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The fastest and best way to memorize basic facts is to use them.
A lot.
Practice manipulating the numbers, experiment with how the numbers and equations relate to each other, play games that require the use of the information, and use materials such as the bead chains, bars, and board.  Doing higher level operations with golden beads, dots, and stamp game also encourages mastery of facts through repeated use.  We also do a lot of work with the decanomial square from Children’s House throughout the elementary years to enforce the relationships between various numbers through multiplication.

Decanomial

We use timed fact quizzes in our homeschool because they are a good measure of progress, but between tests we do little or no drill.  In between quizzes, we use projects and problems to continue exploring the relationships between numbers. 
Here Aidan is working on the “Table A”, “Table B”, “Table C” work.  
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Pretty fancy name, huh?
Table A includes all of the equations to make the numbers 0-50.  Table B covers numbers 51-100.
Table C is a giant table with a box next to each number to write down each of the equations used to make that number.  The idea is to use Table A & Table B to complete Table C.  In addition to reinforcing multiplication skills, Table C provides a visual model for prime numbers and factoring.  While in both homeschool and Montessori we are not limited by grades, for reference, Tim used this work with his fourth grade Montessori 9-12 students.

Both Tables A, B, & C and the Decanomial Square are now available in my Teachers Pay Teachers store by clicking on the links above!

Basic facts are important and kids do need to learn them, but there is a lot available outside of traditional drill and practice style learning!