Number sense practice for grade 3

This is a 40-question timed test in the elementary number sense format — ten minutes, no calculator, no scratch paper, +5 for a correct answer and −4 for a wrong or skipped one up to the last question attempted. It is pitched at grade 3: two-digit addition and subtraction, the ×5, ×9, ×11 and ×25 shortcuts, place value, Roman numerals, simple fractions and the first estimation questions.

Every question here has a shortcut behind it. Where a grade 3 child would normally multiply 36 by 15 the long way, the contest method is ×10 then add half: 360 + 180 = 540. Where they would borrow across zeros for 1000 − 258, the method is 9−2, 9−5, 10−8 straight off. Those shortcuts are what the score measures, more than arithmetic ability.

Also available: the full 80-question test · grade 4.

Common questions

How is a number sense test scored?

Five points for each correct answer and minus four for each wrong or skipped question, counted only up to the last question attempted. Questions after that point cost nothing, which is why attempting fewer questions accurately usually beats rushing.

What are the starred questions?

Every tenth question is an estimation question. Any answer within five percent of the exact value scores full marks, so they are the cheapest points on the paper: round one factor up and the other down, write it, move on.

Can my child use scratch paper or a calculator?

No. The number sense format allows neither, and answers are written once with no erasing. That is what makes shortcuts essential rather than optional.

What is a good score?

It depends on grade and experience. Rather than chase a number, re-test every few weeks and watch the trend: attempted, correct, and score all rising together is what progress looks like.