A classic for practicing numbers is the count around the circle game. Easy in concept, but because students tend to learn numbers once then not have much chance to use them after that, they fall out of practice. For that reason, count around the circle is also a good review warm-up for any lesson with many variations.
"When is Christmas?" is a natural extension to the Hi, friends! "When is your birthday?" lesson.
As a younger ALT, I noticed students could ask and answer the birthday question fine, but didn't quite understand the "when" component of the question well enough to carry it over to a question like "When is New Year's Eve?"
The next letter game is played in teams of 4 at the maximum to practice alphabetical order with the goal being trying to recall as quickly as possible the next letter. A perfect warm up for when junior high school first grade are learning how to use the dictionary.
Students ask each other about what they have in their fridge at home, right now. A mundane daily recall activity for all us home cooks but in the English class this becomes a fun thing for students to ask each other about. This activity also includes writing the English words.
There are a few things you can do when teaching the "My name is _______" lesson at elementary school in Japan, like creating name cards/ tags, etc but many require paper and take a bit of time. Here is a quick little game to play that requires nothing except the students and that they can say "My name is _______".