Missing piece
A black square has a piece cut out of it, and you pick the piece that fills the gap exactly. Check its width, its depth and which way round it is.
Chapter 1
What are missing piece questions?
A piece has been cut out of a black square, leaving a gap in its top edge. You pick the piece that fills the gap exactly: no hole left, and nothing poking out.
The gap. Read three things: how wide it is, how far down each wall goes, and where its deepest point is.
The pieces. Five in Rush. Most are close to the gap’s shape, but too wide, too shallow or flipped over.
The rule. A piece may be turned round, but never flipped over.
At Rush’s hardest level most pieces are drawn turned round: chapter 3 shows you how to turn them back. The exam also cuts pieces out of pictures, which is chapter 4.
Which piece fills the gap?
An NVR question from Rush, level 1.
Chapter 2
Solve it in 3 steps.
Here’s the question. In the pictures, a piece dropped into the gap is purple, and the gap’s edge is dashed in gold.
The question
Which piece fills the gap?
An NVR question from Rush, level 1.
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Step 1
Check the width.
The piece’s flat top must be exactly as wide as the gap. Option 3 is far too wide, so it can’t go in. Option 1 is much narrower and would leave a hole beside it. Cross them both out.
3 sticks out 1 leaves a hole -
Step 2
Check how deep it goes.
Look at the gap’s walls and its deepest point. The left wall is short, the right wall a little longer, and the deepest point is near the right wall. Option 2 is the right width but nowhere near as deep: it would leave a hole underneath. Cross it out.
The walls and the deepest point 2 leaves a hole under it -
Step 3
Check it’s the right way round.
The gap’s deepest point is near its right wall. Option 5’s is near its left wall: it’s the gap’s shape flipped over, like a mirror image. You can turn a piece round, but a flipped piece never fits. That leaves option 4, and it fills the gap exactly.
5 is flipped 4 fits exactly
Three mistakes it sets
| The mistake | Do this instead |
|---|---|
| Picking the small copy. Option 1 is the gap’s own shape made smaller, so at a glance it looks just right. | Hold its flat top against the gap’s top. They must be the same width. |
| Falling for the mirror image. Option 5 is exactly the right size and just as deep. But it’s the gap flipped: its deepest point is near the wrong wall. | Always check which wall the deepest point is near, even when the size looks perfect. |
| Flipping a piece to make it fit. You can picture option 5 flipped over into the gap. But a flipped piece is a different piece. | Turn pieces round in your head, but never flip them. |
So it’s option 4. It’s as wide as the gap, as deep at each wall and at its point, and the right way round.
Remember: Width, depth, never flipped.
Chapter 3
When it gets harder.
Rush’s level 2 adds pieces that are wrong at just one corner, and level 3 draws most pieces turned round. The same three checks still find the answer.
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As drawn Upright, it fits Pieces drawn turned
Find the flat top and turn the piece until it’s at the top.
The flat top is a straight edge with a square corner at each end. At level 3 the right piece is always drawn turned, a quarter or a half turn. Here it’s upside down. Trap: a step-shaped piece has two edges like that, so try it both ways up.
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As drawn Upright, it’s flipped Turned and flipped
Turn it upright first, then check which way round it is.
In the same question, this piece is drawn upside down too. Upright, its deepest point is near the left wall, but the gap’s is near the right: it’s flipped. Trap: no turn ever undoes a flip. Every Rush question has a flipped piece, and most have two or more.
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A corner too deep A corner too shallow Wrong at one corner
Run along the bottom of the gap, corner by corner.
From level 2, a piece can match everywhere but one corner. In this step-shaped gap, one piece pokes out below the ledge, and another’s slot stops short of the bottom. Trap: both pass the width check, so look at every corner.
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- Slope
- Point
- Zigzag
- Curve
- Tooth
- Step
Every gap is lopsided
Say what’s lopsided before you look at the pieces.
Rush’s gaps come in six shapes, and none looks the same flipped over. Find the deep end of a slope or step, the point nearer one wall, or the longer wall of a zigzag or tooth. Trap: a curve can look even, so find where it dips lowest.
Chapter 4: In the exam
A piece cut from a picture.
Some practice papers cut a square out of a picture with lines and shading on it. Rush doesn’t ask this one. The checks are the same, plus one more: every line must carry on across the cut.
Which piece fills the gap?
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Step 1
Mark where lines run into the gap.
Follow every line up to the gap’s edge. Here the circle’s edge runs in at the left side and out at the right. The straight line runs in at the bottom and out at the right.
Four places where a line meets the gap’s edge.
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Step 2
Check every line meets its mark.
The right piece has a line ending at each of those four places. Here the pieces are shown the way they go in, so option 2, turned a quarter, is as wrong as option 4, flipped. Option 5’s straight line is in the wrong place. Cross out all three.
1 2 3 4 5 -
Step 3
Check the inside matches.
The shading is inside the circle, under its curved edge. Option 1 has the shading above the curve, so it’s out. Option 3 matches everywhere.
1 2 3 4 5
So it’s option 3. Its lines meet the gap’s edge in all four places, and its shading is inside the circle.
Remember: Every line carries on.
Other ways the exam asks it
- “Which piece completes the shape?” You see a shape and one part of it. The pieces may be drawn turned, so match each edge of the gap to an edge of the piece.
- “Which two pieces make the shape?” Fit the piece with the oddest edge first, then find the one that fills what’s left.
- “Complete the symmetrical picture.” If the picture has a mirror line, the missing part is the mirror image of the part opposite it. Here the flip is the right answer.
Chapter 5
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Check the width.
- Check how deep it goes.
- Check it’s the right way round.
Remember: Width, depth, never flipped.
For parents.
What parents ask us about missing piece.
Questions parents ask
What is a missing piece question in non-verbal reasoning?
It's a shape with a part cut away, and several pieces to choose from. Your child picks the one that fills the gap exactly. It is also called shape completion.
Can the right piece be turned round?
Yes. In Rush's level 3 the right piece is always turned, a quarter or a half turn. Turning never stops a piece fitting. Flipping does, because a flipped piece is a mirror image.
How can I help my child see whether a piece fits?
Cut a notch out of the top of a piece of card, then make three pieces: the right one, one flipped over and one too wide. Let your child try each in the gap, and turn the flipped one every way round: it never fits.
Rush: 11+ Practice & KS2 SATsPractise missing piece in Rush.
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