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# Number sequences

Facility in counting forwards and backwards by ones, starting from any number, is essential knowledge for:

• the development of strategies such as count on and count back.

Use of bead strings can assist in developing an understanding of counting on and counting back as a precursor to the use of number lines.

• Counting all precedes counting on.
The student needs to count the collection again from one when more is added to it.
For example, if having counted 8 buttons, 3 more buttons are added to the collection, a student would count all the buttons again beginning from 1 and ending with 11.
• Count on refers to the ability to start at any number and begin counting.
Being able to count on involves recognising the starting number and including previous numbers.
To count on from 8, a student needs to know the numbers that are immediately before and after 8 as well as the sequence of numbers preceding it.
For example, having counted 8 buttons, if 3 more buttons are added to the collection, a student counts "9, 10, 11".
• Count back is the ability to count backwards from a particular point giving the correct number names as the count.
Count back is used to solve subtraction problems. For example, when solving "Max collected 10 football cards and lost 3", a student might think "9, 8, 7" to find out how many Max had left.
Counting backwards is less familiar for young students than counting forwards because it is not practised as much.
Use of the constant function on a calculator can help improve students' ability to count backwards and to notice that each number in the sequence is one less than the one preceding it.

Many students who experience difficulty with early number operations fail to make the association between the next number in a counting sequence and the action of taking away or adding one object to a set.

Counting on and back in tens helps students to carry out jumping strategies when adding and subtracting two- or three-digit numbers.

Knowledge of the number sequence underpins the early development of multiplication when students use skip counting to solve multiplication and division problems.