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
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.