The near numbers are numbers within two of a given value. For 8, the near numbers are 9, 10, 7, and 6.
When exploring near numbers, students will use counting on or down to find a near number. This is a necessary scaffold, but we want to move students away from counting to automatically knowing close numbers. To achieve this, concrete and visual anchors are necessary for most students.
10 frames and subitizing are natural tools for exploring near numbers. Once students are familiar with a visual pattern, they can be asked to give one more than the number. For example, when they can recognize numbers on a 10 frame, move on to asking for one more than what is shown on the flash card. Each set of near numbers should be explored thoroughly for numbers less than ten before moving on. When they know most of the one more than relationships, they can work on two more than, then one less than, and two less than last.
We want students to transfer their understanding of near numbers to numbers greater than ten, such as knowing two more than 15. This can be explored with the teen numbers in late grade 1, but this explicit connection is usually made in grade 2.