Multiplication and Division Facts to 100
By Grade 6, multiplication and division facts to 100 should be moving toward automatic recall. The double-double strategy is one of the most efficient: 23 x 4 = double(23) x 2 = 46 x 2 = 92. This works because 4 = 2 x 2, so multiplying by 4 is equivalent to doubling twice. The strategy extends: x8 = double three times; x16 = double four times. Students with strategy-based fluency can compute any product mentally, not just facts they memorized.
Double-double strategy
To multiply by 4: double twice. 23 x 4: double 23 = 46, double again = 92. To multiply by 8: double three times. 17 x 8: double 17=34, double 34=68, double 68=136. To multiply by 16: double four times. The doubling strategy works for any power of 2 as a factor, and extends to mixed cases: 12 x 6 = 12 x 2 x 3 = 24 x 3 = 72.
All strategies in combination
Students at Grade 6 should have a personal strategy for every fact. Common strategies: doubles (6x6=36, 7x7=49, 8x8=64, 9x9=81). Distributive: 7x8 = 7x7+7 = 56. Halving-and-doubling: 12x5 = 6x10 = 60. Near-squares: 9x6 = 10x6-6 = 54. Students should choose the fastest reliable strategy for each fact, not the same strategy for all facts.
Facts in context
In Grade 6, facts appear inside much larger computations. 234 x 5: the student uses 4x5=20 (carry 2), 3x5=15+2=17 (carry 1), 2x5=10+1=11. Every column requires a fact. Students whose fact recall is slow will find multi-digit computation exhausting and error-prone. Students with automatic recall can devote cognitive resources to the larger problem structure.