Students using counting-on-and-back strategies

The nature of the learner

Students using counting-on-and-back strategies are able to use their knowledge of both the forward and backward number word sequences to solve addition and subtraction questions. The strategies of counting-up-from counting-up-to, counting-down-from and counting-down-to are confidently used.

The transition from counting-based strategies to collection-based methods is an important development for students. Having a range of strategies other than counting by ones enables students to solve more challenging problems and work more efficiently. Strategies such as using a known fact, deriving a result, adding to ten, partitioning and using subtraction as the inverse of addition, for example, are some of the methods students need to be able to use. Just as a builder’s toolkit contains so much more than a single hammer, students need multiple rich and varied opportunities to develop a “toolkit” of strategies at their disposal. Students should be supported in developing the skills to make choices about strategies based upon the numbers and operations involved in the problem. Students should not be expected to always use the same strategy. Instead, they should be provided with opportunities to investigate a range of methods and strategies.

Students using counting-on-and-back strategies recognise the number sequence as a chain that can be broken. The number six, for example, is the sixth number in this chain. Consequently, to add 6 and 3, it is not necessary to go back to 1 and count up to 6. Instead, the sequence can build on from 6.

Students at this stage are also developing automatic recall of basic addition and subtraction facts. They are able to produce forward and backward number word sequences up to and beyond 100. They can also use their understanding of the base ten number system to solve number tasks, using concrete materials to visually represent the numbers involved.

Students using counting-on-and-back strategies are working towards:

• applying a variety of strategies other than counting by ones to solve arithmetical tasks
• developing a concept of ten as a countable unit
• forming equal groups and finding the total, using skip counting