Multiplication/Help

Notice: Incomplete

Removing unnecessary detail
We're used to this multiplication table: To reduce the mental strain, remove the 10-, 11- and 12-times tables and replace the 1-times tables with a rule of 'one times anything is itself'. If you must, here are some more rules for the 10-times tables and most of the 11-times tables.

10*x= Add a 0

11*x; x<10. Repeat the digit

Truth is, the 10-, 11- and 12-times tables aren't necessary for multiplication to work

Removing duplicates
This is the multiplication table that would now be taught. Notice the duplicates? They can be removed, and the child can be taught to flip the multiplication to solve it: We get this multiplication table, with only 36 facts, a quarter of the original table!

Changing the method
If your child still can't grasp the above multiplication table, just have them remember this list of 19 numbers: To use this table, if you want to do 8*7, you take 8+7, which is 15 and 8-7, which is 1. 15 goes to 56 and 1 goes to 0. Therefore, 8*7=56-0=56.

This works because $$\frac{(a+b)^2}{4}-\frac{(a-b)^2}{4}=ab$$. The numbers in the list go to a quarter of its square. However, you may notice that the odd numbers map to a number that is off by 0.25. They can be omitted as they cancel each other out in the final subtraction for integers.

Explaining why it works should be saved until your child learns algebra. However, if your child asks why before then, here's a visual explanation: