Lesson: 13 x 7 = 28
Student
Teacher
Extensions

Mathematically Meaningful Mistakes

Does 7 times 13 equal 28?

Agnes Nemeth, Ihor Charischak, Don Ploger

 

The Lesson Scenario-More Detail

 

            Teacher writes on board: 13 x 7 =28

 

 This is an easy, straightforward problem. Most kids will (or should) come up with 91. But, many of the students will answer the problem without true understanding of how to multiply: they learned only the procedures of multiplication. We all remember the famous or rather infamous: “take down, carry, and put an x or zero under” expressions that “teach” multiplication without meaning concentrating on nothing else but on the process. 

            Teachers have to make sure that students truly master multiplication (emphasizing place values) at the time when it is first introduced to them. Students will be forever lost in mathematics without the encompassing knowledge of this seemingly simple concept. The lack of mastery of multiplication will make comprehending division and the operations with fraction almost impossible. Let’s look even further:  how can teachers introduce percents, the multiplication of algebraic expressions, or exponents to a student who practices math in a mechanical way but has no number sense? 

            Even when our students answer the above multiplication problem correctly, instead of giving the usual response of “that’s right”, the teacher should probe the students with “Are you sure? I have some evidence to the contrary. Let me show you this video.” (more)

--------------

Another version of the Costello 13x7=28 routine. Enjoy!



Source: Original Version 1.0 developed at CIESE- 
Center for Innovation in Engineering & Science Education (2007)
Revised 3.24.21 currently under construction