+1/+2 (Near Numbers)

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.

Elevator RideThis 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.



  1. Christina says:

    i teach odd and numbers first thing, but only as a framework at this point. I rigged up two little facsimiles of a pool and a beach volley ball court. Students learn that if everyone in the pool must have a buddy, then even numbers work. Even numbers can be divided into equal teams with no odd man out. To teach counting by 2’s I heap a pile of cone fossils on the desk and we have to figure out the fastest way to count them – by 2’s into piles of ten and everyone helps. They seem to catch onto counting by even numbers when it’s useful. Counting backwards by 2’s is another matter. I haven’t found any tricks for teaching odd numbers up and down other than two-stepping using a number line or cuisinaire rods. Any suggestions?

  2. Hi Christina. There are several supports for skip counting and helping students recognize and internalize the patterns.


    Visual: A bit better for even numbers, but lay out 2 dot cards as the student skip counts. For odd numbers, start with a single dot. This is better for smaller numbers where the recognition of ten frame layouts helps.
    Oral. The ‘skipped’ digits are either whispered, or the teacher alternates back and forth with the students so the skipped digits are still being said out loud to ground it to the normal counting sequence.
    Digits/ Symbols. A hundreds chart or numberline is used to aid the skip counting.

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