What number sense looks like in a tutor’s explanation
Number sense means understanding quantities and relationships, not just recalling an answer. These examples show what to listen for when a tutor explains a concept. They are not entry tests or a fixed lesson sequence. Objects, drawings and symbols should explain the same idea. The EEF guidance on objects and representations explains why the connection to the maths matters.
Addition: why does 8 + 5 make 13?
A child may count everything from one or lose track while counting on. A tutor could lay out eight counters, then split five more into two and three: 8 + 2 = 10, then 10 + 3 = 13. Ask the child to show where the five went. A follow-up such as 9 + 5 lets them try making ten again: 9 + 1 + 4 = 14. Listen for the child explaining the split, rather than copying the tutor’s movements.
Fractions: why is three quarters of 20 equal to 15?
Use 20 counters in four equal groups. Each group has five, so one quarter is five and three quarters are three groups of five: 3 × 5 = 15. The child should be able to say why the groups must be equal and why only three are counted. A follow-up with three quarters of 12 gives four groups of three and an answer of nine. A tutor can then connect the grouping to 20 ÷ 4 × 3, rather than beginning with an unexplained rule.

