Now move on to other strategies for solving equations. Begin by asking one participant to think of a number.
Groups: A facilitator or another group member should lead this activity. The leader begins by asking one person to think of a number. That person should write the number on a piece of paper and hold it up for the rest of the group to see, without showing it to the leader. Then, the leader asks the group to volunteer different operations with numbers, such as multiply by 2, subtract 4, add 1, etc. The leader writes these on the board as a flowchart, including about five or six steps. The picture will look something like this:
The leader then asks the groups to run their number through the flowchart, and only reveal their answers. The group can discuss their ideas for figuring out the input. The leader then works backwards, generating a drawing on the board that looks something like this:
Backtracking is a method that can be used before students know anything about formal equation solving. It simply requires that any operations be "undone" to work backwards from the output to the input.
Groups: Work in pairs on Problems B3-B10. In Problem B4, recognize that in order to solve a problem using backtracking, the variable must appear on one side of the equation by itself. This is a limitation that points to the need for alternate methods.
Problem B10 is an example of a problem that is much easier to solve using backtracking.
Groups: Share your thinking on this problem, and see if anyone tried to solve it in a different way.
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