to the ground without the egg breaking.
Algebra tiles help students figure out how to handle operations with binomials and trinomials. If the result is quadratic --- the highest power is x² --- for example, tiles will come in three shapes: large square, rectangle and small square. If you're multiplying "(x + 5) by (x + 4)," for example, you write "x + 5" and set the large square to the right. Then, you put five rectangles in a row going down beneath the square. Beneath the last rectangle, you write "x + 4." Then, in a horizontal row going right from the large square, you put four more rectangles. Then, fill in the grid with small squares, placing them where the vertical and horizontal rectangles would meet if you drew lines from them: you should end up with 20.
To get your answer in ax^2 + bx + c format, a = the number of large squares, b = the number of rectangles, and c = the number of small squares in your diagram. You should get x^2 + 9x + 20.
Part of algebra involves learning such concepts as parallelism, tangency, transformations and perpendicularity. Beacon Learning Center has developed an activity that requires students to understand the concept of perpendicularity while being creative at the same time. Teachers design an obstacle course, either using real obstacles in a hallway or outdoor environment, or draw an obstacle course onto a handout, and require students to move through the course using only perpendicular turns. Students are given protractors and string to mark their path in the hallway/outdoor scenario.
Because it can be confusing to identify the relative value of fractions and decimals, there are some activities that ask students to rank them based on what they think the relative value would be. Algebra Lab's "Where Do I Live?" activity gives students index cards with fractions with an absolute value of less than 1. On a clothesline, the numbers "1," "0" and "-1" are already attached, and the students must attach their index card to the right places with clothespins, interacting with each other to ensure a correct number line. For example, the card "0.6" should go between "1/2" and "2/3."