I seemed to notice that the semesters my boys had phys ed during middle school they were calmer, more attentive, and got better grades. It seems that wasn’t just a coincidence. Research published in August revealed that physically fit kids in Nebraska had better standardized test scores than less fit peers. The study assessed physical fitness using the timed run as the measure but also assessed BMI and then compared both to test scores. BMI wasn’t correlated but better timed run score was. In other words, you might be overweight but if you are ‘in shape’ in the sense that you are active enough to have a fast timed run you are probably pretty active on an ongoing basis and that translated into an association with better test scores.
In a related study, kids were asked to memorize information that was made up on a map and tested on it right away and then later. The more physically fit kids were able to retain the information better and score well on the test at the later date than the less physically fit kids.
I’m not sure how much time is enough to make your kid smarter or how much is optimal for learning but what I do know is that kids who are physically actively get better grades in general. And students who aren’t going to play a sport will do well to ride their bike or go for a run or a swim or walk the dog and you will likely find that the hour a day on the playground or playing field will reap rewards in a calmer demeanor and better learning too.