Misapplying Addition and Subtraction Strategies to Multiplication and Division

Ø  When using the rounding strategy to multiply, some third graders often forget to subtract the additional numbers they used in the investigation. Students confuse the commutative property of addition with the commutative property of multiplication.  When multiplying 57 x 6, Evan used the rounding method to round 57 to 60 and multiplied 60 x 6 = 360 (which is a good strategy).  He then subtracted 3, instead of subtracting 3 x 6, and he got 357 for his answer.  Since Evan added 3 to the initial value, he did not realize that he had to subtract 6 threes (18), not just 1 three.

 

Ideas for Instruction

v Teachers need to reinforce key concepts with tools like the number line (using rulers, yardsticks, and meter sticks instead of premade paper number lines).

v  Play Equal Groupings Games. 

v  Students use a spinner and die to generate two multiplication factors and then draw a representation.

v Play Equal Groupings with dividends and divisors.

v Introduce a partial products strategy where students model the operation of the multiplier on both the tens and ones value of the multiplicand.  For example, 32 x 41 = (30 x 40) + (30 x 1) + (2x40) + (2 x 1).

v  Use the area model to help students see another representation of their multiplication expressions.  Have students use base – ten blocks on centimeter grid paper to construct rectangular arrays to represent the problem. 


Home

Counting with Word Numbers

Thinking Addition means "Join Together" and Subtraction means "Take Away"

Renaming and Regrouping when Adding and Subtracting Two-Digit Numbers

Multiplying Two - Digit Factors by Two- Digit Factor

Understanding the Division Algorithm

Understanding Fractions

Adding and Subtracting Fractions

Representing, Ordering and Adding/Subtracting Decimals