Series
A row of boxes where the picture changes step by step, with one box left empty. Here's how to work out what goes in it, one part at a time.
Chapter 1
What are series questions?
A series is a row of five boxes. From box to box the picture changes in steps, the way 2, 4, 6, 8 goes up in twos. One box is empty, and you pick the picture that goes in it.
Each picture is made of parts: a shape, dots, little lines, a small mark in a corner. Each part follows its own rule, and harder questions change two parts at once.
The row. Five boxes, read from left to right.
The empty box. Often the last one, but it can be anywhere, even the first.
Which goes in the empty box?
An NVR question from Rush, level 2.
Four ways a part can change
-
It takes turns
Two looks swap back and forth, so every other box matches. It can be the shading, the size, the outline or a shape inside.
-
1234
It counts up or down
One more each time, or one fewer: dots, lines, small shapes. Count them in every box.
-
↑→↓←
It turns
The same amount each time, the same way round. Here it’s a quarter turn clockwise, the way a clock’s hands go.
-
It moves round
A small part steps round the box, the same number of places each time. Here it’s one corner clockwise.
Chapter 2
Solve it in 4 steps.
Here’s the question, one part at a time.
The question
Which goes in the empty box?
An NVR question from Rush, level 2.
-
Step 1
Find the parts that change.
Each box has a heart, a row of dots, two short lines and a black circle in the corner. The lines and the circle are the same in every box, so they can’t help you. The heart and the dots change.
The lines and the circle never change.
-
Step 2
Follow one part. Say its rule.
Put your finger on the heart’s point and say where it faces: down, down‑left, gap, up‑left, up. That’s an eighth of a turn clockwise each time. Test it either side of the gap: down‑left, then left, then up‑left. So the gap points left.
↓↙←↖↑An eighth of a turn clockwise each time.
-
Step 3
Then the next part.
Now only the dots. Count them: 5, 4, gap, 2, 1. One fewer each time, so the gap has 3. Test it: 4, then 3, then 2.
54321One fewer dot each time.
-
Step 4
Cross out, one rule at a time.
Pointing left rules out options 1, 4 and 5. Options 2 and 3 both have 3 dots. Last, check the parts that never change: option 3 has a dashed outline round its heart, and no heart in the row has one. That leaves option 2.
12345
Three mistakes it sets
| The mistake | Do this instead |
|---|---|
| Copying the box before the gap. Option 4 is box 2 again: pointing down‑left with 4 dots. Most series offer a copy like this, but the row moves on a step every box. | Take one more step from the box before. The gap can’t match it. |
| Turning too far. Option 5 points up‑left like box 4, and option 1 points up like box 5. They take their turn from the boxes after the gap. | Check the gap against both sides: one step on from box 2, one step back from box 4. |
| Missing a part that never changed. Option 3 turns and counts right, but it has a dashed outline round the heart. | Last of all, check that every part that stayed the same still does. |
So it’s option 2. The heart points left, an eighth of a turn on from box 2, and it has 3 dots, one fewer than box 2.
Remember: One part. Say it. Test it.
Chapter 3
The catches.
Rush’s harder levels use these. Each card is one catch: the rule, an example and the trap.
-
↑↖←↙
Turns: follow one point
Pick the sharpest point and say where it faces.
Up, up‑left, left: an eighth of a turn anticlockwise each time, so next is down‑left. Trap: pointing down is a quarter turn, twice too far. Pointing up‑left has turned back the wrong way, to box 2.
-
Shading that moves round
Count the places it moves, and which way round.
The shaded slice moves two places clockwise each time: top right, bottom, top left, so next is the right‑hand slice. Trap: a slice that hasn’t moved on, has gone a step too far, or went the wrong way round.
-
Two parts moving at once
Follow each moving part on its own.
The shading moves one place clockwise and the dot one place anticlockwise, so next the shading is on the left and the dot top left. Trap: an option with the shading right but the dot wrong, or the two swapped.
-
ABABA
Taking turns: skip a box
Compare boxes 1, 3 and 5, then 2 and 4.
Next door, the size and the shading both change. Skip a box and 1, 3 and 5 match, so box 4 matches box 2. Trap: ruling out a copy. A copy of the box next door is wrong, but a copy of the box two back can be right.
-
↓←↑→↓
The gap at the start
Work backwards from box 2.
The point goes left, up, right, down: a quarter turn clockwise. One step back from left is down. The dots go 4, 3, 2, 1, so box 1 has 5. Trap: turning on from box 2 instead of back, which points up.
-
Round the edge: eight places
Count all eight places, not just the corners.
The triangle moves one place clockwise: top, top right, right, bottom right, so next is the middle of the bottom edge. Trap: jumping on to the next corner, bottom left, as if it only stopped at corners.
Chapter 4: In the exam
Three changes at once.
Some exam series change three parts at once, and some hide a mirror image among the options. Rush keeps to two changes, but the same steps crack three.
Which comes next?
-
Step 1
Follow the turn.
Follow the top of the pole: up, right, down, left. A quarter turn clockwise each time, so next it points up again. Option B points down: out.
ABCDE -
Step 2
Count.
The dots go 5, 4, 3, 2, one fewer each time, so next is 1. Option E has 2: out.
ABCDE -
Step 3
Check the shading.
Black, white, black, white: it takes turns, so next is black. Option D is white: out.
ABCDE -
Step 4
Turned, or flipped?
A and C both point up. In box 1 the flag flies on the right of the pole. In A it’s on the left: A is a mirror image, and no amount of turning makes one. Out.
ABCDE
So it’s C. It points up, a quarter turn on from box 4, with 1 dot, in black, and its flag on the right of the pole.
Remember: Rule by rule. Then the mirror.
Other ways the exam asks it
- Taking turns in threes. White, striped, black, then white again. If boxes 1 and 3 don’t match, compare box 1 with box 4.
- Up, then back down. 1, 2, 3, 2, 1 dots. The middle box is the top, and the row reads the same from either end.
- Two whole pictures taking turns. Boxes 1, 3 and 5 follow one rule, and boxes 2 and 4 another. Skip a box, as in chapter 3.
Chapter 5
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Find the parts that change.
- Follow one part. Say its rule.
- Then the next part.
- Cross out, one rule at a time.
Remember: One part. Say it. Test it.
For parents.
What parents ask us about series.
Questions parents ask
What is a series question in non-verbal reasoning?
It's a row of figures that changes in a regular way, with one figure missing. Your child works out what changes from box to box and picks the figure that fits the gap. The gap is often at the end, but it can be anywhere in the row, including the first box.
How many rules can one series have?
Easier questions have one. Most harder ones have two, such as a turn and a count running together. Some papers go up to three. The method is the same: look at one feature at a time and cross out options as you go.
What if nothing seems to follow a pattern?
Try skipping a box, since a rule that takes turns is hard to see between neighbours. Then look for movement: a shaded slice or a small corner mark stepping round. If a feature still fits no rule after those checks, decide on the features that do.
Is a shape series like a number sequence?
The thinking is the same: find the step, check it holds all the way along, then take one more step. The difference is that one picture can carry two or three sequences at once, one for each feature, so the skill is pulling them apart and following each one.
Rush: 11+ Practice & KS2 SATsPractise series in Rush.
- What Comes Next as 100-second games, easy at first and harder as your child improves
- Every miss kept with the right answer and why
- What Comes Next is in Premium, and six other games are free
On the App Store for iPhone and iPad
Six other games are free, plus a new family game every day. What Comes Next is in Premium: all 41 games are £24.99 a year after a free week1, or £3.99 a month.