Doubling and Halving: What is it?

 Doubling and halving is a multiplication strategy where a student will create a simpler problem by doubling one factor and halving the other. 

In some cases, the halving-and-doubling process can be applied more than once to simplify a multiplication expression. 

12×15

=6×30 

= 3×60 

= 180 

Students must have a solid understanding of the associative property in order to make sense of this strategy and allow students to see a multiplication question in different arrangements.

Supporting Students Using Doubling and Halving

Representing using the array model may be useful to help students visualize the process. 

For example, 4x4 can be modelled using square tiles arranged in an array. Without changing the number of tiles, the tiles can be rearranged to form a 2x8 array.

Using grid paper to physically create arrays help provide a concrete representation of how this strategy works. Students may benefit from opportunity to create arrays, cut the arrays into halves and shift the portion to double the other factor. Educators may be strategic with the original chosen array size, allowing students to 'double and halve' multiple times. The use of square tiles is another way for students to explore, however may be a bit more difficult for students to see.

When students are comfortable with halving and doubling, carefully planned activities will help them to generalize the strategy – that is, multiplying one number in the multiplication expression by a factor, and dividing the other number in the expression by the same factor, results in the same product as that for the original expression.

For more information, please refer to  A Guide to Effective Instruction in Mathematics, Grades 4 to 6 Volume 3 Multiplication

Where to Next?

Once students are comfortable with using 'Doubling and Halving', they can be encouraged to use partial products and standard/alternate algorithms for multiplication.

Looking to learn more? Check out the recorded session!