Math Strand: Number sense and numeration
Overview:
Doubling and Halving is a multiplication strategy where a student will create a simpler problem by doubling one factor and halving the other. For example, to solve 18 x 15 a student might:
Halving and doubling can also be represented using an array model. 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.
The halving-and-doubling strategy is practical for many types of multiplication problems that students in the junior grades will experience. The associative property can be used to illustrate how the strategy works.
26×5=(13×2)×5
= 13×(2×5)
= 13 × 10
= 1300
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
Where to next?
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.
Source: A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Number Sense and Numeration, Grades 4 to 6 Volume 3 Multiplication
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