Acquiring ‘number sense’ is a key step in learning maths.

Number sense, as defined in maths education, includes the ability to understand quantities and their relationships, to understand number patterns, and to be competent with simple mathematical operations.

There is an extensive academic literature on number sense. This link gives an excellent brief overview for the non-specialist: https://nrich.maths.org/2477

Researchers have correlated good number sense with proficiency in areas such as mental calculation and problem solving. There is general agreement that it is a core skill for progress in maths and in other quantitative subjects.

For example, a child can learn mechanically to calculate that 14 + 10 = 24. However, a child who makes a mistake in a calculation and writes 14 + 10 = 15 will not easily identify this as an error without the intuition – and confidence – of number sense. Similarly, a child who calculates a person’s height as 350cm is more likely to pick up the error if they estimate quantities and compare numbers as a matter of course.