Alternative Multiplication Strategies/Processes

This first strategy/process appears similar to the traditional algorithm for multiplication. The difference is that it enables students to utilize place value and maintain an understanding of the numbers throughout the process. It provides another way for students to represent the kind of thinking they have been doing with cluster problems. It is introduced to students at Grade 4.

Strategy #1: Multiply 43 x 27

43 think: (40 + 3)

In this model, students multiply the numbers but the difference is they record the subproduct each time they multiply and retain* the place value of the numbers they’re multiplying. x 27

21 x (20 + 7)

1. (7 x 3)

280 2. (7 x 40*)

60 3. (20* x 3)

+ 800 4. (20* x 40

1,161

Strategy #2: Organizing sub-products of 43 x 27 using a rectangular area model

### (note: This model is used with algebraic expression in middle and high school)

Step 1: Label the dimensions of a rectangle with the numbers to multiply (note numbers are expressed as a place value sum – numbers are decomposed)

20+

7

40 + 3

Step 2: Find the area of each inner rectangle by multiplying its dimensions

40 + 3

20+

**800 60 **

7

**280 21 **

Step 3: Add up all the areas of the inner rectangles.

40 + 3

20+

**800 + **

7

** 280 + **

**60 **

**21 **

** 860 **

**+301**

** 1,161 **