Athena.

All free lessons / Non-Verbal Reasoning / Non-verbal reasoning: shape sequences

Non-Verbal Reasoning · Visual patterns

Non-verbal reasoning: shape sequences

A free preview from the Athena Learning Library — the same lesson registered students learn from.

In this lesson: Identify a visual sequence rule.

Before you start

Counting in order — 1, 2, 3 — is a sequence. Shapes can count too: here they count with their sides.

Watch it happen

Count the sides

A sequence: triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides).

Count the sides out loud: a triangle has 3, a square has 4, a pentagon has 5. The shapes gain exactly one side at each step. What must come next?

Step 1 of 2

The idea

Start simply: in these sequence questions, usually only one thing is changing, step by step. Everything else about the figures — the shading, the size, the direction — stays exactly the same. Your job is to find that one steady change and carry it on.

Use this routine. Look at the first two figures and ask: what is different? Check one feature at a time. Has the number of sides changed? Has a dot been added? Has the shape turned? Ignore features that stay the same, because they are not the rule. Then test your idea on the third figure: the same change must happen again, by the same amount.

If the change happens twice in the same way, trust it. Carry it on once more to build the next figure. For example, if each figure gains one side, count the sides in the last figure and add one. Be careful not to invent extra changes: if the shading never changed in the given figures, it should not change in your answer either.

Worked example

The shapes in the row follow a rule. What shape comes next?

Four shapes in a row: a square (4 sides), a pentagon (5 sides), a hexagon (6 sides) and a heptagon (7 sides).
  1. Count the sides in each box: 4, 5, 6, 7. Every shape has exactly one more side than the shape before it.
    Four shapes in a row: a square (4 sides), a pentagon (5 sides), a hexagon (6 sides) and a heptagon (7 sides).
  2. So the rule is +1 side each step. The shape after the 7-sided heptagon must have 8 sides.
  3. An 8-sided shape is an octagon — the ringed shape in the last picture. (A real test would offer several shapes; count the sides of each option and only the octagon fits the rule.)
    Four shapes in a row: a square (4 sides), a pentagon (5 sides), a hexagon (6 sides) and a heptagon (7 sides).

Answer: An octagon (8 sides) — the shapes gain one side at every step: 4, 5, 6, 7, 8.

Try one yourself

Start the same rule one step earlier: triangle, square, pentagon, hexagon — what comes next?

Four shapes in a row: a triangle (3 sides), a square (4 sides), a pentagon (5 sides) and a hexagon (6 sides).

Watch out

Quick check

Try these on your own first — then reveal each answer.

1. One shape in this row is hidden. The row follows the +1 side rule. What is the hidden shape?

A square (4 sides), a pentagon (5 sides), a hidden shape, and a heptagon (7 sides).

2. What shape comes after the octagon if the +1 side rule keeps going?

Three shapes in a row: a hexagon (6 sides), a heptagon (7 sides) and an octagon (8 sides).

Practise this concept

Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.

Create a free account to practiseSign in