Essential Question:  How can you develop and test "invented" procedures for solving problems?

CCSS:  2.NBT.7, 7.EE.1, Mathematical practice #2,#3,#7  TEKS: 2.4D, 6.3C, Process Standard G

Grade levels:  2-12

Instructional format:  video, student discussion, group discussion

Time:

Supplies:  video, older student note-taker, younger student note-taker

Lesson:  Show the video above.  The video is of a second grader that developed his own method for solving subtraction with regrouping (or borrowing).  The video cues younger students to replicate the method that they see by trying it on a few problems.  Then, ask the children to compare methods - which is easier for them to remember, why do you think Donald's method works, etc.  Have younger students use the following note-maker to keep track of their work.   For older students - can they prove why Donald's method always works?  This is a proof that requires the use of negative numbers, so early secondary students could prove showing each step with representative negative numbers, while older secondary students could write a proof using variables, operations, and properties.  Have students use the following note-maker to keep track of their work.

Extension/follow-up:  Have students try to create their own original procedure for any mathematical process, such as adding multi-digit numbers or even adding/subtracting fractions.  Have them present their "new" method and then use classmates to test (or prove) their procedures.