NVR: shape sequences with figures

Watch it happen

Watch a sequence grow

Figure 1 is a white square. Fix it in your mind — a sequence changes by exactly the same rule at every step.

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The idea

A sequence question may change several things at once, so looking at the whole figure and hoping to spot 'the pattern' usually fails. Instead, split the figure into features and give each feature its own little sequence. The changes are simple once they are separated.

Use columns in your mind. First track direction only: which way does the shape point each time, and how many degrees does it turn? Next track shading only: does it repeat, alternate or cycle through three shadings? Then track numbers only: dots, sides or extra parts, counting up, down or repeating. Size can have its own pattern too, such as growing then shrinking.

Work across all the given figures for one feature before moving to the next, and write each mini-rule in words. Finally, build the next figure by applying every mini-rule at once: new direction, new shading, new number. If your finished figure is not among the choices, only one mini-rule is likely to be wrong, so recheck the features one at a time instead of starting again.

Worked example

The first four figures of a sequence are shown in the picture, with the fifth missing. Work out the fifth figure.

1. Track the direction on its own: the arrow starts pointing up and turns 90° anticlockwise at each step, so in the fifth figure it is pointing up.

   

2. Track the shading on its own: white, light grey, dark grey, black — it moves one step through the shading cycle (white, light grey, dark grey, black) at each step, so the fifth figure is white.

   

3. Put the tracks together: the fifth figure is a white arrow pointing up.

   

Answer: A white arrow pointing up — the rule is that the arrow turns 90° anticlockwise and the shading moves one step darker (white → light grey → dark grey → black, then back to white).

Try one yourself

Another sequence, with its fifth figure missing. What is the fifth figure?

Watch out

• Tracking only the loudest change, such as the dots, and forgetting the turn or the shading.
• Guessing the next shading — alternating means odd positions match each other and even positions match each other; check both.
• After a full turn of four quarter turns the direction repeats, so the 5th figure points the same way as the 1st.