Dragon+Box+Classroom+Showdown+Learning+Environment

Introduction
Students will be competing in two teams to solve Algebraic puzzles involving isolating the variable that are created by the other team in as little time as possible. Puzzle Solvers must solve the puzzle correctly and in no more moves than the Puzzle Creator specifies.

Purpose
The specific purpose of this game is to help students start seeing Algebra problems as puzzles, not problems. This activity works best after students have become familiar with the paid app [|DragonBox Algebra] because it can help transfer the knowledge learned in that game into the classroom, but the activity can also be played by students who have no familiarity with the game.

Objective

 * Students will create a Algebraic puzzle based on isolating the variable, along with a solution
 * Students will solve puzzles created by other students

Materials

 * DragonBox Showdown Worksheets (download below)
 * Pencils and scrap paper
 * [|DragonBox Algebra game (optional)]
 * Timer (optional - for some possible variations)

Worksheet
The same worksheet is used as the Puzzle Worksheet and the Answer Worksheet; Puzzle Makers fill out the whole Answer Sheet, but only fill out the Start and the number of steps it takes to solve for the Puzzle Worksheet, so another student can use it to solve the puzzle.

PDF version:

Word version (in case you want to edit):

Set Up

 * Have students play through t[|he DragonBox Algebra game] previously to this activity, available on the iPad and other formats. This is a paid app and, while recommended, this is an optional step.
 * Explain the basic premise of how the puzzles work to the class, with examples -- see below (especially important if they have not had experience with DragonBox Algebra).
 * As best as possible, split students into two teams of equal ability
 * Students will use scrap sheets of paper to develop puzzles needing from 1-9 steps to solve
 * Teachers can choose to have a required minimum number of steps, i..e, 4-9 steps. The worksheet does not allow for more than 9 steps.
 * Students will use the DragonBox Showdown Worksheets to write out the problem and the full solution (Answer Sheet); it will be helpful if they label this with their name or some other labeling system
 * Teacher will verify that a student's puzzle is correct (see options)
 * optional: have verification part of the scoring: 1 pt for each puzzle made correct the first time.
 * optional: trust that the students have correct puzzles and then, if a puzzle is not solved in the showdown, check and see if the solution was correct; award points to opposite team if solution is incorrect (better for more advanced classes)
 * Students will use another Worksheet to copy ONLY the start of the puzzle (Puzzle Worksheet), marking how many steps another student should solve the puzzle in, and label this worksheet the same as the answer so they can be easily paired together (i.e., with the student's name).
 * At this point, each student should have the following:
 * 1 Answer Sheet (worksheet with the problem and the step-by-step solution)
 * 1 Puzzle Worksheet (worksheet with the problem only and the number of steps it can be solved in)

How the Puzzles Work
The basic idea for the puzzles is to begin with an Algebraic equation that does not have the variable isolated; the puzzle is "solved" when the variable is isolated. For instance, X/Y + 7=42 could be an initial "puzzle" that the puzzle solver would have to solve for X. For sake of simplicity, the variable that has to be solved for should always be "X".

Puzzle Solvers (and Puzzle Makers as they construct the puzzle) work through the puzzle one step at a time. A step is something done to the equation, with all the necessary operations. For instance, in the puzzle above, subtracting 7 from the left side is a step; however, since 7 MUST be subtracted from the other side as well, this is part of the SAME step. So... X/Y +7 (-7) =42 (-7) --> X/Y=35 is ONE step, with 7 be subtracted from both sides.

For another example of what a step is, if we have X/Y=35, the next step is to multiply the left side by Y; you MUST multiply all sides by Y, so the next step would be: X/Y(Y)=35(Y) --> X=35Y.

Last example: If, initially, a student wanted to solve X/Y + 7=42 by multiplying X/Y by Y, that ONE step would include multiplying all elements by Y: Y(X/Y + 7)=42(Y) ---> X + 7Y=42Y would, again be ONE step. The next step would be to subtract 7Y from both sides to give us X=35Y.

Both examples took 2 steps and came up with the correct answer; in terms of this puzzle, both are equally correct because they solved the equation in the smallest number of steps.

The Showdown!
The basic premise is that puzzles from one team will be given to another team to solve. The Puzzle Solver must solve the puzzle in equal or lesser steps than the Puzzle Maker (as specified on the Puzzle Worksheet); they do NOT have to do the same steps in the same order, but they cannot take more steps.

Suggested Method:
The students will have a showdown with the other team, one at a time. A table should be set up with chairs on the opposite sides. The teacher should sit at the side of the table between the two chairs. Plenty of scrap paper should be available.

Teams line up on their sides, each with their Puzzle sheets and Answer sheets (both constructed from the Worksheet provided). One at a time (either randomly or based on ability as decided by the teacher), a player from each team will sit at the Showdown Table and give their puzzle to the teacher. The teacher will swap the puzzles, giving the puzzle created by Team 1 to Team 2 and vice versa. The teacher should hold on to the answer sheets as reference (especially if they haven't previously checked to see if the solution is correct).

The students will then race to solve the problem, using the scrap sheet if required. The winning player will be the first one of the two that has solved their puzzle in equal to or lesser steps than the number written on the Puzzle worksheet. Although students can use the scrap paper for trail and error, each step must be written out in the boxes provided before they can say the puzzle is solved.

When a student claims to have solved the puzzle and written the appropriate steps down, the teacher will verify that the puzzle has been solved correctly. They can ask the student to clarify any steps written in the box that are not clear. If the teacher verifies that the puzzle was correctly solved, 1 point will be awarded to that team. If the puzzle was solved incorrectly, 1 point will be awarded to the other team.

The team with the most points (won the most showdowns!) at the end wins.

Variations

 * A time limit can be given to the Showdown players; if no one has solved the puzzle in the time, no points are awarded
 * If the showdown needs to be done quickly, all students can swap with other students at the same time; the teacher will run a timer for a set number of time (i.e. 3 minutes). At the end of the 3 minutes, the number of solved puzzles from each side can be tallied to see which team won
 * Instead of students going head-to-head, this can be constructed like a rally. Each student stays at the table until they solve the problem, then the next student on their team goes. The first team to get through all of their players wins. The teacher can set a maximum time (i.e., 5 minutes) where a student is deemed "stumped" and the team can move on as if they had solved the problem (this would help in case their is very weak students on a team who may not solve the puzzle at all).
 * All students must complete their puzzle, even if they lose the showdown. This can be done at the table and part of the scoring (i.e., 2 points awarded to the student who wins the showdown, 1 point awarded to the student who solves the puzzle second, 0 points awarded if the puzzle is not solved). It can also be done after the showdown (i.e., the student who loses the showdown must finish solving the puzzle on their own at their desk).

Principles of Learning

 * Active, Critical Learning Principle
 * Students are actively creating and solving Algebraic puzzles
 * Semiotic Principle
 * Students are engaging with Algebraic symbols and actions]
 * "Psychosocial Moratorium" Principle
 * All that is at stake in not solving the puzzle quickly is losing a game, not failing a quiz.
 * Identity Principle
 * Students play at being puzzle creators and puzzle solvers
 * Practice Principle
 * Students get practice at Algebra in the (hopefully) non-boring context of a game
 * "Regime of Competence" Principle
 * Since students, not academics, are making the puzzles, they are more likely to be at the level of the puzzle solver; further, by matching up students of similar abilities in the showdown, teachers can make full use of this principle.
 * Probing Principle
 * Solving the puzzle involves trying different steps and seeing if they work
 * Multiple Routes Principle
 * There is often more than one way to solve a puzzle; students also have the freedom to choose how to make their puzzle
 * Situated Meaning Principle
 * Because this deals with Algebra, the signs are very contextualized
 * Discovery Principle
 * Students discover the solution to the puzzle themselves
 * Transfer Principle
 * A major goal is the transfer of one activity (solving puzzles in this game or in DragonBox Algebra) to another (solving algebraic equations in math class) or, if students have not played DragonBox Algebra, they should be able to transfer the idea of solving these puzzles to solving Algebra problems.