The table 1-9 is to be learned by heart, even without fixing the graphic representation. This can be useful to focus on some properties, or to do memorization exercises (memorization, however, must then be maintained without referring to the graphic representation).
You can do various activities with the multiplication tables. For example, we can find/consolidate that
Obviously, the use of software like this must be preceded and/or accompanied by other types of activities, possibly relying on animations that can be put online, such as these (other animations can be found here).