Construction Short Problems: Age 11-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Construction: Age 11-16.

We have put together a selection of these short problems as printable worksheets:

Printable worksheet: Age 14-16 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in turquoise pots.
    problem

    Folded A4

    Age
    11 to 14
    Challenge level
    1 out of 3

    What shapes can be made by folding an A4 sheet of paper only once?

  • Small pepper seedlings in turquoise pots.
    problem

    Defined Distances

    Age
    11 to 14
    Challenge level
    2 out of 3

    Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

  • Small pepper seedlings in turquoise pots.
    problem

    Contact Circles

    Age
    14 to 16
    Challenge level
    1 out of 3

    These four touching circles have another circle hiding amongst them...

  • Small pepper seedlings in turquoise pots.
    problem

    Either Side

    Age
    14 to 16
    Challenge level
    2 out of 3

    A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

  • Small pepper seedlings in turquoise pots.
    problem

    Pink and White

    Age
    14 to 16
    Challenge level
    2 out of 3

    The white square slides once around the pink square. Through what distance does the point P on the white square move?

  • Small pepper seedlings in turquoise pots.
    problem

    Snail's Pace

    Age
    14 to 16
    Challenge level
    2 out of 3

    A snail is at the corner of a cube. What proportion of the cube's surface can the snail reach within an hour?

  • Small pepper seedlings in turquoise pots.
    problem

    Triangular Wheel

    Age
    14 to 16
    Challenge level
    2 out of 3

    An equilateral triangle is rolled along a line. What is the length of the path traced out by one of its vertices?

  • Small pepper seedlings in turquoise pots.
    problem

    3-Sided

    Age
    14 to 16
    Challenge level
    2 out of 3

    How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?