You have two good paragraphs and an awkward join. The first describes a busy kitchen; the next begins an argument between siblings. Adding “meanwhile” does little if the reader cannot feel what carries from one paragraph into the other. Sometimes the bridge is already sitting on the table.
Look for something that can continue
Choose a concrete detail near the end of the first paragraph: a kettle, a dropped spoon, a chair left out. Ask whether it has a legitimate role in the next moment. Do not plant an object solely to satisfy a technique; use something that belongs to the scene.
Here is an original miniature example: “The kettle clicked off behind them.” The next paragraph might begin, “Mara reached for two cups. Her brother put one back.” The kettle makes the tea-making action plausible, and the returned cup begins to reveal a disagreement.
Change the job of the detail
Repeating an object is most useful when something happens to it. A cup first belongs to the kitchen routine, then becomes part of an interaction. The second paragraph moves forward instead of restating the first in slightly different language.
Try writing the join once with the repeated detail and once without it. Read both aloud. Which version lets you follow the change without explaining it twice? There is no obligation to keep the bridge if the direct cut feels sharper.
Watch for an accidental promise
A detail given special emphasis can make readers expect it to matter later. If the kettle receives half a paragraph but never contributes again, you may have enlarged its importance beyond your intention. Reduce the emphasis or give it a useful consequence.
The method also works in an essay when the next paragraph develops a concrete example already introduced. Our note on choosing a paragraph break addresses where to divide the material; this exercise asks what remains connected across that division. Keep the join only if it makes the movement easier to follow and leaves both paragraphs doing distinct work.