So learn a section of the table, go off and do something else, write out what you learned in that first section, and try to learn a new section. This involves repeated practice and exposure. To truly commit the periodic table to memory, you need to access the part of your brain responsible for long-term memory. Cramming might serve for short-term memorization, like for a test the very next day, but you won't remember anything a few days later. You'll remember the table much better if you spread out the memorization process over multiple sessions instead of cramming the entire table at once. Rather than attempting to memorize all of the elements at once, learn one group at a time, master that group, and then learn the next group until you know the whole table. It may be helpful to view an ordered list of the elements. You could memorize element groups (different color groups), go one row at a time, or memorize in sets of 20 elements. How you memorize the table depends on what works best for you and your learning style, but here are some recommendations that may help: Once you have the table, you need to learn it.
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