GEMS Algebraic Website
Activity 1: The Fabulous Function Machine
Students are introduced to Professor Arbegla and her amazing machine. They suggest numbers (and later geometric shapes) to go into the machine, and then analyze what comes out. Students learn to look for patterns as a key strategy to decode the "secret rule" the machine is following for each new function. Students are introduced to the use of T-tables to organize the data, as well as the use of variables to write algebraic expressions for the computational operations the machine is performing. Students begin to build skills, strategies, and tools that will help them do algebra.
Activity 2: Malfunctions in the Function Machine
Professor Arbegla's invention appears to be acting up. She sends a letter to your class, describing the problem (the same number that goes in, comes out) and asking your students for assistance. The malfunction introduces the class to the identity element for addition and / or multiplication. Students may also discover other computational operations, in which a number goes into the machine and comes out the same. After the lcas has solved this problem, a second letter arrives from the professor, describing a new malfunction this time, no matter what the number goes into the machine, the number seven comes out.
Activity 3: The Morph Machine
Students are introduced to a new two-step machine that you, yourself have created. When students put numbers into the Morph Machine, the numbers go into the "transformer chamber" and a series of operations are applied on them. Then you put the resulting "morphed" numbers into the machine's "restorer chamber" and -- "magically" -- are able to determine the original numbers what went in. The magic is the use of inverse operations, or simplifying an algebraic expression.
Activity 4: Professor LaBarge Scales
The use of a scale provides the context to solve equations for one or more variables. In this model, the scale represents an equation and the weights represent number and / or variables. In the first session, students are introduced to the scale itself, given some of the weights on the scale, and asked to find the values of the unknown weights. They sue variables to express these equations algebraically. In the second session they are given more equations to balance -- some with a single solution and others with an infinite set of solutions.
Activity 5: The Distributive Property
Another letter arrives from Professor Arbegla. This time there is no problem to solve. Instead, the professor shares her great multiplication discovery, known in mathematics as the distributive property or law of operation. In Session 1, students are introduced to the distributive property of addition, and have opportunities to apply it to problems. At the end of the first session, students use algebra to generalize this property. In Session 2, students discover that there is also a distributive property of subtraction, and learn to write its algebraic expression. Finally, they apply what they have learned about both distributive properties as they solve a variety of problems.
Activity 6: Algebra in Action
Students explore the area and perimeter functions for rectangles. In the first session, they are introduced to the commutative property of multiplication as they investigate a room with an area of 36 square feet and see the impact of length and width on the room's size. In the second session, students create a standard unit of measure, a square foot. Using that unit, the class concretely measures and maps to scale the length and width of an enclosure with an area of 36 square feet, to see its actual size. Using string, they measure the perimeter of the rectangle, and distinguish between the area and perimeter measurements. In the final session, students solve area problems with variables to find an unknown in the equation -- the length, width, or area.