This is unlike muscle, which can hold glucose in reserve. After nine or more hours of not eating, you are in a fasting condition. Blood glucose levels are very low and need to be replenished. To keep up mental work requires a large turnover of brain glucose. If glucose levels are inadequate, the brain can't do the work as well.
Breakfast helps to replenish blood glucose levels.
There are multiple scientific studies that show that eating breakfast improves academic performance, including improved math scores, better working memory and increased verbal skills. The studies also show an improved attitude toward school, as well as less depression, anxiety and hyperactivity. These studies are so compelling that there is a national effort to provide free and reduced breakfast programs in all public schools so that everyone can take advantage of its benefits. Skipping breakfast may be contributing to your headaches as well, since low blood sugar can cause them. Plus, you may not be getting enough fluids.