A little magic.
My Algebra 2 students love choice. OK, who doesn't? The trick has been to get them to feel like they're choosing when what they're really doing is a ton of Algebra 2. Meh heh heh... Does it sound like magic? Well, there may be a little! But what teaching doesn't involve a little magic here and there?
You get to choose
This "the blob activity" is a fun one my school does in Algebra 2. Students need to shift the vertices of vertex-form functions (absolute value, radical, quadratic and cubic) into a blob somewhere on the grid. For instance in the picture below, students could record y = (x + 2.9)^2 + 3.5 and be right! They like that there is an infinite number of possibilities for right answers.
In this Algebra 2 mix match game there are 2 stacks of cards. On each of the cards in stack 1 are function types (absolute value, radical and quadratic) and instructions on whether to graph or write the equation. On each of the cards in stack 2 are function characteristics. The characteristics include: a range interval, an increasing interval or a decreasing interval.
Each student in the group takes a turn choosing a card from each pile to make a "mix-match" of function and characteristic. Students then graph or write the equation and then check each other. There is summary sheet at the end that can be used to award credit.
Putting the graphing sheets in plastic page protectors lets students use dry erase markers and reuse the graph sheet throughout the entire activity. Each student gets his or her own equation recording sheet.
The next day
My students lose a lot of information overnight, especially in the early days of a unit or after a holiday break. These Quick Check sheets have been working so well as warm ups/ We've used them for all vertex-form functions and now with factored-form quadratics. I project an equation (or graph) onto the board and they know what to do. Sometimes we start with a graph and I ask them to write the equation, other times we start with an equation that I ask them to graph.