Gamification is the application of game-design elements and game principles to non-game situations. Gamification provides extrinsic reinforcement that helps turn your child's intrinsic motivations into action.
In other words, gamification turns your child's life into a game, where all the boring stuff such as homework and chores are turn into "quests", which are more appealling and engaging to them. When your child complete these "quests", he will receive "rewards" in the form of "experience points" or "gold". Your child can then use these rewards to help him "level up" his in game character or unlock additional game features.
Habitica is a habit-building and productivity app that help your turn your child's life into a game. When your child complete tasks, they will receive in-game rewards to level up their in game character and unlock additional game features such as battle armor and pets. You can also set custom rewards such as "longer screen time", which your child can redeem with in-game currency earned from completing tasks. When they fail to complete their tasks on time, they will receive punishment in the form of damage dealt to their in game character.
These in-game rewards and punishment (extrinsic motivation) will help to keep your child motivated to build good habits and complete their assigned tasks on time.
Enter activities that your child has to do daily or on a particular day of the week in the Dailies column
Add activities or treats which you want to use to motivate your child in the Rewards column
EpicWin is another to-do list app that helps it's users gamifiy their lives. With EpicWin, your child can create an avatar to progress with. Completing tasks will reward your child with experience points and loot, which will go towards developing their in-game avatar.