Before starting school, many children reason logically about concepts that are basic to their later mathematical learning. We describe a measure of quantitative reasoning that was administered to children at school entry (mean age 5.8 years) and accounted for more variance in a mathematical attainment test than general cognitive ability 16 months later. We present the test's subscales, its test-retest reliability and its specific relationship to a more advanced mathematical reasoning test, used to assess children aged seven to nine years, which predicts mathematical achievement at 11 and 14 years, after controlling for IQ and working memory. The use of this test as an assessment for mathematics learning in preschool or at the start of primary school could help teachers of young children identify those who might benefit from specific instruction on quantitative reasoning in order to prevent difficulties in mathematics learning.