How Can You Make Almost Any Math Lesson Deeper?

I am currently at a regional NCTM math conference on algebra readiness.  I am going to share one of the things I learned at the conference.  Use conjectures while teaching math to make the task deeper.  For example, when teaching the commutative property, have students find at least three pairs of equations with factors that have switched places and allow  students to draw a conclusion.

3×4 = 12

4×3=12

7×6 =42

6×7=42

4×9=36

9×4 =36

Ask students what they notice about the factors that have switched places.  Hopefully, students will say that the products are the same when the factors have switched places.  Ask students if this is always true.  Allow students to experiment with their conjecture by using other examples.   Ask other students if they can prove this wrong.  When all minds are settled on the conjecture and agree, then reveal the name of their conjecture as the commutative property.  Teaching with this method of discussing conjectures allows students to take ownership of their learning and be involved in the process of discovering mathematical concepts.  Less reteaching will occur and your teaching will be closely aligned with Common Core Standards.