Multiplying Two - Digit Factors by Two - Digit Factor


Ø  When students do not have a complete understanding of place value as well as what it means to multiply, it’s not uncommon that they combine algorithms for multiplying with the algorithm for addition. 

 

Ø  When multiplying two digit factors by two digit factors, students often forget to multiply by both digits. For example, when multiplying 56 x 23, Micah got the answer of 118.  Micah multiplied the 3 by 6 to get 18. He wrote the number 8 down and regroups into the tens place. Then he multiplied 2 times 5 and gets 10 as the product.  He adds the regrouped 1 to the 10 and records 11, leaving the incorrect answer of 118. Instead of viewing fifty-six and twenty-three as whole numbers, he regarded the numbers as separate digits. 

 

Ideas for Instruction

v Common error patterns can be avoided if multiplication problems are introduced in a way that emphasizes making sense.  For example, when a student finds the product of 356 x 8 = 2,848, ask students, “Does that answer make sense to you?”and explain your reasoning; “When I think about whether it makes sense, I think that 8 three hundreds is twenty – four hundred .  Since the first factor is greater than 300, the product should be greater than 2,400, but still sort of close.  So to me, your answer makes sense.”

v Use rectangular arrays as models.  They can be linked to repeated addition. 

v Model cross-product problems using arrays that illustrate the commutative and the distributive properties of multiplication. 

v Students can use estimation in story problems. Teachers should provide a context for the numbers in the real world.

The school cafeteria is being set up for the choral assembly to be performed on Monday night.  Eighteen chairs are in each of 21 rows.  How many people will have seats at this performance?

§  If there was only 1 row of 18 chairs, how many chars would there be?

§   What if there were 2 rows? How many chairs would there be? What did you do to get the answer?

§   Can you figure out how many chairs there would be if there were 10 rows with 18 chairs in each row?

§  Can you make an estimate about the number of chairs there would be in 21 rows?

§  Give student pairs centimeter grid paper, connecting cubes, square tiles, base-ten blocks, and chart paper to display their final answer and the strategy that was used.
 
 
 
 
 

No comments:

Post a Comment

Subscribe to: Posts (Atom)