• Free
  • Grades 5–7
  • 3 sections · 3 questions

Where does it land?

Three patterns that repeat, and one mistake that fits all three: the count you want is never quite the count you divided for.

  • Answer key on its own page
  • Reopen this exact paper
  • Letter & A4 ready
Ready to printWhere does it land?
Where does it land? — printable test paper

The answer key prints on a separate page.

What's on this test

Section 1 is posts along a fence. Divide the length by the gap and you have counted the gaps, not the posts — and whether the answer is one more, one fewer or exactly the same depends on where the ends are. Section 2 is the last digit of a number with dozens of digits: powers of 7 end in 7, 9, 3, 1 and then start over, so the only work is deciding where the hundredth one falls. Section 3 asks for a number from what it leaves when divided, and the sieve's step grows every time a condition is applied.

How the paper is put together

The order is deliberate, and the second section is where the sheet turns. A child who has just learned on section 1 to add one meets a question where an even division lands them on the LAST member of the cycle rather than the first — the same fencepost, pointing the other way. Nothing that worked as a rule on the first question survives the second.