## Number models that support the use of five as a base^{1}

Engaging students in creating finger patterns for numbers is one way of emphasising the parts of a number. Finger patterns can also assist students in recognising how many more is needed to make ten.

*Seven as a group of five and two*

The ten-frame is a device that mirrors the “two hands to make ten” structure. The ten-frame, developed by Wirtz (1980), is composed of two rows of five squares. Numbers are formed by placing dots, counters or other objects within the squares of the ten-frame. Ten frames can support the use of five as a base.

It is also possible to use structured number strips to the same end. Structured number strips (Figure 3) use ten linear spaces. They represent numbers greater than five with the first five lozenge shapes in one colour and the next five in a different colour.

*Figure 3. Structured number strip for seven.*

^{1}Gravemeijer et al. note that supporting the development of five as a reference point is not new. See for example Hatano’s (1982) use of 5-tiles, Fletcher’s (1988) 5-frames and even Wirtz’s (1980) 10-frames.

The use of five as a numerical composite within other numbers can assist in developing effective partitioning of numbers. In turn the idea of partitioning and combining draws on subitising and numerical composites.

*Figure 4. Six plus seven as (5 + 5) + 3 or (6 + 6) + 1 or (7 + 7) – 1.*

In Figure 4, six plus seven can be seen as 10 + 3 (making ten vertically) or the total can be obtained by using ‘near doubles’. Structured number cards incorporate the idea of 5-tiles, 10-frames and the arithmetic rack *(rekenrek)*.