Translation and Movement Sequences

Translation (movement) sequences involve shapes changing their position within the box from one step to the next. Unlike rotation (which changes the angle of a shape in place), translation changes where the shape is located. These patterns range from simple linear movement to complex bouncing paths.

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Types of Movement

Linear Translation

A shape moves in a straight line, one step at a time, in a consistent direction.

Direction	Movement per step
Right	One position to the right
Left	One position to the left
Up	One position upward
Down	One position downward
Diagonal	One position in a diagonal direction

Worked Example: Rightward Movement

Imagine the box divided into a 3×3 grid:

Sequence:

• Box 1: A black circle in position (1,1) — top-left
• Box 2: A black circle in position (1,2) — top-centre
• Box 3: A black circle in position (1,3) — top-right

Next: The circle has moved one step right each time. If the grid has only 3 columns, what happens at the edge? Two possibilities:

1. Wrap around: The circle returns to position (1,1) — top-left
2. Drop down and reverse: The circle moves to (2,3) — middle-right — and begins moving left
3. Bounce: The circle reverses direction and moves to (1,2) — top-centre

The answer depends on the question — look at the answer options to determine which convention is being used.

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Bouncing Movement

Bouncing occurs when a shape reaches the edge of the box and reverses direction, like a ball bouncing off a wall.

Worked Example: Horizontal Bounce

Using a 5-position horizontal grid:

Sequence:

• Box 1: Circle at position 1 (far left)
• Box 2: Circle at position 2
• Box 3: Circle at position 3 (centre)
• Box 4: Circle at position 4

Next: Position 5 (far right). After that, the circle would bounce back: position 4, then 3, then 2, then 1, and bounce again.

Worked Example: Diagonal Bounce

Sequence (positions on a 3×3 grid):

• Box 1: Circle at (1,1) — top-left
• Box 2: Circle at (2,2) — centre
• Box 3: Circle at (3,3) — bottom-right
• Box 4: Circle at (2,2) — centre (bounced back)

Next: Circle at (1,1) — top-left (continuing the bounce).

The circle moves diagonally, hits the bottom-right corner, and bounces back the way it came.

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Wrapping Movement

In wrapping movement, a shape that exits one side of the box re-enters from the opposite side.

Worked Example: Rightward Wrap

Using a 3-column grid:

Sequence:

• Box 1: Square in column 1
• Box 2: Square in column 2
• Box 3: Square in column 3
• Box 4: Square in column 1 (wrapped from right edge back to left)

Next: Square in column 2 (the cycle continues).

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Multi-Shape Movement

In harder questions, multiple shapes move independently or in coordinated patterns.

Worked Example: Two Shapes Moving in Opposite Directions

Sequence (5-position horizontal grid):

• Box 1: Black circle at position 1, white triangle at position 5
• Box 2: Black circle at position 2, white triangle at position 4
• Box 3: Black circle at position 3, white triangle at position 3 (they meet in the centre!)
• Box 4: Black circle at position 4, white triangle at position 2 (they pass through each other)

Next (Box 5): Black circle at position 5, white triangle at position 1.

Pattern: The circle moves right, the triangle moves left, both by one position per step. They pass through each other when they meet.

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Clockwise and Anticlockwise Movement Through Positions

Shapes often move through the four corners or edges of the box in a circular pattern.

Worked Example: Clockwise Corner Movement