The near numbers are numbers within two of any given number. For example, 8+1 or 6+2.
Many programs approach these facts as counting on. However, we need to move students beyond counting to automatically ‘knowing’ numbers that are near the given number.
Concrete and visual materials need to be used for counting on strategies, or children tend to approach these in a rote fashion. Ten frames are particularly useful for this. Once students can recognize a number such as 6 on a ten frame, they can be asked what one or two more would be. They can visualize adding a dots to the ten frame, and make the connection to 8 without counting on. Subitizing plates are also used for +1 and +2, particularly with ordered patterns such as those that show up on standard dice.
Many addition fact guides use count on as a strategy for +3 facts. These facts can usually be approached with a more efficient strategy, as near numbers become less useful the further the numbers are apart.
This game (from the guide to effective instruction ) has students roll a dice to move up an elevator. It can also serve as scaffold to help students count on, rather than count all.