Don't Miss!

While visiting independently working students, I found one student who was in the tremendous agony over 4 times 9.  His equation appeared to be 4x9=40.  This student has been placed in the higher group in the pretest and the worksheet was a review.  "How did you come up with this answer," I asked.  Disorganized circled fours are scattered in his notebook.  Evidently, it is impossible to count these circles.  Messy!

Teacher: "Do you remember the strategy for times 4?" 
Student: "Double double." 
Teacher:"What is 9 plus 9?
Student:"18."
Teacher:"What is 18+18?"
Student:"36."
Student:"But 4x9 is 40.  I am right!"

Teacher: "What is the strategy for times 9?"
Student: "Times 10 minus one set."
Teacher: "4 times 10?"
Student: "40."
Teacher: "40 minus 9?"
Student: "36."
Student : "But 4x 9 is 40!!!!"

Is it a kind of misconception or misunderstanding?   This student's personality could have contributed a big role in his agonized maze.  Here is what I have done.  Going back to the beginning. 

• Legible hand writing!
• Use repeated addition.  
• Re draw circles in one line with number 4 inside.  
• Make an array of 4x9.  
• Draw a number lines that indicates skips of 4

Each time,  he compared products between x9 and x10.  He was no longer so upset.  There are so much evidence that proved the fact.  Finally, "I think 4 times 9 is 36."

A individual progress monitoring is imperative all times for every student.  It is a warning and caution when your use differentiated groups.  Create the system that you can monitor all students periodically.  Otherwise, some kiddos fall like sand through your fingers.